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Blankenship, Elise. "Conserved solvent networks in GPCR activation." Case Western Reserve University School of Graduate Studies / OhioLINK, 2016. http://rave.ohiolink.edu/etdc/view?acc_num=case1458221506.
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Klose, Markus, Inge Lindemann, Minella Christian Bonatto, Katja Pinkert, Martin Zier, Lars Giebeler, Pau Nolis, et al. "Unusual oxidation behavior of light metal hydride by tetrahydrofuran solvent molecules confined in ordered mesoporous carbon." Cambridge University Press, 2014. https://tud.qucosa.de/id/qucosa%3A39011.
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Confining light metal hydrides in micro- or mesoporous scaffolds is considered to be a promising way to overcome the existing challenges for these materials, e.g. their application in hydrogen storage. Different techniques exist which allow us to homogeneously fill pores of a host matrix with the respective hydride, thus yielding well defined composite materials. For this report, the ordered mesoporous carbon CMK-3 was taken as a support for LiAlH₄ realized by a solution impregnation method to improve the hydrogen desorption behavior of LiAlH₄ by nanoconfinement effects. It is shown that upon heating, LiAlH₄ is unusually oxidized by coordinated tetrahydrofuran solvent molecules. The important result of the herein described work is the finding of a final composite containing nanoscale aluminum oxide inside the pores of the CMK-3 carbon host instead of a metal or alloy. This newly observed unusual oxidation behavior has major implications when applying these compounds for the targeted synthesis of homogeneous metal–carbon composite materials.
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Zhang, Ying. "Synthesis and Determination of the Local Structure and Phase Evolution of Unique Boehmite-Derived Mesoporous Doped Aluminas." BYU ScholarsArchive, 2018. https://scholarsarchive.byu.edu/etd/7105.
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Mesoporous alumina (Al2O3) in the gamma (γ) phase is widely used as a support in catalytic applications because of its high surface area, large pore volume, acid-base characteristics, and thermal stability. To improve the thermal stability of gamma alumina, dopants such as lanthanum, magnesium, zirconia, and silica are often introduced. Current laboratory-based methods for synthesizing gamma alumina generally involve 10-15 steps and/or use toxic, expensive surfactants and solvents. Industrial methods, while simpler, lack control of pore properties and surface chemistry. In contrast, we have developed an innovative solvent deficient, one-step method that is able to synthesize a wide range of pure and silica-doped aluminas with high surface areas, pore volumes from 0.3 to 1.8 cm3/g, and pore diameters from 5 to 40 nm. More significantly, our silica-doped aluminas are stable up to temperatures as high as 1300<°>C, which is 200<°>C higher than other pure and doped gamma alumina materials.The usefulness of gamma-alumina as a catalyst support is dependent on its favorable combination of textural, thermal, structural, and chemical properties, yet the relationship between structure and these other properties is still not clearly understood due to the poorly crystallized nature of the material. In particular, the mechanism by which the gamma structure is stabilized thermally by so many dopants is still not well understood. Based on our previous PDF experiments on pure and La-doped alumina, we have developed a hypothesis regarding the mechanism by which dopants increase thermal stability. To validate or refute this hypothesis, we collected PDF data on a wider range of laboratory and industrial alumina samples. Herein, we have utilized PDF analysis to study the local to intermediate-range structure of a series of our pure and silica-doped aluminas calcined at 50<°>C intervals between 50 and 1300<°>C as well as pure and silica-doped aluminas from commercial sources and other synthetic methods. This thorough study of alumina local structure will allow us to separate general trends in the local structure from idiosyncrasies based on synthetic method/conditions, and it will help us identify the structural features responsible for improved thermal stability. Having access to these PDF experiments, we have validated our current hypothesis on the nature of stabilization afforded by dopants and, more generally, developed a better understanding of the role structure plays in the properties of aluminas.
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Alton, Ken. "Dijkstra-like ordered upwind methods for solving static Hamilton-Jacobi equations." Thesis, University of British Columbia, 2010. http://hdl.handle.net/2429/25030.
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The solution of a static Hamilton-Jacobi Partial Differential Equation (HJ PDE) can be used to determine the change of shape in a surface for etching/deposition/lithography applications, to provide the first-arrival time of a wavefront emanating from a source for seismic applications, or to compute the minimal-time trajectory of a robot trying to reach a goal. HJ PDEs are nonlinear so theory and methods for solving linear PDEs do not directly apply. An efficient way to approximate the solution is to emulate the causal property of this class of HJ PDE: the solution at a particular
point only depends on values backwards along the characteristic that passes through that point and solution values always increase along characteristics. In our discretization of the HJ PDE we enforce an analogous causal property, that the solution value at a grid node may only depend on the values of nodes in its numerical stencil which are smaller. This causal property is related but not the same thing as an upwinding property of schemes for time dependent problems. The solution to such a discretized system of equations can be efficiently computed using a Dijkstra-like method in a single pass through the grid nodes in order of nondecreasing value. We develop two Dijkstra-like methods for solving two subclasses of static HJ PDEs. The first method is an extension of the Fast Marching Method for isotropic Eikonal equations and it can be used to solve a class of axis-aligned anisotropic HJ PDEs on an orthogonal grid. The second method solves general convex static HJ PDEs on simplicial grids by computing stencils for a causal discretization in an initial pass through the grid nodes, and then solving the discretization in a second Dijkstra-like pass through the nodes. This method is suitable for computing solutions on highly nonuniform grids, which may be useful for extending it to an error-control method based on adaptive grid refinement.
