Dissertations / Theses on the topic 'Summation method'
To see the other types of publications on this topic, follow the link: Summation method.
Create a spot-on reference in APA, MLA, Chicago, Harvard, and other styles
Consult the top 47 dissertations / theses for your research on the topic 'Summation method.'
Next to every source in the list of references, there is an 'Add to bibliography' button. Press on it, and we will generate automatically the bibliographic reference to the chosen work in the citation style you need: APA, MLA, Harvard, Chicago, Vancouver, etc.
You can also download the full text of the academic publication as pdf and read online its abstract whenever available in the metadata.
Browse dissertations / theses on a wide variety of disciplines and organise your bibliography correctly.
1
Andersson, Johan. "Summation formulae and zeta functions." Doctoral thesis, Stockholm : Department of Mathematics, Stockholm University, 2006. http://urn.kb.se/resolve?urn=urn:nbn:se:su:diva-1074.
Full text
2
SOARES, ALBERTO. "A MODEL POWER FLOWS BASED ON THE POWER SUMMATION METHOD." PONTIFÍCIA UNIVERSIDADE CATÓLICA DO RIO DE JANEIRO, 1992. http://www.maxwell.vrac.puc-rio.br/Busca_etds.php?strSecao=resultado&nrSeq=8982@1.
Full textAbstract:
CONSELHO NACIONAL DE DESENVOLVIMENTO CIENTÍFICO E TECNOLÓGICOEste trabalho apresenta uma metodologia para o cálculo de Fluxo de Potência em redes radiais através do Método de Soma de Potências, que explora as características dos parâmetros da rede bem como a sua topologia, constituindo- se em um método bastante rápido e robusto. Propõe-se também uma nova metodologia para o controle de tensão na rede através de rotinas de sensibilidade visando a efetuação de manobras ou cortes de carga na rede. São apresentados testes com sistemas realistas.
This work presents a methodology for radial power flows based on the power Summation Method, able to exploit the network particular characteristics in order to achieve accuracy and efficiency. This work also presents a novel model for radial network control based on sensitivity coefficients that evaluate load transfer or curtailment effects on network performance. Some tests with realistic systems are presented.
3
Aggarwal, Keshav. "Subconvexity Bounds and Simplified Delta Methods." The Ohio State University, 2019. http://rave.ohiolink.edu/etdc/view?acc_num=osu1555064743753817.
Full text
4
Belo, Eduardo Morgado. "The use of the complex summation method for formulating algorithms for decoupling vertical/horizontal motions of rolling aircraft." Thesis, University of Southampton, 1987. https://eprints.soton.ac.uk/52286/.
Full text
5
Pippig, Michael. "Massively Parallel, Fast Fourier Transforms and Particle-Mesh Methods: Massiv parallele schnelle Fourier-Transformationen und Teilchen-Gitter-Methoden." Doctoral thesis, Universitätsverlag der Technischen Universität Chemnitz, 2015. https://monarch.qucosa.de/id/qucosa%3A20398.
Full textAbstract:
The present thesis provides a modularized view on the structure of fast numerical methods for computing Coulomb interactions between charged particles in three-dimensional space. Thereby, the common structure is given in terms of three self-contained algorithmic frameworks that are built on top of each other, namely fast Fourier transform (FFT), nonequispaced fast Fourier transform (NFFT) and NFFT based particle-mesh methods (P²NFFT). For each of these frameworks algorithmic enhancement and parallel implementations are presented with special emphasis on scalability up to hundreds of thousands of parallel processes.
In the context of FFT massively parallel algorithms are composed from hardware adaptive low level modules provided by the FFTW software library. The new algorithmic NFFT concepts include pruned NFFT, interlacing, analytic differentiation, and optimized deconvolution in Fourier space with respect to a mean square aliasing error. Enabled by these generalized concepts it is shown that NFFT provides a unified access to particle-mesh methods. Especially, mixed-periodic boundary conditions are handled in a consistent way and interlacing can be incorporated more efficiently. Heuristic approaches for parameter tuning are presented on the basis of thorough error estimates.Die vorliegende Dissertation beschreibt einen modularisierten Blick auf die Struktur schneller numerischer Methoden für die Berechnung der Coulomb-Wechselwirkungen zwischen Ladungen im dreidimensionalen Raum. Die gemeinsame Struktur ist geprägt durch drei selbstständige und auf einander aufbauenden Algorithmen, nämlich der schnellen Fourier-Transformation (FFT), der nicht äquidistanten schnellen Fourier-Transformation (NFFT) und der NFFT-basierten Teilchen-Gitter-Methode (P²NFFT). Für jeden dieser Algorithmen werden Verbesserungen und parallele Implementierungen vorgestellt mit besonderem Augenmerk auf massiv paralleler Skalierbarkeit. Im Kontext der FFT werden parallele Algorithmen aus den Hardware adaptiven Modulen der FFTW Softwarebibliothek zusammengesetzt. Die neuen NFFT-Konzepte beinhalten abgeschnittene NFFT, Versatz, analytische Differentiation und optimierte Entfaltung im Fourier-Raum bezüglich des mittleren quadratischen Aliasfehlers. Mit Hilfe dieser Verallgemeinerungen bietet die NFFT einen vereinheitlichten Zugang zu Teilchen-Gitter-Methoden. Insbesondere gemischt periodische Randbedingungen werden einheitlich behandelt und Versatz wird effizienter umgesetzt. Heuristiken für die Parameterwahl werden auf Basis sorgfältiger Fehlerabschätzungen angegeben.
6
Le, Bel Paul David. "Performance Evaluation of a Low Impact Development Retrofit for Urban Stormwater Treatment." Thesis, Virginia Tech, 2013. http://hdl.handle.net/10919/48656.
Full textAbstract:
The goal of Low Impact Development (LID) is to mimic the pre-development hydrologic regime of a catchment through infiltration, filtration, storage, evaporation, and detention of post-development runoff using small-scale hydrologic controls close to the source. A LID facility located in Northern Virginia was examined for pollutant removal and hydrologic performance. The treatment train included four in-line grass swales followed by a bioretention cell with a gravel base. The facility retained 85% of the rainfall. Influent and effluent pollutant loads were calculated using three common substitution methods for datasets censored by values below the analytical detection limit. The Summation of Loads (SOL) method was used to facilitate understanding of how data censoring affected performance results when substitution methods were used. The SOL analysis showed positive removal performance for most nutrient species, sediment, oxygen demanding substances, selected trace metals and total petroleum hydrocarbons. Negative performance was observed for oxidized nitrogen, total dissolved solids and oil & grease. LID facility influent and effluent loads were also compared using the Effluent Probability Method (EPM). The EPM analysis showed statistically significant (p d 0.05) pollutant load removal performance over the entire range of sampled events for total suspended solids, total phosphorus, total nitrogen, total Kjeldahl nitrogen, ammonia nitrogen, chemical oxygen demand, copper, zinc and alkalinity. EPM analysis did not show significant removals of oxidized nitrogen, total dissolved solids, orthophosphate phosphorus and hardness.Master of Science
7
Simko, Andrew Jack. "Performance Analysis of an Urban Stormwater Best Management Practice Retrofit." Thesis, Virginia Tech, 2014. http://hdl.handle.net/10919/64931.