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Sadakane, Koichiro. "Novel Ordered Structures in a Binary Solvents Mixture, Induced by Solvation and External Field." 京都大学 (Kyoto University), 2010. http://hdl.handle.net/2433/120635.
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McHale, Mary E. R. "Chemical Equilibria in Binary Solvents." Thesis, University of North Texas, 1997. https://digital.library.unt.edu/ark:/67531/metadc278936/.
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Dissertation research involves development of Mobile Order Theory thermodynamic models to mathematically describe and predict the solubility, spectral properties, protonation equilibrium constants and two-phase partitioning behavior of solutes dissolved in binary solvent mixtures of analytical importance. Information gained provide a better understanding of solute-solvent and solvent-solvent interactions at the molecular level, which will facilitate the development of better chemical separation methods based upon both gas-liquid and high-performance liquid chromatography, and better analysis methods based upon complexiometric and spectroscopic methods. Dissertation research emphasizes chemical equilibria in systems containing alcohol cosolvents with the understanding that knowledge gained will be transferable to more environmentally friendly aqueous-organic solvent mixtures.
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Turner, Michael. "High-order mesh generation for CFD solvers." Thesis, Imperial College London, 2017. http://hdl.handle.net/10044/1/57956.
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The generation of curvilinear, high-order meshes for CFD applications remains a significant bottleneck in the progress and application of high-order CFD methods. These methods have superior numerical accuracy over low-order methods due to their use of piecewise polynomial representations of domains and solutions. As such they are viewed as a potential source of higher fidelity simulations with a view of industrial application [81]. The current state of the art in high-order mesh generation does not provide a reliable and efficient approach which would be required in an industrial setting. This thesis investigates the generation of high-order curvilinear meshes for CFD applications. It focuses around the design and algorithms of an open-source high- order mesh generator, NekMesh, which has been created as part of this project and is part of the Nektar++ high-order CFD suite. The program aims to create high-order meshes directly from CAD as automatically and robustly as possible. This means that all parts of the high-order meshing problem must be addressed including CAD handling and linear mesh generation. A significant contribution of this thesis to high-order mesh generation is the work on a variational approach to the generation of curved meshes. This has been encompassed in a framework within NekMesh. It has been shown to be able to apply several high-order mesh generation methods found throughout the literature and unify them in one context. In addition to this the algorithms used within this framework mitigate a significant amount of the high computational cost associated with high-order mesh generation and attempts to address robustness issues. In addition to the work on NekMesh this thesis also explores using a semi- structured approach to linear mesh generation which can address several robustness issues. It also applies several the methods created to industrially relevant examples.
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Duke, Elizabeth R. "Solving higher order dynamic equations on time scales as first order systems." Huntington, WV : [Marshall University Libraries], 2006. http://www.marshall.edu/etd/descript.asp?ref=653.
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Moysiadi, Aliki. "Relaxation of longitudinal and singlet nuclear spin order as a function of solvent viscosity." Thesis, University of Southampton, 2018. https://eprints.soton.ac.uk/425870/.
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Extending the storage time of nuclear spin order is an important issue in modern NMR spectroscopy since many NMR and MRI applications are limited by the lifetime of spin states. Under normal circumstances the survival of spin magnetization is limited by longitudinal relaxation (T1) which brings the magnetization back to equilibrium within a few seconds. The conversion of longitudinal into singlet order can extend that lifetime to tens of minutes up to an hour. Most nuclear spin relaxation mechanisms in liquids are a function of the correlation time τc of the molecule, which is linked to the molecular tumbling, and inversely proportional to viscosity. Therefore a lower viscosity would reduce the influence of those mechanisms. The increase in the lifetime of longitudinal (T1) and singlet order (TS) is shown here as the viscosity of common organic solvents decreases. The study includes measurements in liquid and supercritical CO2, that oer an extremely low viscosity regime. The further extension of spin order lifetimes for a singlet bearing molecule in liquid CO2 is presented. There appears to be an upper limit to the extension of the singlet order lifetime that is caused by relaxation mechanisms acting in different directions.
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Versteeg, Edward Bruce. "The effect of order of presentation and experience on problem solving." PDXScholar, 1986. https://pdxscholar.library.pdx.edu/open_access_etds/3689.
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The effects of order of presentation and amount of experience on errors and solution time were investigated. An interactive narrative puzzle was presented on a computer screen to 60 undergraduate students. Solution of the problem involved the integration of two path segments. Subjects in the Forward Condition were presented the path segments in the order in which they had to be traversed for solution. Subjects in the Backward Condition were exposed to the opposite order of presentation. Amount of experience was varied by permitting one, three, or five readings of the narrative.
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Lin, Yuan. "High-order finite difference methods for solving heat equations /." Available to subscribers only, 2008. http://proquest.umi.com/pqdweb?did=1559848541&sid=1&Fmt=2&clientId=1509&RQT=309&VName=PQD.
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Thesis (Ph. D.)--Southern Illinois University Carbondale, 2008."Department of Mathematics." Keywords: High-order finite difference, Heat equations Includes bibliographical references (p. 64-68). Also available online.
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Alhojilan, Yazid Yousef M. "Higher-order numerical scheme for solving stochastic differential equations." Thesis, University of Edinburgh, 2016. http://hdl.handle.net/1842/15973.
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We present a new pathwise approximation method for stochastic differential equations driven by Brownian motion which does not require simulation of the stochastic integrals. The method is developed to give Wasserstein bounds O(h3/2) and O(h2) which are better than the Euler and Milstein strong error rates O(√h) and O(h) respectively, where h is the step-size. It assumes nondegeneracy of the diffusion matrix. We have used the Taylor expansion but generate an approximation to the expansion as a whole rather than generating individual terms. We replace the iterated stochastic integrals in the method by random variables with the same moments conditional on the linear term. We use a version of perturbation method and a technique from optimal transport theory to find a coupling which gives a good approximation in Lp sense. This new method is a Runge-Kutta method or so-called derivative-free method. We have implemented this new method in MATLAB. The performance of the method has been studied for degenerate matrices. We have given the details of proof for order h3/2 and the outline of the proof for order h2.
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De, Fina Karina M. "Thermodynamics of Mobile Order Theory: Solubility and Partition Aspects." Thesis, University of North Texas, 2004. https://digital.library.unt.edu/ark:/67531/metadc4626/.
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The purpose of this thesis is to analyze the thermochemical properties of solutes in nonelectrolyte pure solvents and to develop mathematical expressions with the ability to describe and predict solution behavior using mobile order theory. Solubilities of pesticides (monuron, diuron, and hexachlorobenzene), polycyclic aromatic hydrocarbons (biphenyl, acenaphthene, and phenanthrene), and the organometallic ferrocene were studied in a wide array of solvents. Mobile order theory predictive equations were derived and percent average absolute deviations between experimental and calculated mole fraction solubilities for each solute were as follows: monuron in 21 non-alcoholic solvents (48.4%), diuron in 28 non-alcoholic solvents (60.1%), hexachlorobenzene (210%), biphenyl (13.0%), acenaphthene (37.8%), phenanthrene (41.3%), and ferrocene (107.8%). Solute descriptors using the Abraham solvation model were also calculated for monuron and diuron. Coefficients in the general solvation equation were known for all the solvents and solute descriptors calculated using multilinear regression techniques.
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Person, Axelle. "Solving homogeneous linear differential equations of order 4 in terms of equations of smaller order." Rennes 1, 2002. http://www.theses.fr/2002REN1A007.
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Chiang, Weng Cheng Venus. "High-order finite difference methods for solving convection diffusion equations." Thesis, University of Macau, 2008. http://umaclib3.umac.mo/record=b1807119.
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Wagner, Carlee F. "Improving shock-capturing robustness for higher-order finite element solvers." Thesis, Massachusetts Institute of Technology, 2015. http://hdl.handle.net/1721.1/101498.
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Thesis: S.M., Massachusetts Institute of Technology, Department of Aeronautics and Astronautics, 2015.Cataloged from PDF version of thesis.
Includes bibliographical references (pages 81-91).
Simulation of high speed flows where shock waves play a significant role is still an area of development in computational fluid dynamics. Numerical simulation of discontinuities such as shock waves often suffer from nonphysical oscillations which can pollute the solution accuracy. Grid adaptation, along with shock-capturing methods such as artificial viscosity, can be used to resolve the shock by targeting the key flow features for grid refinement. This is a powerful tool, but cannot proceed without first converging on an initially coarse, unrefined mesh. These coarse meshes suffer the most from nonphysical oscillations, and many algorithms abort the solve process when detecting nonphysical values. In order to improve the robustness of grid adaptation on initially coarse meshes, this thesis presents methods to converge solutions in the presence of nonphysical oscillations. A high order discontinuous Galerkin (DG) framework is used to discretize Burgers' equation and the Euler equations. Dissipation-based globalization methods are investigated using both a pre-defined continuation schedule and a variable continuation schedule based on homotopy methods, and Burgers' equation is used as a test bed for comparing these continuation methods. For the Euler equations, a set of surrogate variables based on the primitive variables (density, velocity, and temperature) are developed to allow the convergence of solutions with nonphysical oscillations. The surrogate variables are applied to a flow with a strong shock feature, with and without continuation methods, to demonstrate their robustness in comparison to the primitive variables using physicality checks and pseudo-time continuation.
by Carlee F. Wagner.
S.M.
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Moore, John Pease IV. "An arbitrarily high-order, unstructured, free-wake panel solver." Thesis, Massachusetts Institute of Technology, 2013. http://hdl.handle.net/1721.1/85811.
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Thesis: S.M., Massachusetts Institute of Technology, Department of Aeronautics and Astronautics, 2013.Cataloged from PDF version of thesis.
Includes bibliographical references (pages 69-71).
A high-order panel code capable of solving the potential flow equation about arbitrary curved geometries is presented. A new method for integrating curved, high-order panels using adaptive Gaussian quadrature is detailed. Furthermore, automated wake handling is addressed and a method to robustly solve for the steady-state free-wake rollup is proposed. Finally, a Fast Multipole Method with a complexity that scales as O(N) is also presented so that large problems can be handled using only a linear mesh. Results are presented to demonstrate high order accuracy and agreement with other inviscid solvers for a variety of test cases.
by John Pease Moore IV.
S.M.
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Yagoub, Hemza. "Variable-step variable-order 3-stage Hermite-Birkhoff ODEDDE solver of order 5 to 15." Thesis, University of Ottawa (Canada), 2009. http://hdl.handle.net/10393/28075.