Full textAbstract:
Historically, the primary objective of traditional stormwater best management practices (BMPs) was to attenuate peak runoff discharges from urban areas. There has been growing demand to construct BMPs that improve stormwater runoff quality to reduce pollutant loading into downstream water bodies. A BMP located in Herndon, Virginia was retrofitted in 2009. Previously a dry detention pond, the new BMP design contains permanent wet pools as well as elements of Low Impact Development practices. A performance analysis was conducted on the retrofit to determine if the BMP was removing pollutants from stormwater runoff. Two mass-based methods were utilized for the performance analysis: the Summation of Loads Method and Effluent Probability Method. The Kaplan-Meier method and Robust Regression on ordered statistics (ROS) were used to make it possible to include censored datasets in the analysis. Analysis with the SOL method showed removal of suspended sediment, nitrogen, iron, and copper. Export of dissolved solids, phosphorus, organic carbon, and manganese was observed. The results of the Effluent Probability Method showed statistically significant reductions of sediment, iron, and copper across the entire range of monitored storm event sizes (p-value≤0.05). There was no statistical difference between the influent and effluent loads of nitrogen. Negative performance of dissolved solids, phosphorus, organic carbon, and manganese were observed for the entire range of monitored storm event sizes. The results of both methods indicated that the BMP retrofit is effectively removing sediment but failing to achieve significant nutrient reductions. This may be due to the creation of anoxic conditions from the oxygen demand of the micropool sediments and microbial degradation of vegetation within the BMP. Removal of the sediment bed and harvesting of the vegetation would likely improve the performance of the BMP.Master of Science
8
Pippig, Michael. "Massively Parallel, Fast Fourier Transforms and Particle-Mesh Methods." Doctoral thesis, Universitätsbibliothek Chemnitz, 2016. http://nbn-resolving.de/urn:nbn:de:bsz:ch1-qucosa-197359.
Full textAbstract:
The present thesis provides a modularized view on the structure of fast numerical methods for computing Coulomb interactions between charged particles in three-dimensional space. Thereby, the common structure is given in terms of three self-contained algorithmic frameworks that are built on top of each other, namely fast Fourier transform (FFT), nonequispaced fast Fourier transform (NFFT) and NFFT based particle-mesh methods (P²NFFT). For each of these frameworks algorithmic enhancement and parallel implementations are presented with special emphasis on scalability up to hundreds of thousands of parallel processes. In the context of FFT massively parallel algorithms are composed from hardware adaptive low level modules provided by the FFTW software library. The new algorithmic NFFT concepts include pruned NFFT, interlacing, analytic differentiation, and optimized deconvolution in Fourier space with respect to a mean square aliasing error. Enabled by these generalized concepts it is shown that NFFT provides a unified access to particle-mesh methods. Especially, mixed-periodic boundary conditions are handled in a consistent way and interlacing can be incorporated more efficiently. Heuristic approaches for parameter tuning are presented on the basis of thorough error estimatesDie vorliegende Dissertation beschreibt einen modularisierten Blick auf die Struktur schneller numerischer Methoden für die Berechnung der Coulomb-Wechselwirkungen zwischen Ladungen im dreidimensionalen Raum. Die gemeinsame Struktur ist geprägt durch drei selbstständige und auf einander aufbauenden Algorithmen, nämlich der schnellen Fourier-Transformation (FFT), der nicht äquidistanten schnellen Fourier-Transformation (NFFT) und der NFFT-basierten Teilchen-Gitter-Methode (P²NFFT). Für jeden dieser Algorithmen werden Verbesserungen und parallele Implementierungen vorgestellt mit besonderem Augenmerk auf massiv paralleler Skalierbarkeit. Im Kontext der FFT werden parallele Algorithmen aus den Hardware adaptiven Modulen der FFTW Softwarebibliothek zusammengesetzt. Die neuen NFFT-Konzepte beinhalten abgeschnittene NFFT, Versatz, analytische Differentiation und optimierte Entfaltung im Fourier-Raum bezüglich des mittleren quadratischen Aliasfehlers. Mit Hilfe dieser Verallgemeinerungen bietet die NFFT einen vereinheitlichten Zugang zu Teilchen-Gitter-Methoden. Insbesondere gemischt periodische Randbedingungen werden einheitlich behandelt und Versatz wird effizienter umgesetzt. Heuristiken für die Parameterwahl werden auf Basis sorgfältiger Fehlerabschätzungen angegeben
9
Tameling, Daniel Verfasser], Ahmed E. [Akademischer Betreuer] Ismail, Paolo [Akademischer Betreuer] Bientinesi, and Alexander [Akademischer Betreuer] [Mitsos. "Design, implementation, and error analysis of the multilevel summation method for dispersion / Daniel Tameling ; Ahmed E. Ismail, Paolo Bientinesi, Alexander Mitsos." Aachen : Universitätsbibliothek der RWTH Aachen, 2018. http://d-nb.info/1162900377/34.
Full text
10
Tameling, Daniel [Verfasser], Ahmed E. Akademischer Betreuer] Ismail, Paolo [Akademischer Betreuer] Bientinesi, and Alexander [Akademischer Betreuer] [Mitsos. "Design, implementation, and error analysis of the multilevel summation method for dispersion / Daniel Tameling ; Ahmed E. Ismail, Paolo Bientinesi, Alexander Mitsos." Aachen : Universitätsbibliothek der RWTH Aachen, 2018. http://d-nb.info/1162900377/34.
Full text
11
Kåhlman, Niklas. "Summation By Parts Finite Difference Methods with Simultaneous Approximation Terms for the Heat Equation with Discontinuous Coefficients." Thesis, Linnéuniversitetet, Institutionen för matematik (MA), 2019. http://urn.kb.se/resolve?urn=urn:nbn:se:lnu:diva-84777.
Full textAbstract:
In this thesis we will investigate how the SBP-SAT finite difference method behave with and without an interface. As model problem, we consider the heat equation with piecewise constant coefficients. The thesis is split in two main parts. In the first part we look at the heat equation in one-dimension, and in the second part we expand the problem to a two-dimensional domain. We show how the SAT-parameters are chosen such that the scheme is dual consistent and stable. Then, we perform numerical experiments, now looking at the static case. In the one-dimensional case we see that the second order SBP-SAT method with an interface converge with an order of two, while the second order SBP-SAT method without an interface converge with an order of one.
12
Ravindran, Hari Alangat. "On Shifted Convolution Sums Involving the Fourier Coefficients of Theta Functions Attached to Quadratic Forms." The Ohio State University, 2014. http://rave.ohiolink.edu/etdc/view?acc_num=osu1406039690.
Full text
13
Wang, Siyang. "Finite Difference and Discontinuous Galerkin Methods for Wave Equations." Doctoral thesis, Uppsala universitet, Avdelningen för beräkningsvetenskap, 2017. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-320614.
Full textAbstract:
Wave propagation problems can be modeled by partial differential equations. In this thesis, we study wave propagation in fluids and in solids, modeled by the acoustic wave equation and the elastic wave equation, respectively. In real-world applications, waves often propagate in heterogeneous media with complex geometries, which makes it impossible to derive exact solutions to the governing equations. Alternatively, we seek approximated solutions by constructing numerical methods and implementing on modern computers. An efficient numerical method produces accurate approximations at low computational cost. There are many choices of numerical methods for solving partial differential equations. Which method is more efficient than the others depends on the particular problem we consider. In this thesis, we study two numerical methods: the finite difference method and the discontinuous Galerkin method. The finite difference method is conceptually simple and easy to implement, but has difficulties in handling complex geometries of the computational domain. We construct high order finite difference methods for wave propagation in heterogeneous media with complex geometries. In addition, we derive error estimates to a class of finite difference operators applied to the acoustic wave equation. The discontinuous Galerkin method is flexible with complex geometries. Moreover, the discontinuous nature between elements makes the method suitable for multiphysics problems. We use an energy based discontinuous Galerkin method to solve a coupled acoustic-elastic problem.
14
Nestler, Franziska. "Efficient Computation of Electrostatic Interactions in Particle Systems Based on Nonequispaced Fast Fourier Transforms." Universitätsverlag der Technischen Universität Chemnitz, 2017. https://monarch.qucosa.de/id/qucosa%3A23376.
Full textAbstract:
The present thesis is dedicated to the efficient computation of electrostatic interactions in particle systems, which is of great importance in the field of molecular dynamics simulations. In order to compute the therefor required physical quantities with only O(N log N) arithmetic operations, so called particle-mesh methods make use of the well-known Ewald summation approach and the fast Fourier transform (FFT). Typically, such methods are able to handle systems of point charges subject to periodic boundary conditions in all spatial directions. However, periodicity is not always desired in all three dimensions and, moreover, also interactions to dipoles play an important role in many applications.
Within the scope of the present work, we consider the particle-particle NFFT method (P²NFFT), a particle-mesh approach based on the fast Fourier transform for nonequispaced data (NFFT). An extension of this method for mixed periodic as well as open boundary conditions is presented. Furthermore, the method is appropriately modified in order to treat particle systems containing both charges and dipoles. Consequently, an efficient algorithm for mixed charge-dipole systems, that additionally allows a unified handling of various types of periodic boundary conditions, is presented for the first time. Appropriate error estimates as well as parameter tuning strategies are developed and verified by numerical examples.Die vorliegende Arbeit widmet sich der Berechnung elektrostatischer Wechselwirkungen in Partikelsystemen, was beispielsweise im Bereich der molekulardynamischen Simulationen eine zentrale Rolle spielt. Um die dafür benötigten physikalischen Größen mit lediglich O(N log N) arithmetischen Operationen zu berechnen, nutzen sogenannte Teilchen-Gitter-Methoden die Ewald-Summation sowie die schnelle Fourier-Transformation (FFT). Typischerweise können derartige Verfahren Systeme von Punktladungen unter periodischen Randbedingungen in allen Raumrichtungen handhaben. Periodizität ist jedoch nicht immer bezüglich aller drei Dimensionen erwünscht. Des Weiteren spielen auch Wechselwirkungen zu Dipolen in vielen Anwendungen eine wichtige Rolle. Zentraler Gegenstand dieser Arbeit ist die Partikel-Partikel-NFFT Methode (P²NFFT), ein Teilchen-Gitter-Verfahren, welches auf der schnellen Fouriertransformation für nichtäquidistante Daten (NFFT) basiert. Eine Erweiterung dieses Verfahrens auf gemischt periodische sowie offene Randbedingungen wird vorgestellt. Außerdem wird die Methode für die Behandlung von Partikelsystemen, in denen sowohl Ladungen als auch Dipole vorliegen, angepasst. Somit wird erstmalig ein effizienter Algorithmus für gemischte Ladungs-Dipol-Systeme präsentiert, der zusätzlich die Behandlung sämtlicher Arten von Randbedingungen mit einem einheitlichen Zugang erlaubt. Entsprechende Fehlerabschätzungen sowie Strategien für die Parameterwahl werden entwickelt und anhand numerischer Beispiele verifiziert.
15
Almquist, Martin. "Efficient Simulation of Wave Phenomena." Doctoral thesis, Uppsala universitet, Avdelningen för beräkningsvetenskap, 2017. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-310124.
Full textAbstract:
Wave phenomena appear in many fields of science such as acoustics, geophysics, and quantum mechanics. They can often be described by partial differential equations (PDEs). As PDEs typically are too difficult to solve by hand, the only option is to compute approximate solutions by implementing numerical methods on computers. Ideally, the numerical methods should produce accurate solutions at low computational cost. For wave propagation problems, high-order finite difference methods are known to be computationally cheap, but historically it has been difficult to construct stable methods. Thus, they have not been guaranteed to produce reasonable results. In this thesis we consider finite difference methods on summation-by-parts (SBP) form. To impose boundary and interface conditions we use the simultaneous approximation term (SAT) method. The SBP-SAT technique is designed such that the numerical solution mimics the energy estimates satisfied by the true solution. Hence, SBP-SAT schemes are energy-stable by construction and guaranteed to converge to the true solution of well-posed linear PDE. The SBP-SAT framework provides a means to derive high-order methods without jeopardizing stability. Thus, they overcome most of the drawbacks historically associated with finite difference methods. This thesis consists of three parts. The first part is devoted to improving existing SBP-SAT methods. In Papers I and II, we derive schemes with improved accuracy compared to standard schemes. In Paper III, we present an embedded boundary method that makes it easier to cope with complex geometries. The second part of the thesis shows how to apply the SBP-SAT method to wave propagation problems in acoustics (Paper IV) and quantum mechanics (Papers V and VI). The third part of the thesis, consisting of Paper VII, presents an efficient, fully explicit time-integration scheme well suited for locally refined meshes.
16
Zhang, Huaijian. "Boundary Integral Techniques in Three Dimensions for Deep Water Waves." The Ohio State University, 2011. http://rave.ohiolink.edu/etdc/view?acc_num=osu1306712208.
Full text
17
Mattsson, Ken. "Summation-by-Parts Operators for High Order Finite Difference Methods." Doctoral thesis, Uppsala : Acta Universitatis Upsaliensis : Univ.-bibl. [distributör], 2003. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-3434.
Full text
18
Lundquist, Tomas. "High order summation-by-parts methods in time and space." Doctoral thesis, Linköpings universitet, Beräkningsmatematik, 2016. http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-126172.
Full textAbstract:
This thesis develops the methodology for solving initial boundary value problems with the use of summation-by-parts discretizations. The combination of high orders of accuracy and a systematic approach to construct provably stable boundary and interface procedures makes this methodology especially suitable for scientific computations with high demands on efficiency and robustness. Most classes of high order methods can be applied in a way that satisfies a summation-by-parts rule. These include, but are not limited to, finite difference, spectral and nodal discontinuous Galerkin methods. In the first part of this thesis, the summation-by-parts methodology is extended to the time domain, enabling fully discrete formulations with superior stability properties. The resulting time discretization technique is closely related to fully implicit Runge-Kutta methods, and may alternatively be formulated as either a global method or as a family of multi-stage methods. Both first and second order derivatives in time are considered. In the latter case also including mixed initial and boundary conditions (i.e. conditions involving derivatives in both space and time). The second part of the thesis deals with summation-by-parts discretizations on multi-block and hybrid meshes. A new formulation of general multi-block couplings in several dimensions is presented and analyzed. It collects all multi-block, multi-element and hybrid summation-by-parts schemes into a single compact framework. The new framework includes a generalized description of non-conforming interfaces based on so called summation-by-parts preserving interpolation operators, for which a new theoretical accuracy result is presented.
19
Pivodová, Alena. "Návrh železobetonového objektu s ohledem na požadavky požární odolnosti." Master's thesis, Vysoké učení technické v Brně. Fakulta stavební, 2019. http://www.nusl.cz/ntk/nusl-392070.
Full textAbstract:
The diploma thesis deals with an analysis of internal forces of B4 reinforced construction of an office building. Analysis takes into account interaction with subsoil and when designing structural parts of the building, different requirements for fire resistance of a structure are taken into account. A Dlubal RFEM 5.17 program was used for finite element analysis, and model functionality verification was performer by using a summation of moments method. The thesis deals with the design and assessment of a point-supported slab, column, inner and external walls.
20
Nystrand, Thomas. "Summation By Part Methods for Poisson's Equation with Discontinuous Variable Coefficients." Thesis, Uppsala universitet, Institutionen för informationsteknologi, 2014. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-235418.
Full textAbstract:
Nowadays there is an ever increasing demand to obtain more accurate numericalsimulation results while at the same time using fewer computations. One area withsuch a demand is oil reservoir simulations, which builds upon Poisson's equation withvariable coefficients (PEWVC). This thesis focuses on applying and testing a high ordernumerical scheme to solve the PEWVC, namely Summation By Parts - SimultaneousApproximation Term (SBP-SAT). The thesis opens with proving that the method isconvergent at arbitrary high orders given sufficiently smooth coefficients. Theconvergence is furthermore verified in practice by test cases on the Poisson'sequation with smoothly variable permeability coefficients. To balance observed lowerboundary flux convergence, the SBP-SAT method was modified with additionalpenalty terms that were subsequently shown to work as expected. Finally theSBP-SAT method was tested on a semi-realistic model of an oil reservoir withdiscontinuous permeability. The correctness of the resulting pressure distributionvaried and it was shown that flux leakage was the probable cause. Hence theproposed SBP-SAT method performs, as expected, very well in continuous settingsbut typically allows undesirable leakage in discontinuous settings. There are possiblefixes, but these are outside the scope of this thesis.
21
Lee, Dong Ryeol. "A distributed kernel summation framework for machine learning and scientific applications." Diss., Georgia Institute of Technology, 2012. http://hdl.handle.net/1853/44727.