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This thesis presents the variable-step variable-order 3-stage Hermite-Birkhoff numerical solver HB515DDE of order 5 to 15. This method can solve ordinary and delay differential equations (ODEs/DDEs) with state-dependent, non-vanishing, small, vanishing and asymptotically vanishing delays. Delayed values are computed using Hermite interpolation and small delays are dealt with using extrapolation. Discontinuities in DDEs are located by a bisection method. HB515DDE was tested and compared with other solvers. The results are given along with the convergence theory which supports the experimentation.
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Lyon, Mark Bruno Oscar P. Bruno Oscar P. "High-order unconditionally-stable FC-AD PDE solvers for general domains /." Diss., Pasadena, Calif. : California Institute of Technology, 2009. http://resolver.caltech.edu/CaltechETD:etd-07312008-102751.
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Li, Lulu Ph D. Massachusetts Institute of Technology. "A low order acceleration scheme for solving the neutron transport equation." Thesis, Massachusetts Institute of Technology, 2013. http://hdl.handle.net/1721.1/86422.
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Thesis: S.M., Massachusetts Institute of Technology, Department of Nuclear Science and Engineering, 2013.This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.
Cataloged from student-submitted PDF version of thesis.
Includes bibliographical references (pages 111-115).
The Methods of Characteristics (MOC) is a widely used technique for solving partial differential equations, and has been applied to the neutron transport problems for many years. The MOC method requires many transport iterations to solve large heterogeneous LWR reactor problems with high dominance ratio, and effective acceleration schemes are necessary to make MOC method practical. Various acceleration methods have been developed using low-order diffusion methods for approximating the scalar flux correction to the high-order scalar flux, and limited work has been performed using a low-order transport solution to accelerate the high-order transport solution. This work proposes a Low Order Operator (LOO) acceleration scheme for accelerating the transport equation. More specifically, LOO uses a coarsely discretized grid and iteratively solves the low-order system using MOC transport approximations. By conserving the first-order spatial and angular moments, LOO is proposed to capture more angular effects compared with CMFD. Two variations of the LOO method, together with the CMFD method, are implemented in the OpenMOC framework, which is a 2D MOC solver written to solve the 2D heterogeneous reactor problems. Based on the test cases performed in this work, LOO tends to reduce the number of transport sweeps required compared with the commonly used CMFD acceleration method. LOO also does not rely on under-relaxation as CMFD does to converge typical LWR problems tested in this work. The advantage of LOO over CMFD is more profound for problems with strong angular effects.
by Lulu Li.
S.M.
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Okuno, Takayuki. "Studies on Algorithms for Solving Generalized Second-Order Cone Programming Problems." 京都大学 (Kyoto University), 2013. http://hdl.handle.net/2433/174846.
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Billman, Albin. "Solving flow shop problems using a forward-chaining partial-order planner." Thesis, Mälardalens högskola, Akademin för innovation, design och teknik, 2016. http://urn.kb.se/resolve?urn=urn:nbn:se:mdh:diva-30890.
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Planning is the task of putting together a sequence of actions that takes a start state to a goal state. Since planning is a crucial part of human intelligence it is also a crucial part of artificial intelligence. As with human planning there are many different ways of AI planning and many different problems to plan. This thesis aims to discover how well a specific way of AI planning performs on a specific sort of problem. The planner that was investigated is called the POPF planner which is a forward-chaining partial-order planner which is an attempt at merging two different ways of planning. This was done to see how well this relatively uncommon method of planning compares to other more traditional methods of planning such as forward-chaining planners when solving a flow shop problem. A flow shop problem is a problem regarding minimizing the idle time for a facility that contains a number of m machines that need to do n jobs. Each of the n jobs 1…n have to be processed on m machines 1…m in that order. Tests were done to see how the POPF planner performed in comparison to planners that work differently. This was done by creating a flow shop problem suitable for testing and then testing the POPF planner on the problem and comparing the results to two other planners. The other planners being the COLIN and TFD planners which both work differently from each other and the POPF planner. Suggestions were also made for how the POPF planner could potentially be improved using additional methods such as landmarks. The results of the test show that the POPF planner is better than the COLIN planner and as good if not better than the TFD planner depending on the complexity of the problem. An additional test was done using the POPStar planner that specializes in the sorts of problem that was created for testing. This POPStar planner outperformed the other planners as expected but it loses in flexibility since it cannot solve problems defined in PDDL. The final results show that the POPF planner performs on a similar level to other general planners when it comes to solving flow shop problems while still having some of the benefits of being a partial-order planner such as being more flexible than a totally-ordered planner.
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Khurshid, Hassan. "High-order incompressible Navier-stokes equations solver for blood flow." Wichita State University, 2012. http://hdl.handle.net/10057/5520.