Full textAbstract:
The class of computational problems I consider in
this thesis share the common trait of requiring
consideration of pairs (or higher-order tuples)
of data points. I focus on the problem of kernel
summation operations ubiquitous in many data
mining and scientific algorithms.
In machine learning, kernel summations appear in
popular kernel methods which can model nonlinear
structures in data. Kernel methods include many
non-parametric methods such as kernel density
estimation, kernel regression, Gaussian process
regression, kernel PCA, and kernel support vector
machines (SVM). In computational physics,
kernel summations occur inside the classical
N-body problem for simulating positions of a set
of celestial bodies or atoms.
This thesis attempts to marry, for the first
time, the best relevant techniques in parallel
computing, where kernel summations are in low
dimensions, with the best general-dimension
algorithms from the machine learning literature.
We provide a unified, efficient parallel
kernel summation framework that can utilize:
(1) various types of deterministic and
probabilistic approximations that may be
suitable for both low and high-dimensional
problems with a large number of data points;
(2) indexing the data using any multi-dimensional
binary tree with both distributed memory (MPI)
and shared memory (OpenMP/Intel TBB) parallelism;
(3) a dynamic load balancing scheme to adjust
work imbalances during the computation.
I will first summarize my previous research in
serial kernel summation algorithms. This work
started from Greengard/Rokhlin's earlier work on
fast multipole methods for the purpose of
approximating potential sums of many particles.
The contributions of this part of this thesis
include the followings: (1) reinterpretation of
Greengard/Rokhlin's work for the computer science
community; (2) the extension of the algorithms to
use a larger class of approximation strategies,
i.e. probabilistic error bounds via Monte Carlo
techniques; (3) the multibody series expansion:
the generalization of the theory of fast
multipole methods to handle interactions of more
than two entities; (4) the first O(N) proof of
the batch approximate kernel summation using a
notion of intrinsic dimensionality. Then I move
onto the problem of parallelization of the kernel
summations and tackling the scaling of two other
kernel methods, Gaussian process regression
(kernel matrix inversion) and kernel PCA (kernel
matrix eigendecomposition).
The artifact of this thesis has contributed to an
open-source machine learning package called
MLPACK which has been first demonstrated at the
NIPS 2008 and subsequently at the NIPS 2011 Big
Learning Workshop. Completing a portion of this
thesis involved utilization of high performance
computing resource at XSEDE (eXtreme Science and
Engineering Discovery Environment) and NERSC
(National Energy Research Scientific Computing
Center).
22
Nestler, Franziska. "Parameter Tuning for the NFFT Based Fast Ewald Summation." Universitätsbibliothek Chemnitz, 2016. http://nbn-resolving.de/urn:nbn:de:bsz:ch1-qucosa-209377.
Full textAbstract:
The computation of the Coulomb potentials and forces in charged particle systems under 3d-periodic boundary conditions is possible in an efficient way by utilizing the Ewald summation formulas and applying the fast Fourier transform (FFT). In this paper we consider the particle-particle NFFT (P2NFFT) approach, which is based on the fast Fourier transform for nonequispaced data (NFFT) and compare the error behaviors regarding different window functions, which are used in order to approximate the given continuous charge distribution by a mesh based charge density. Typically B-splines are applied in the scope of particle mesh methods, as for instance within the well-known particle-particle particle-mesh (P3M) algorithm. The publicly available P2NFFT algorithm allows the application of an oversampled FFT as well as the usage of different window functions. We consider for the first time also an approximation by Bessel functions and show how the resulting root mean square errors in the forces can be predicted precisely and efficiently. The results show that, if the parameters are tuned appropriately, the Bessel window function is in many cases even the better choice in terms of computational costs. Moreover, the results indicate that it is often advantageous in terms of efficiency to spend some oversampling within the NFFT while using a window function with a smaller support.
23
Nestler, Franziska. "Parameter tuning for the NFFT based fast Ewald summation." Universitätsbibliothek Chemnitz, 2015. http://nbn-resolving.de/urn:nbn:de:bsz:ch1-qucosa-162901.
Full textAbstract:
The computation of the Coulomb potentials and forces in charged particle systems under 3d-periodic boundary conditions is possible in an efficient way by utilizing the Ewald summation formulas and applying the fast Fourier transform (FFT). In this paper we consider the particle-particle NFFT (P2NFFT) approach, which is based on the fast Fourier transform for nonequispaced data (NFFT) and compare the error behaviors regarding different window functions, which are used in order to approximate the given continuous charge distribution by a mesh based charge density. While typically B-splines are applied in the scope of particle mesh methods, we consider for the first time also an approximation by Bessel functions. We show how the resulting root mean square errors in the forces can be predicted precisely and efficiently. The results show that if the parameters are tuned appropriately the Bessel window function can keep up with the B-spline window and is in many cases even the better choice with respect to computational costs.
24
Eriksson, Sofia. "Stable Numerical Methods with Boundary and Interface Treatment for Applications in Aerodynamics." Doctoral thesis, Uppsala universitet, Avdelningen för beräkningsvetenskap, 2012. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-182953.
Full textAbstract:
In numerical simulations, problems stemming from aerodynamics pose many challenges for the method used. Some of these are addressed in this thesis, such as the fluid interacting with objects, the presence of shocks, and various types of boundary conditions. Scenarios of the kind mentioned above are described mathematically by initial boundary value problems (IBVPs). We discretize the IBVPs using high order accurate finite difference schemes on summation by parts form (SBP), combined with weakly imposed boundary conditions, a technique called simultaneous approximation term (SAT). By using the energy method, stability can be shown. The weak implementation is compared to the more commonly used strong implementation, and it is shown that the weak technique enhances the rate of convergence to steady state for problems with solid wall boundary conditions. The analysis is carried out for a linear problem and supported numerically by simulations of the fully non-linear Navier–Stokes equations. Another aspect of the boundary treatment is observed for fluid structure interaction problems. When exposed to eigenfrequencies, the coupled system starts oscillating, a phenomenon called flutter. We show that the strong implementation sometimes cause instabilities that can be mistaken for flutter. Most numerical schemes dealing with flows including shocks are first order accurate to avoid spurious oscillations in the solution. By modifying the SBP-SAT technique, a conservative and energy stable scheme is derived where the order of accuracy can be lowered locally. The new scheme is coupled to a shock-capturing scheme and it retains the high accuracy in smooth regions. For problems with complicated geometry, one strategy is to couple the finite difference method to the finite volume method. We analyze the accuracy of the latter on unstructured grids. For grids of bad quality the truncation error can be of zeroth order, indicating that the method is inconsistent, but we show that some of the accuracy is recovered. We also consider artificial boundary closures on unbounded domains. Non-reflecting boundary conditions for an incompletely parabolic problem are derived, and it is shown that they yield well-posedness. The SBP-SAT methodology is employed, and we prove that the discretized problem is stable.
25
Svärd, Magnus. "Stable High-Order Finite Difference Methods for Aerodynamics." Doctoral thesis, Uppsala universitet, Avdelningen för teknisk databehandling, 2004. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-4621.
Full textAbstract:
In this thesis, the numerical solution of time-dependent partial differential equations (PDE) is studied. In particular high-order finite difference methods on Summation-by-parts (SBP) form are analysed and applied to model problems as well as the PDEs governing aerodynamics. The SBP property together with an implementation of boundary conditions called SAT (Simultaneous Approximation Term), yields stability by energy estimates. The first derivative SBP operators were originally derived for Cartesian grids. Since aerodynamic computations are the ultimate goal, the scheme must also be stable on curvilinear grids. We prove that stability on curvilinear grids is only achieved for a subclass of the SBP operators. Furthermore, aerodynamics often requires addition of artificial dissipation and we derive an SBP version. With the SBP-SAT technique it is possible to split the computational domain into a multi-block structure which simplifies grid generation and more complex geometries can be resolved. To resolve extremely complex geometries an unstructured discretisation method must be used. Hence, we have studied a finite volume approximation of the Laplacian. It can be shown to be on SBP form and a new boundary treatment is derived. Based on the Laplacian scheme, we also derive an SBP artificial dissipation for finite volume schemes. We derive a new set of boundary conditions that leads to an energy estimate for the linearised three-dimensional Navier-Stokes equations. The new boundary conditions will be used to construct a stable SBP-SAT discretisation. To obtain an energy estimate for the discrete equation, it is necessary to discretise all the second derivatives by using the first derivative approximation twice. According to previous theory that would imply a degradation of formal accuracy but we present a proof that this is not the case.
26
Wirnsberger, Peter. "Computer simulation and theoretical prediction of thermally induced polarisation." Thesis, University of Cambridge, 2018. https://www.repository.cam.ac.uk/handle/1810/282988.
Full textAbstract:
In this thesis, we study the phenomenon of thermally induced polarisation using a combination of theory and computer simulation. Molecules of sufficiently low symmetry exhibit thermo-molecular orientation when subjected to a temperature gradient, leading to considerable electrostatic fields in polar liquids. Here, we first use non-equilibrium molecular dynamics simulations to study this interesting effect numerically. To this end, we propose an integration algorithm to impose a constant heat flux in simulations and show that it greatly improves energy conservation compared to a previous algorithm. We next investigate the thermal polarisation of water and find that truncation of electrostatic interactions can lead to severe artefacts, such as the wrong sign of polarisation and an overestimation of the electric field. We further show that the quadrupole-moment contribution to the electric field is significant and responsible for an inversion of its sign. To facilitate the theoretical description of electrostatic interactions, we propose a new dipolar model fluid as a perturbation of a Stockmayer fluid. Using this modified Stockmayer model, we provide numerical evidence for the recently proposed phenomenon of thermally induced monopoles. We show that the electrostatic field generated by a pair of heated/cooled colloidal particles immersed in such a solvent can be trivially described by two Coulomb charges. Finally, we propose a mean-field theory to predict the thermo-polarisation effect exhibited by our model fluid theoretically, and demonstrate near quantitative agreement with simulation results.
27
Berg, Jens. "Stable and High-Order Finite Difference Methods for Multiphysics Flow Problems." Doctoral thesis, Uppsala universitet, Avdelningen för beräkningsvetenskap, 2013. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-187204.
Full textAbstract:
Partial differential equations (PDEs) are used to model various phenomena in nature and society, ranging from the motion of fluids and electromagnetic waves to the stock market and traffic jams. There are many methods for numerically approximating solutions to PDEs. Some of the most commonly used ones are the finite volume method, the finite element method, and the finite difference method. All methods have their strengths and weaknesses, and it is the problem at hand that determines which method that is suitable. In this thesis, we focus on the finite difference method which is conceptually easy to understand, has high-order accuracy, and can be efficiently implemented in computer software. We use the finite difference method on summation-by-parts (SBP) form, together with a weak implementation of the boundary conditions called the simultaneous approximation term (SAT). Together, SBP and SAT provide a technique for overcoming most of the drawbacks of the finite difference method. The SBP-SAT technique can be used to derive energy stable schemes for any linearly well-posed initial boundary value problem. The stability is not restricted by the order of accuracy, as long as the numerical scheme can be written in SBP form. The weak boundary conditions can be extended to interfaces which are used either in domain decomposition for geometric flexibility, or for coupling of different physics models. The contributions in this thesis are twofold. The first part, papers I-IV, develops stable boundary and interface procedures for computational fluid dynamics problems, in particular for problems related to the Navier-Stokes equations and conjugate heat transfer. The second part, papers V-VI, utilizes duality to construct numerical schemes which are not only energy stable, but also dual consistent. Dual consistency alone ensures superconvergence of linear integral functionals from the solutions of SBP-SAT discretizations. By simultaneously considering well-posedness of the primal and dual problems, new advanced boundary conditions can be derived. The new duality based boundary conditions are imposed by SATs, which by construction of the continuous boundary conditions ensure energy stability, dual consistency, and functional superconvergence of the SBP-SAT schemes.
28
Nissen, Anna. "High Order Finite Difference Methods with Artificial Boundary Treatment in Quantum Dynamics." Doctoral thesis, Uppsala universitet, Avdelningen för teknisk databehandling, 2011. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-159856.
Full textAbstract:
The investigation of the dynamics of chemical reactions, both from the theoretical and experimental side, has drawn an increasing interest since Ahmed H. Zewail was awarded the 1999 Nobel Prize in Chemistry for his work on femtochemistry. On the experimental side, new techniques such as femtosecond lasers and attosecond lasers enable laser control of chemical reactions. Numerical simulations serve as a valuable complement to experimental techniques, not only for validation of experimental results, but also for simulation of processes that cannot be investigated through experiments. With increasing computer capacity, more and more physical phenomena fall within the range of what is possible to simulate. Also, the development of new, efficient numerical methods further increases the possibilities. The focus of this thesis is twofold; numerical methods for chemical reactions including dissociative states and methods that can deal with coexistence of spatial regions with very different physical properties. Dissociative chemical reactions are reactions where molecules break up into smaller components. The dissociation can occur spontaneously, e.g. by radioactive decay, or be induced by adding energy to the system, e.g. in terms of a laser field. Quantities of interest can for instance be the reaction probabilities of possible chemical reactions. This thesis discusses a boundary treatment model based on the perfectly matched layer (PML) approach to accurately describe dynamics of chemical reactions including dissociative states. The limitations of the method are investigated and errors introduced by the PML are quantified. The ability of a numerical method to adapt to different scales is important in the study of more complex chemical systems. One application of interest is long-range molecules, where the atoms are affected by chemical attractive forces that lead to fast movement in the region where they are close to each other and exhibits a relative motion of the atoms that is very slow in the long-range region. A numerical method that allows for spatial adaptivity is presented, based on the summation-by-parts-simultaneous approximation term (SBP-SAT) methodology. The accuracy and the robustness of the numerical method are investigated.eSSENCE
29
Hedblom, Maria, and Fanny Magnusson. "Det tar mycket tid i början men vinsterna är stora... : Formativ bedömning i matematikundervisning." Thesis, Högskolan i Borås, Akademin för bibliotek, information, pedagogik och IT, 2016. http://urn.kb.se/resolve?urn=urn:nbn:se:hb:diva-10174.
Full textAbstract:
Denna studie berör formativ bedömning i matematik i grundskolans tidiga år. Studien harundersökt bedömningsformen i forskning samt praktiken.Studiens syfte var att undersöka hur grundskolans tidiga år arbetar med formativ bedömning imatematik och hur detta påverkar eleverna i undervisningen. Utgångspunkten för studien varett sociokulturellt perspektiv. Genom forskning, litteratur och en inblick i verksamheten haren djupare förståelse kring bedömningsformen skapats och nya perspektiv upptäckts. ISkolverket (2011a, s.15) framgår det att bedömningskulturen i klassrummet påverkarindividers inställningar till lärande och detta är drivkraften bakom denna studie.I bakgrunden har olika delar som är av betydelse för den formativa bedömningen lyfts fram.Dessa delar är definition av bedömning, feedback, formativ bedömning, Skolverkets tre steg iden formativa bedömningen, formativ och summativ bedömning i samspel eller motsättning,bedömning i matematik och matematik i Lgr 11.En kvalitativ metod användes till denna studie. Utifrån den kvalitativa metoden valdes tvåredskap vilka var intervju och observation.Resultatet framhävde att bedömning är en stor del i undervisningen men trots det ettsvårtolkat begrepp. Formativ bedömning anses enligt deltagande lärare vara ett effektivtredskap i matematikundervisning men tiden räcker inte alltid till. Alla de deltagande lärarna,forskning och det sociokulturella perspektivet understryker att samtal och dialog ärbetydelsefullt för att den formativa bedömningen ska fungera som ett effektivt redskap iundervisning. Även om inte alla deltagande lärare hade full kännedom om Skolverkets(2011c) tre steg arbetade lärarna omedvetet utifrån stegen.
30
Duru, Kenneth. "Perfectly Matched Layers and High Order Difference Methods for Wave Equations." Doctoral thesis, Uppsala universitet, Avdelningen för beräkningsvetenskap, 2012. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-173009.