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A high-order finite difference solver was written to solve the incompressible Navier-Stokes (NS) equations and was applied to analyze the blood flow. First, a computer code was written to solve incompressible Navier- Stokes equations using the exact projection method/fractional step scheme. A fifth-order weighted essentially nonoscillatory (WENO) spatial operator was applied to the convective terms of Navier-Stokes equations. The diffusion term was solved by using a sixth-order compact central difference scheme. A fractional step scheme in conjunction with the third-order Runge-Kutta total variation diminishing (RK TVD) scheme was used for the time discretization. At this stage, non-Newtonian effects and the pulsatile nature of the flow were not included. The developed Newtonian flow code was tested using benchmark problems for incompressible flow, namely, the driven cavity flow, Couette flow, Taylor-Green vortex problem, double shear layer problem, and skewed cavity flow. The results were compared with existing published experimental data in order to build confidence that the computer code was working properly in the simple blood flow conditions, i.e., as a Newtonian fluid. In the second stage, the backward-facing step was analyzed for Newtonian steady and pulsatile flow, and for non-Newtonian steady and pulsatile flow. The results were compared with experimental data and found to be in agreement. In the third stage, the computer program was extended to three dimensions. Flow through an infinite long pipe and through a 90-degree bend was carried out. The velocity profile in the pipe and at different locations of the bend was obtained, and the numerical values indicate good agreement with analytical and experimental values.Thesis (Ph.D.)--Wichita State University, College of Engineering, Dept. of Aerospace Engineering
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Chilton, Sven. "A fourth-order adaptive mesh refinement solver for Maxwell's Equations." Thesis, University of California, Berkeley, 2014. http://pqdtopen.proquest.com/#viewpdf?dispub=3616542.
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We present a fourth-order accurate, multilevel Maxwell solver, discretized in space with a finite volume approach and advanced in time with the classical fourth-order Runge Kutta method (RK4). Electric fields are decomposed into divergence-free and curl-free parts; we solve for the divergence-free parts of Faraday's Law and the Ampère-Maxwell Law while imposing Gauss' Laws as initial conditions. We employ a damping scheme inspired by the Advanced Weather Research and Forecasting Model to eliminate non-physical waves reflected off of coarse-fine grid boundaries, and Kreiss-Oliger artificial dissipation to remove standing wave instabilities. Surprisingly, artificial dissipation appears to damp the spuriously reflected waves at least as effectively as the atmospheric community's damping scheme.
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Fidkowski, Krzysztof J. 1981. "A high-order discontinuous Galerkin multigrid solver for aerodynamic applications." Thesis, Massachusetts Institute of Technology, 2004. http://hdl.handle.net/1721.1/16657.
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Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Aeronautics and Astronautics, 2004.Includes bibliographical references (p. 87-90).
This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.
Results are presented from the development of a high-order discontinuous Galerkin finite element solver using p-multigrid with line Jacobi smoothing. The line smoothing algorithm is presented for unstructured meshes, and p-multigrid is outlined for the nonlinear Euler equations of gas dynamics. Analysis of 2-D advection shows the improved performance of line implicit versus block implicit relaxation. Through a mesh refinement study, the accuracy of the discretization is determined to be the optimal O(h[superscript]P+l) for smooth problems in 2-D and 3-D. The multigrid convergence rate is found to be independent of the interpolation order but weakly dependent on the grid size. Timing studies for each problem indicate that higher order is advantageous over grid refinement when high accuracy is required. Finally, parallel versions of the 2-D and 3-D solvers demonstrate close to ideal coarse-grain scalability.
by Krzysztof J. Fidkowski.
S.M.
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Heminger, Michael Alan. "Dynamic Grid Motion in a High-Order Computational Aeroacoustic Solver." University of Toledo / OhioLINK, 2010. http://rave.ohiolink.edu/etdc/view?acc_num=toledo1272550725.
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Galbraith, Marshall C. "A Discontinuous Galerkin Chimera Overset Solver." University of Cincinnati / OhioLINK, 2013. http://rave.ohiolink.edu/etdc/view?acc_num=ucin1384427339.
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Christofori, Pamela. "The effect of direct instruction math curriculum on higher-order problem solving." [Tampa, Fla.] : University of South Florida, 2005. http://purl.fcla.edu/fcla/etd/SFE0001287.
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Dunn, Kyle George. "An Integral Equation Method for Solving Second-Order Viscoelastic Cell Motility Models." Digital WPI, 2014. https://digitalcommons.wpi.edu/etd-theses/578.
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For years, researchers have studied the movement of cells and mathematicians have attempted to model the movement of the cell using various methods. This work is an extension of the work done by Zheltukhin and Lui (2011), Mathematical Biosciences 229:30-40, who simulated the stress and displacement of a one-dimensional cell using a model based on viscoelastic theory. The report is divided into three main parts. The first part considers viscoelastic models with a first-order constitutive equation and uses the standard linear model as an example. The second part extends the results of the first to models with second-order constitutive equations. In this part, the two examples studied are Burger model and a Kelvin-Voigt element connected with a dashpot in series. In the third part, the effects of substrate with variable stiffness are explored. Here, the effective adhesion coefficient is changed from a constant to a spatially-dependent function. Numerical results are generated using two different functions for the adhesion coefficient. Results of this thesis show that stress on the cell varies greatly across each part of the cell depending on the constitute equation we use, while the position and velocity of the cell remain essentially unchanged from a large-scale point of view.
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Yano, Masayuki Ph D. Massachusetts Institute of Technology. "Massively parallel solver for the high-order Galerkin Least-Squares method." Thesis, Massachusetts Institute of Technology, 2009. http://hdl.handle.net/1721.1/54217.
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Thesis (S.M.)--Massachusetts Institute of Technology, Computation for Design and Optimization Program, 2009.This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.
Cataloged from student submitted PDF version of thesis.
Includes bibliographical references (p. 85-91).