Full textAbstract:
The perfectly matched layer (PML) is a novel technique to simulate the absorption of waves in unbounded domains. The underlying equations are often a system of second order hyperbolic partial differential equations. In the numerical treatment, second order systems are often rewritten and solved as first order systems. There are several benefits with solving the equations in second order formulation, though. However, while the theory and numerical methods for first order hyperbolic systems are well developed, numerical techniques to solve second order hyperbolic systems are less complete. We construct a strongly well-posed PML for second order systems in two space dimensions, focusing on the equations of linear elasto-dynamics. In the continuous setting, the stability of both first order and second order formulations are linearly equivalent. We have found that if the so-called geometric stability condition is violated, approximating the first order PML with standard central differences leads to a high frequency instability at most resolutions. In the second order setting growth occurs only if growing modes are well resolved. We determine the number of grid points that can be used in the PML to ensure a discretely stable PML, for several anisotropic elastic materials. We study the stability of the PML for problems where physical boundaries are important. First, we consider the PML in a waveguide governed by the scalar wave equation. To ensure the accuracy and the stability of the discrete PML, we derived a set of equivalent boundary conditions. Second, we consider the PML for second order symmetric hyperbolic systems on a half-plane. For a class of stable boundary conditions, we derive transformed boundary conditions and prove the stability of the corresponding half-plane problem. Third, we extend the stability analysis to rectangular elastic waveguides, and demonstrate the stability of the discrete PML. Building on high order summation-by-parts operators, we derive high order accurate and strictly stable finite difference approximations for second order time-dependent hyperbolic systems on bounded domains. Natural and mixed boundary conditions are imposed weakly using the simultaneous approximation term method. Dirichlet boundary conditions are imposed strongly by injection. By constructing continuous strict energy estimates and analogous discrete strict energy estimates, we prove strict stability.
31
Friedrich, Lucas [Verfasser], Gregor [Gutachter] Gassner, and Thomas [Gutachter] Sonar. "Entropy Stable Summation-by-Parts Methods for Hyperbolic Conservation Laws on h/p Non-Conforming Meshes / Lucas Friedrich ; Gutachter: Gregor Gassner, Thomas Sonar." Köln : Universitäts- und Stadtbibliothek Köln, 2019. http://d-nb.info/1179910567/34.
Full text
32
Malmkvist, Erika, and Charlotta Nilsson. "Individanpassad rättning - en metod för bedömning?" Thesis, Malmö högskola, Lärarutbildningen (LUT), 2007. http://urn.kb.se/resolve?urn=urn:nbn:se:mau:diva-27888.
Full textAbstract:
Vi har en uppfattning om att rättning har en funktion som metod inom skrivprocessen och som formativ bedömning. Rätt utförd rättning kan fylla flera funktioner i undervisningen. Denna studies syfte är att se på rättningens olika funktioner. Ett annat syfte med studien är att se på förhållandet mellan rättning och bedömning. Vi har valt att avgränsa oss till svensklärare som arbetar inom skolår 7-9, på gymnasiet samt på komvux eftersom att det är där man finner ämneslärarna. Studien genomfördes med hjälp av två separata enkätundersökningar vilka till form var både kvantitativa och kvalitativa. Studiens resultat ger indikationer om att lärare ser rättning som en undervisningsmetod och inte en bedömningsgrund. Rättning är i stor utsträckning en individanpassad metod i undervisningen. Då rättningen inte är likriktad är det av allra största vikt att bedömningen utgår från målen eftersom bedömningen är betygsgrundande. Resultatet visar även att rättningen har olika funktioner i utbildningen: som instrument för språkutveckling, formativ bedömning, identifiering av elevernas kunskaper och språkliga brister samt att den används som metod i undervisningen.
33
Florence, Gregory Wayne. "Teacher Supervision Methods in Virginia." VCU Scholars Compass, 2005. http://hdl.handle.net/10156/1787.
Full text
34
Wirthig, Daniel. "Att bedöma i hem- och konsumentkunskap : En studie om hem- och kunskapslärares bedömningspraxis och tankar om kunskapskraven." Thesis, Umeå universitet, Institutionen för kostvetenskap, 2017. http://urn.kb.se/resolve?urn=urn:nbn:se:umu:diva-130433.
Full textAbstract:
Bakgrund: I Sverige har vi ett mål- och kunskapsrelaterat betygssystem som innebär att den enskilda läraren ska bedöma och betygsätta elevernas kunskaper utifrån skolans styrdokument på ett sätt som är både rättssäkert och likvärdigt. Arbetet med bedömning och betygsättning kan vara särskilt komplicerat för hem- och konsumentkunskapslärare eftersom ämnet innehåller en stor blandning av teoretiska och praktiska förmågor som ska bedömas på endast 118 undervisningstimmar. Syfte: Undersökningens syfte var att undersöka hem- och konsumentkunskapslärares arbete med och tankar om bedömning. Metod: Två metoder användes; en elektronisk enkät som besvarades av 94 verksamma hem- och konsumentkunskapslärare och sex semistrukturerade intervjuer. Intervjuerna analyserades med innehållsanalys. Resultat: En majoritet (74 %) av hem- och konsumentkunskapslärarna som besvarade enkäten ansåg att ämnets kunskapskrav var för omfattande i förhållande till undervisningstiden. Några av lärarna i intervjuerna förklarade att den snäva tidsramen försämrade möjligheterna till rättvisa bedömningar. I både enkäten och intervjuerna framkom det att vanliga bedömningsmetoder i HK var löpande bedömning, praktiska prov och skriftliga prov. Alla intervjurespondenterna arbetade med formativ bedömning och det fanns även indikationer på att en stor del av enkätrespondenterna arbetade med formativ bedömning. Några lärare förklarade att de såg formativ bedömning som en naturlig metod i hem- och konsumentkunskapsämnet. Slutsats: Många av hem- och konsumentkunskapslärarna använde flera olika bedömningsmetoder för att bedöma sina elever trots den snäva tidsramen. Hem- och konsumentkunskapslärares förutsättningar att genomföra rättvisa bedömningar med hög kvalité kan dock förbättras om det finns med ett bedömningsperspektiv när det på organisatorisk nivå beslutas om vilka ramar som ska gälla för hem- och konsumentkunskapsundervisningen, till exempel gruppstorlek och tidfördelningen mellan årskurser.
35
Agboola, Oluwaseun O. "Inclusive Teaching Strategies: An Evaluation of Course Structure and Summative Assessment in Introductory Biology." Digital Commons @ East Tennessee State University, 2017. https://dc.etsu.edu/etd/3221.
Full textAbstract:
Several active learning strategies have been used when increasing the structure of a course as increasing course structure has been known to improve student learning in introductory STEM courses. Much has been studied on the value of frequent formative assessment; however, few studies have evaluated the effective modes of delivering summative assessment. This study examines the use of summative assessment as an inclusive teaching practice to improve first generation college student success in introductory biology and also uses faculty surveys to find out how instructors structure their introductory biology course and why they are structured that way. Final exams were evaluated by Bloom’s Taxonomy of Learning. Survey results showed that many instructors used online activities most of the time to supplement face-to-face courses. However, student and faculty viewpoints on assessments offer many interesting insights into how instructors may modify teaching strategies to increase the success of diverse student populations.
36
O'Reilly, Ossian. "Coupled High-Order Finite Difference and Unstructured Finite Volume Methods for Earthquake Rupture Dynamics in Complex Geometries." Thesis, Uppsala universitet, Institutionen för informationsteknologi, 2011. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-155471.
Full textAbstract:
The linear elastodynamic two-dimensional anti-plane stress problem, where deformations occur in only one direction is considered for one sided non-planar faults. Fault dynamics are modeled using purely velocity dependent friction laws, and applied on boundaries with complex geometry. Summation-by-parts operators and energy estimates are used to couple a high-order finite difference method with an unstructured finite volume method. The unstructured finite volume method is used near the fault and the high-order finite difference method further away from the fault where no complex geometry is present. Boundary conditions are imposed weakly on characteristic form using the simultaneous approximation term technique, allowing explicit time integration to be used. Numerical computations are performed to verify the accuracy and time stability, of the method.