A high-order Galerkin Least-Squares (GLS) finite element discretization is combined with massively parallel implicit solvers. The stabilization parameter of the GLS discretization is modified to improve the resolution characteristics and the condition number for the high-order interpolation. The Balancing Domain Decomposition by Constraints (BDDC) algorithm is applied to the linear systems arising from the two-dimensional, high-order discretization of the Poisson equation, the advection-diffusion equation, and the Euler equation. The Robin-Robin interface condition is extended to the Euler equation using the entropy-symmetrized variables. The BDDC method maintains scalability for the high-order discretization for the diffusion-dominated flows. The Robin-Robin interface condition improves the performance of the method significantly for the advection-diffusion equation and the Euler equation. The BDDC method based on the inexact local solvers with incomplete factorization maintains the scalability of the exact counterpart with a proper reordering.
by Masayuki Yano.
S.M.
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Moro-Ludeña, David. "An adaptive high order Reynolds-averaged Navier-Stokes solver with transition prediction." Thesis, Massachusetts Institute of Technology, 2015. http://hdl.handle.net/1721.1/97355.
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Thesis: Ph. D., Massachusetts Institute of Technology, Department of Aeronautics and Astronautics, 2015.Cataloged from PDF version of thesis.
Includes bibliographical references (pages 219-239).
The use of simulation techniques in applied aerodynamics has increased dramatically in the last three decades fostered by the growth in computational power. However, the state of the art discretization in industrial solvers remains nominally second order accurate, which makes them unfeasible to resolve multi-scale phenomena such as turbulence or acoustics, and limits their efficiency in terms of the error per degree of freedom. In recent years, the CFD community has put significant effort into the development of high order methods for fluid dynamics, with the goal of overcoming these barriers. This dissertation focuses on the application of high order hybridizable discontinuous Galerkin schemes to solve the equations that govern compressible turbulent flows. In particular, this thesis describes a novel methodology to adapt the boundary layer mesh to the solution "on the fly", based on a measure of the boundary layer thickness that drives the position of the nodes in the mesh, without changing its topology. The proposed algorithm produces accurate solutions with a reduced number of degrees of freedom, by leveraging the combination of mesh adaptivity with the high order of convergence of the discretization. In addition, the active tracking of the boundary layer reduces the nonlinear stiffness and improves the robustness of the numerical solution. A new shock capturing technique based on the addition of artificial viscosity is developed to handle shocks. The model is driven by a non-dimensional form of the divergence of the velocity, designed so that sub-cell shock resolution is achieved when a high order discretization is used, independently of the element size. The approach is extended to include the effect of transition to turbulence using an envelope eN method. This takes advantage of the structure of the mesh and requires the solution of a surface PDE for the transition criterion, which is discretized using a novel surface hybridizable discontinuous Galerkin scheme. The resulting method can simulate transition to turbulence in attached and separated flows, and can also accommodate long-scale unsteadiness in which the transition location evolves in time.
by David Moro-Ludeña.
Ph. D.
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Wyatt, Sarah Alice. "Issues in Interpolatory Model Reduction: Inexact Solves, Second-order Systems and DAEs." Diss., Virginia Tech, 2012. http://hdl.handle.net/10919/27668.
Full textAbstract:
Dynamical systems are mathematical models characterized by a set of differential or difference equations.
Model reduction aims to replace the original system with a reduced system of significantly smaller dimension that still describes the important dynamics of the large-scale
model. Interpolatory model reduction methods define a reduced model that interpolates the full model at selected interpolation points. The reduced model may be obtained through a Krylov reduction process or by using the Iterative Rational Krylov Algorithm (IRKA), which iterates this Krylov reduction process to obtain an optimal $\mathcal{H}_2$ reduced model.
This dissertation studies interpolatory model reduction for first-order descriptor systems, second-order systems, and DAEs. The main computational cost of interpolatory model reduction is the associated linear systems. Especially in the large-scale setting, inexact solves become desirable if not necessary. With the introduction of inexact solutions, however, exact interpolation no longer holds. While the effect of this loss of interpolation has previously been studied, we extend the discussion to the preconditioned case. Then we utilize IRKA's convergence behavior to develop preconditioner updates.
We also consider the interpolatory framework for DAEs and second-order systems. While interpolation results still hold, the singularity associated with the DAE often results in unbounded model reduction errors. Therefore, we present a theorem that guarantees interpolation and a bounded model reduction error. Since this theorem relies on expensive projectors, we demonstrate how interpolation can be achieved without explicitly computing the projectors for index-1 and Hessenberg index-2 DAEs. Finally, we study reduction techniques for second-order systems. Many of the existing methods for second-order systems rely on the model's associated first-order system, which results in computations of a $2n$ system. As a result, we present an IRKA framework for the reduction of second-order systems that does not involve the associated $2n$ system. The resulting algorithm is shown to be effective for several dynamical systems.Ph. D.
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Jalali, Alireza. "An adaptive higher-order unstructured finite volume solver for turbulent compressible flows." Thesis, University of British Columbia, 2017. http://hdl.handle.net/2429/60365.