37
Abbas, Qaisar. "Weak Boundary and Interface Procedures for Wave and Flow Problems." Doctoral thesis, Uppsala universitet, Avdelningen för teknisk databehandling, 2011. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-159440.
Full textAbstract:
In this thesis, we have analyzed the accuracy and stability aspects of weak boundary and interface conditions (WBCs) for high order finite difference methods on Summations-By-Parts (SBP) form. The numerical technique has been applied to wave propagation and flow problems. The advantage of WBCs over strong boundary conditions is that stability of the numerical scheme can be proven. The boundary procedures in the advection-diffusion equation for a boundary layer problem is analyzed. By performing Navier-Stokes calculations, it is shown that most of the conclusions from the model problem carries over to the fully nonlinear case. The work was complemented to include the new idea of using WBCs on multiple grid points in a region, where the data is known, instead of at a single point. It was shown that we can achieve high accuracy, an increased rate of convergence to steady-state and non-reflecting boundary conditions by using this approach. Using the SBP technique and WBCs, we have worked out how to construct conservative and energy stable hybrid schemes for shocks using two different approaches. In the first method, we combine a high order finite difference scheme with a second order MUSCL scheme. In the second method, a procedure to locally change the order of accuracy of the finite difference schemes is developed. The main purpose is to obtain a higher order accurate scheme in smooth regions and a low order non-oscillatory scheme in the vicinity of shocks. Furthermore, we have analyzed the energy stability of the MUSCL scheme, by reformulating the scheme in the framework of SBP and artificial dissipation operators. It was found that many of the standard slope limiters in the MUSCL scheme do not lead to a negative semi-definite dissipation matrix, as required to get pointwise stability. Finally, high order simulations of shock diffracting over a convex wall with two facets were performed. The numerical study is done for a range of Reynolds numbers. By monitoring the velocities at the solid wall, it was shown that the computations were resolved in the boundary layer. Schlieren images from the computational results were obtained which displayed new interesting flow features.
38
Mongalo, Lucky. "Assessment practices of adult educators in Mamelodi Adult Learning Centers." Thesis, University of the Western Cape, 2008. http://etd.uwc.ac.za/index.php?module=etd&action=viewtitle&id=gen8Srv25Nme4_2105_1271020736.
Full textAbstract:
This study explores the assessment practices of adult educators in Mamelodi Adult Learning Centers using a qualitative methodology. The study recognizes that assessment is an important activity within the education and training enterprise since it can be used to improve the quality of teaching as well as improve and support the learning process. The study sets out to investigate how Mamelodi adult educators conceptualize assessment
the skills levels of these educators
the nature of support and training these educators received to enhance their assessment practices
the different assessment methods employed by the adult educators to assess learners
and the educational validity and efficacy of these practices.
39
Nestler, Franziska. "An NFFT based approach to the efficient computation of dipole-dipole interactions under different periodic boundary conditions." Universitätsbibliothek Chemnitz, 2015. http://nbn-resolving.de/urn:nbn:de:bsz:ch1-qucosa-171040.
Full textAbstract:
We present an efficient method to compute the electrostatic fields, torques and forces in dipolar systems, which is based on the fast Fourier transform for nonequispaced data (NFFT). We consider 3d-periodic, 2d-periodic, 1d-periodic as well as 0d-periodic (open) boundary conditions. The method is based on the corresponding Ewald formulas, which immediately lead to an efficient algorithm only in the 3d-periodic case. In the other cases we apply the NFFT based fast summation in order to approximate the contributions of the nonperiodic dimensions in Fourier space. This is done by regularizing or periodizing the involved functions, which depend on the distances of the particles regarding the nonperiodic dimensions. The final algorithm enables a unified treatment of all types of periodic boundary conditions, for which only the precomputation step has to be adjusted.
40
Eriksson, Maria. "Teachers' and students' experiences and perceptions of formative assessment." Thesis, Malmö högskola, Fakulteten för lärande och samhälle (LS), 2016. http://urn.kb.se/resolve?urn=urn:nbn:se:mau:diva-30565.
Full textAbstract:
This research paper looks at teachers’ views, and use, of formative assessment in the subject of English 6. It also highlights students understanding and processing of feedback and their opinions of eight assessment tools. The study was carried out using mixed methods research with individual teacher interviews, a student focus group interview, and a questionnaire. My finding shows the difficulties with identifying formative assessment and working with this in a way that helps students in their development of English 6, and the need for tools to make feedback and guidance clearer for students. Furthermore, this study identifies the need for guidance from the Swedish national agency of education regarding how teachers should incorporate formative assessment in their classroom.
41
Rizzi, Leandro Gutierrez. "Simulações numéricas de Monte Carlo aplicadas no estudo das transições de fase do modelo de Ising dipolar bidimensional." Universidade de São Paulo, 2009. http://www.teses.usp.br/teses/disponiveis/59/59135/tde-23052009-134513/.
Full textAbstract:
O modelo de Ising dipolar bidimensional inclui, além da interação ferromagnética entre os primeiros vizinhos, interações de longo alcance entre os momentos de dipolo magnético dos spins. A presença da interação dipolar muda completamente o sistema, apresentando um rico diagrama de fase, cujas características têm originado inúmeros estudos na literatura. Além disso, a possibilidade de explicar fenômenos observados em filmes magnéticos ultrafinos, os quais possuem diversas aplicações em àreas tecnológicas, também motiva o estudo deste modelo. O estado fundamental ferromagnético do modelo de Ising puro é alterado para uma série de fases do tipo faixas, as quais consistem em domínios ferromagnéticos de largura $h$ com magnetizações opostas. A largura das faixas depende da razao $\\delta$ das intensidades dos acoplamentos ferromagnético e dipolar. Através de simulações de Monte Carlo e técnicas de repesagem em histogramas múltiplos identificamos as temperaturas críticas de tamanho finito para as transições de fase quando $\\delta=2$, o que corresponde a $h=2$. Calculamos o calor específico e a susceptibilidade do parâmetro de ordem, no intervalo de temperaturas onde as transições são observadas, para diferentes tamanhos de rede. As técnicas de repesagem permitem-nos explorar e identificar máximos distintos nessas funções da temperatura e, desse modo, estimar as temperaturas críticas de tamanho finito com grande precisão. Apresentamos evidências numéricas da existência de uma fase nemática de Ising para tamanhos grandes de rede. Em nossas simulações, observamos esta fase para tamanhos de rede a partir de $L=48$. Para verificar o quanto a interação dipolar de longo alcance afeta as estimativas físicas, nós calculamos o tempo de autocorrelação integrado nas séries temporais da energia. Inferimos daí quão severo é o critical slowing down (decaimento lento crítico) para esse sistema próximo às transições de fase termodinâmicas. Os resultados obtidos utilizando um algoritmo de atualização local foram comparados com os resultados obtidos utilizando o algoritmo multicanônico.Two-dimensional spin model with nearest-neighbor ferromagnetic interaction and long-range dipolar interactions exhibit a rich phase diagram, whose characteristics have been exploited by several studies in the recent literature. Furthermore, the possibility of explain observed phenomena in ultrathin magnetic films, which have many technological applications, also motivates the study of this model. The presence of dipolar interaction term changes the ferromagnetic ground state expected for the pure Ising model to a series of striped phases, which consist of ferromagnetic domains of width $h$ with opposite magnetization. The width of the stripes depends on the ratio $\\delta$ of the ferromagnetic and dipolar couplings. Monte Carlo simulations and reweighting multiple histograms techniques allow us to identify the finite-size critical temperatures of the phase transitions when $\\delta=2$, which corresponds to $h=2$. We calculate, for different lattice sizes, the specific heat and susceptibility of the order parameter around the transition temperatures by means of reweighting techniques. This allows us to identify in these observables, as functions of temperature, the distinct maxima and thereby to estimate the finite-size critical temperatures with high precision. We present numerical evidence of the existence of a Ising nematic phase for large lattice sizes. Our results show that simulations need to be performed for lattice sizes at least as large as $L=48$ to clearly observe the Ising nematic phase. To access how the long-range dipolar interaction may affect physical estimates we also evaluate the integrated autocorrelation time in energy time series. This allows us to infer how severe is the critical slowing down for this system with long-range interaction and nearby thermodynamic phase transitions. The results obtained using a local update algorithm are compared with results obtained using the multicanonical algorithm.