Full textAbstract:
The design of aircraft depends increasingly on the use of Computational Fluid Dynamics (CFD) in which numerical methods are employed to obtain approximate solutions for fluid flows. One route to improve the numerical accuracy of CFD simulations is higher-order discretization methods. Moreover, finite volume discretizations are the method of choice in commercial CFD solvers and also in computational aerodynamics because of intrinsic conservative and shock-capturing properties. Considering that nearly all practical flows with aerodynamic applications are classified as turbulent, we develop a higher-order finite volume solver for the Reynolds Averaged Navier-Stokes (RANS) solution of turbulent compressible flows on unstructured meshes. Higher-order flow solvers must account for boundary curvature. Since turbulent flow simulations require anisotropic cells in shear layers, we use an elasticity analogy to project the boundary curvature into the interior faces and prevent faces from intersecting near curved boundaries. Furthermore, we improve the accuracy of solution reconstruction and output quantities on highly anisotropic cells with curvature using a local curvilinear coordinate system. A robust turbulence model for higher-order discretizations is fully coupled to the system of RANS equations and an efficient solution strategy is adopted for the convergence to the steady-state solution. We present our higher-order results for simple and complicated configurations in two dimensions. These results are verified by comparison against well-established numerical and experimental values in the literature. Our results show the advantages of higher-order methods in obtaining a more accurate solution with fewer degrees of freedom and also fast and efficient convergence to the steady-state solutions. Moreover, we propose an hp-adaptation algorithm for the unstructured finite volume solver based on residual-based and adjoint-based error indicators. In this approach, we enhance the local accuracy of the discretization via h-refinement or p-enrichment based on the smoothness of the solution. Mesh refinement is carried out by local cell division and introducing non-conforming interfaces in the mesh while order enrichment is obtained by local increase of the polynomial order in the reconstruction process. Our results show that this strategy leads to accuracy and efficiency
improvements for several types of compressible flow problems.Applied Science, Faculty of
Mechanical Engineering, Department of
Graduate
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Hoshyari, Shayan. "A higher-order unstructured finite volume solver for three-dimensional compressible flows." Thesis, University of British Columbia, 2017. http://hdl.handle.net/2429/62846.
Full textAbstract:
High-order accurate numerical discretization methods are attractive for their potential to significantly reduce the computational costs compared to the traditional second-order methods. Among the various unstructured higher-order discretization schemes, the k-exact reconstruction finite volume method is of interest for its straightforward mathematical formulation, and its compatibility with the current lower-order industrial solvers. However, current three-dimensional finite volume solvers are limited to the solution of inviscid and laminar viscous flow problems. Since three-dimensional turbulent flows appear in many industrial applications, the current thesis takes the first step towards the development of a three-dimensional higher-order finite volume solver for the solution of both inviscid and viscous turbulent steady-state flow problems. The k-exact finite volume formulation of the governing equations is rederived in a dimension-independent manner, where the negative Spalart-Allmaras turbulence model is employed. This one-equation model is reasonably accurate for many flow conditions, and its simplicity makes it a good starting point for the development of numerical algorithms. Then, the three-dimensional mesh preprocessing steps for a finite volume simulation are presented, including higher-order accurate numerical quadrature, and capturing the boundary curvature in highly anisotropic meshes. Also, the issues of k-exact reconstruction in handling highly anisotropic meshes are reviewed and addressed. Since three-dimensional problems can require much more memory than their two-dimensional counter-parts, solution methods that work in two dimensions might not be feasible in three dimensions anymore. As an attempt to overcome this issue, a practical and parallel scalable method for the solution of the discretized system of nonlinear equations is presented. Finally, the solution of four three-dimensional test problems are studied: Poisson’s equation in a cubic domain, inviscid flow over a sphere, turbulent flow over a flat plate, and turbulent flow over an extruded NACA 0012 airfoil. The solution is verified, and the resource consumption of the flow solver is measured. The results demonstrate the benefit and practicality of using higher-order methods for obtaining a certain level of accuracy.Applied Science, Faculty of
Mechanical Engineering, Department of
Graduate
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Cabezas, García José Xavier. "Heuristic methods for solving two discrete optimization problems." Thesis, University of Edinburgh, 2018. http://hdl.handle.net/1842/31093.
Full textAbstract:
In this thesis we study two discrete optimization problems: Traffic Light Synchronization and Location with Customers Orderings. A widely used approach to solve the synchronization of traffic lights on transport networks is the maximization of the time during which cars start at one end of a street and can go to the other without stopping for a red light (bandwidth maximization). The mixed integer linear model found in the literature, named MAXBAND, can be solved by optimization solvers only for small instances. In this manuscript we review in detail all the constraints of the original linear model, including those that describe all the cyclic routes in the graph, and we generalize some bounds for integer variables which so far had been presented only for problems that do not consider cycles. Furthermore, we summarized the first systematic algorithm to solve a simpler version of the problem on a single street. We also propose a solution algorithm that uses Tabu Search and Variable Neighbourhood Search and we carry out a computational study. In addition we propose a linear formulation for the shortest path problem with traffic lights constraints (SPTL). On the other hand, the simple plant location problem with order (SPLPO) is a variant of the simple plant location problem (SPLP) where the customers have preferences on the facilities which will serve them. In particular, customers define their preferences by ranking each of the potential facilities. Even though the SPLP has been widely studied in the literature, the SPLPO has been studied much less and the size of the instances that can be solved is very limited. In this manuscript, we propose a heuristic that uses a Lagrangean relaxation output as a starting point of a semi-Lagrangean relaxation algorithm to find good feasible solutions (often the optimal solution). We also carry out a computational study to illustrate the good performance of our method. Last, we introduce the partial and stochastic versions of SPLPO and apply the Lagrangean algorithm proposed for the deterministic case to then show examples and results.