42
Chou, Jou-Ting, and 周柔廷. "Runge-Kutta-Nyström and Summation by Parts Difference Method for Wave Equation." Thesis, 2018. http://ndltd.ncl.edu.tw/handle/ts6uec.
Full textAbstract:
碩士國立中興大學
應用數學系所
106
In this thesis, we compute the approximate solution of the wave equation in two different boundary conditions. One is zero and the other is not. We use SBP operators and construct the computation scheme by Runge-Kutta-Nyström method and penalty method. Then we test the cases by the program and the result of the approximate solution is accurate and converge by refining grid.
43
Ashtaputre, Pranav. "Dynamic behavior of microcantilevers subjected to fluid-structure interaction using mode-summation method." Thesis, 2012. http://spectrum.library.concordia.ca/36301/1/Ashtaputre_MASc_S2012.pdf.
Full textAbstract:
ABSTRACT
Dynamic behavior of microcantilevers subjected to fluid-structure interaction using Mode Summation method
Pranav Ashtaputre
Several Microsystems exhibit interaction of flexible structures such as beams, plates, membranes with fluid. Some of these systems are micropumps, flow sensors and micro valves. It is crucial to consider the effects of fluid parameters such as density, viscosity, velocity and pressure loading while designing these systems. The design of these systems demand a numerical model to understand the dynamic behavior of various elements involved in these systems. Microcantilever is an important structure which exhibits interaction with fluids in various microsystems. The present thesis focuses on the numerical modeling of dynamics of a microcantilever vibrating under the action of fluid loading. Natural frequencies and mode shapes of cantilever are obtained using characteristic orthogonal polynomials in the Rayleigh Ritz method. Numerical model is formed by solving Euler Bernoulli Equation of beam using mode summation method with normal modes of cantilever. The excitation frequency and fluid pressures are obtained from experimental results are explored for modeling and verification purposes. The results are obtained for the tip deflection of the beam. The results are validated with the results obtained in earlier experiments. The deflection amplitudes from the numerical model and those from experiment are found to be in agreement with each other. A parametric study is also presented with different sizes of microcantilever. The effect of different lengths and widths of microcantilever on the deflection amplitudes is presented. However, the effect of structural deformation due to the changes in fluid pressure is not considered. The model can be further extended to explore the dynamics of microplate used in micropumps with the help of precise fluid pressure data for a particular dynamic system and mode shapes obtained in free vibration analysis. The model provides the first step towards finding a solution to the problems involving fluid loading on microsystems.
44
Chang, Chun-Ting, and 張郡庭. "Multi-block Summation-by-parts Finite Difference Method for Advection Equation on Cubed Sphere." Thesis, 2018. http://ndltd.ncl.edu.tw/handle/4u486a.
Full textAbstract:
碩士國立中興大學
應用數學系所
106
In this paper,on spherical surface the approximate solution of advection equation, we use high-order-accurate scheme to compute. The scheme uses cubed sphere grid to construct multi-block computational mesh. We use summation-by-parts finite difference method for spatial derivative, penalty method to impose the boundary and interface conditions weakly and Runge-Kutta method for time integration. We give a mathematical analysis to prove the stability. Finally, we give a series of test by code and the result of approximate solution match the analysis result.
45
Dragos, Jack. "Improved determination of hadron matrix elements using the variational method." Thesis, 2017. http://hdl.handle.net/2440/106302.
Full textAbstract:
Utilising lattice QCD to calculate nucleon matrix elements has had a huge impact on the knowledge of the structure of nucleons. From the comparison to experimental data, to the new insights into the structure of nucleons, the practices of lattice QCD has cemented itself as a fundamental field for particle physics. Some key contributions to the understanding of nucleon structure lattice QCD can provide are parameters needed for the beyond standard model (BSM) extensions, understanding the size of the nucleons via the charge radii and the decomposition of the spin and angular momentum of the quarks and gluons within the nucleon. But the extraction of hadron matrix elements in lattice QCD using the standard two- and three-point correlator functions demands careful attention to systematic uncertainties. Although other systematics including discretisation, renormalisation and chiral extrapolation effects need to be analysed, one of the most recent and emerging sources of systematic error is contamination from excited-states. This thesis applies the variational method to calculate the axial vector current gA [A subscript], the scalar current gS [S subscript], the tensor current gT [T subscript] and the quark momentum fraction hxi of the nucleon and we compare the results to the more commonly used summation and two-exponential fit methods. Proceeding with the same comparison of methods, we extend the calculation to non-zero momentum transfer to access the vector form factors for both the proton and neutron, as well as the iso-vector combination of the axial and induced pseudoscalar form factors for the proton. The results demonstrate how excited-states affect the extraction of nucleon matrix elements and in the process discovering that the variational approach offers a more efficient and robust method for the determination of nucleon matrix elements. Through this demonstration of how excited-states impact lattice QCD calculation and how we can use methods to suppress these excited-states, we can hope to achieve higher and higher precision determinations of nucleon matrix elements form lattice QCD which will aid in our understanding of the structure of nucleons.Thesis (Ph.D.) -- University of Adelaide, School of Physical Sciences, 2017.
46
Mellef, Mehdi. "The effect of the load level on the fire resistance of partially encased columns." Master's thesis, 2018. http://hdl.handle.net/10198/23297.
Full textAbstract:
Mestrado de dupla diplomação com a Université Libre de TunisPartially encased composite columns (PEC) present better structural performance under fire situation than simple steel columns. Thus, it is not possible to calculate the fire resistance of its components, taking just into account the temperature of the steel, because the concrete increases considerably the fire resistance of the column. However, the annex G of EN 1994-1-2presents the balanced summation method to determine the fire resistance of the partially encased columns, by calculating the buckling resistance around the weak axis when exposed to the standard fire curve ISO834 for different fire ratings. Thereafter a new proposal was presented to improve this simple method, taking into consideration the average temperature of all components of the cross section, the residual height of the web based on 400ºC isothermal and the residual concrete area based on the 500ºC isothermal. Later the finite element method is used to calculate the buckling resistance of partially encased columns using an incremental and iterative procedure, investigating the behavior of thirty different PEC cross sections, being ten of each specified steel profile series (HEA, HEB and HD) for two different columns height (3 and 4 meter). The results of the numerical solution are compared with the balanced summation method of annex G from EN 1994-1-2 as well the new proposed solution model.
47
Gragg, Zelma Jane. "Pilot Study of a "Quality of Use" Scale with an Elementary Reading Program." Thesis, 2011. http://hdl.handle.net/1969.1/ETD-TAMU-2011-05-9092.
Full textAbstract:
This study developed a summative scale that could be administered in a short time period to determine the Quality of Use (QOU) of an intervention used by teachers. The scale can be completed in less than an hour using easily attainable information. The QOU scale was applied to an elementary reading program to determine if the program results were dependent upon the quality of the fidelity of teacher use.
The study focused on use of the Linguistic Pattern Series (LPS) portion of the Integrated Skills Method (ISM) Reading Program by 20 special education teachers in 13 elementary schools in San Antonio, Texas. Progress is measured by the use of the Decoding Skills Test (DST) (ISM Teaching Systems, Inc., 2004-b). To determine each teacher's QOU, a summative scale was developed composed of five items (Initial Placement, Frequency of Direct Instruction, Materials – LPS, Materials – Literature/Test Prep, and Scheduling) that possessed low-moderate cohesiveness of Alpha=.71.
Results of the study showed a correlation between QOU summary scores and residualized DST Raw Score Grade Equivalent (RSGE) gains. The QOU could predict .771^2 = 50 percent of score variance. This is a strong prediction for a non-student external measure in education.