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Sherer, Scott Eric. "Investigation of high-order and optimized interpolation methods with implementation in a high-order overset grid fluid dynamics solver /." The Ohio State University, 2002. http://rave.ohiolink.edu/etdc/view?acc_num=osu1486462702465327.
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Li, Yi. "Variable-step variable-order 3-stage Hermite-Birkhoff ODE solver of order 5 to 15 with a C++ program." Thesis, University of Ottawa (Canada), 2008. http://hdl.handle.net/10393/28001.
Full textAbstract:
Variable-step variable-order 3-stage Hermite-Birkhoff (HB) methods HB( p)3 of order p = 5 to 15 are constructed for solving nonstiff differential equations. Forcing a Taylor expansion of the numerical solution to agree with an expansion of the true solution leads to multistep and Runge-Kutta type order conditions which are reorganized into linear confluent Vandermonde-type systems of HB type. Fast algorithms are developed for solving these systems in O(p2) operations to obtain HB interpolation polynomials in terms of generalized Lagrange basis functions. The order and stepsize of these methods are controlled by four local error estimators. These methods, when programmed in Matlab, are superior to Matlab's ode113 in solving several problems often used to test higher order ODE solvers on the basis of the number of steps, CPU time, and maximum global error. On the other hand, HB(5-15)3 are programmed in object-oriented C++ and the Dormand-Prince 13-stage nested Runge-Kutta pair DP(8,7)13M are programmed in C. DP(8,7) is found to use less CPU time, have smaller maximum global error but require a larger number of function evaluations than HB(5-15)3. However, for expensive equations, such as the Cubicwave, HB(5-15)3 is superior. In the C++ program, array and matrix are considered to be new objects. Algorithms, testing programs and new objects are structured separately as header files.
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Zigic, Dragan. "Homotopy methods for solving the optimal projection equations for the reduced order model problem." Thesis, This resource online, 1991. http://scholar.lib.vt.edu/theses/available/etd-11242009-020145/.
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Buck, Rebecca Arlene. "Integrating the Least-Cost Grade-Mix Solver into ROMI." Thesis, Virginia Tech, 2009. http://hdl.handle.net/10919/36339.
Full textAbstract:
Up to 70 percent of rough mill manufacturing expenses stem from raw material (lumber) cost. Rough mill costs can be reduced by optimizing the lumber grade or grades that are purchased. This solution is known as the least-cost lumber grade-mix solution. The least-cost lumber grade-mix solutions has been a topic of great interest to both the secondary hardwood industry and to academia since even small changes in raw material cost can contribute to substantial reduction in rough mill expenses.
A statistical model was developed for finding the least-cost lumber grade-mix which uses the rough mill simulator, ROMI-RIP 2.0, and the statistical package, SAS 8.2. The SAS 8.2-based least-cost lumber grade-mix model was validated by comparing SAS 8.2-based least-cost grade-mix solutions to OPTIGRAMI 2.0, a least-cost lumber grade-mix solver that relies on linear modeling. The SAS 8.2-based least-cost lumber grade-mix solver found lower cost solutions in 9 of 10 cutting bills that were tested. The SAS 8.2-based least-cost lumber grade-mix solver was packaged with ROMI 3.0, an updated version of ROMI-RIP, and provided to industry free of charge by the USDA Forest Service. The USDA Forest Service also purchased a SAS server license to allow least-cost lumber grade-mix solver users free access to SAS 8.2. However, industry users were reluctant to use the USDA Forest Service SAS server since it requires the user to enter individual cost and yield data to a government computer. This solution also required the user to have internet access and limited access to one user at any time. Thus, the goal of this research was to incorporate the least-cost lumber grade-mix solver into ROMI using the free, open source statistical package R 2.7.2. An R 2.7.2-based least-cost lumber grade-mix solver was developed and validated by comparing the R 2.7.2-based least-cost lumber grade-mix solutions to the updated SAS 9.2-based least-cost lumber grade-mix solutions. No differences were found in the least-cost lumber grade-mix solutions from either solver. Thus, a new least-cost lumber grade-mix solver using the R 2.7.2 open source statistical package was created. R 2.7.2 is installed on each personal computer on which the USDA Forest Serviceâ s ROMI rough mill simulation software is installed and, thus, no external computing resources are needed when solving the least-cost lumber grade-mix problem.Master of Science
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Zhang, Yu. "Variable-step variable-order 3-stage Hermite-Birkhoff-Obrechkoff ODE solver of order 4 to 14 with a C program." Thesis, University of Ottawa (Canada), 2007. http://hdl.handle.net/10393/27500.
Full textAbstract:
Variable-step variable-order 3-stage Hermite-Birkhoff-Obrechkoff methods of order 4 to 14, denoted by HBO(4-14)3, are constructed for solving nonstiff systems of first-order differential equations of the form y' = f (x, y), y( x0) = y0. These methods use y' and y" as in Obrechkoff's method. Forcing a Taylor expansion of the numerical solution to agree with an expansion of the true solution leads to multistep- and Runge-Kutta-type order conditions which are reorganized into linear Vandermonde-type systems. Fast algorithms are developed for solving these systems to obtain Hermite-Birkhoff interpolation polynomials in terms of generalized Lagrange basis functions. The new methods have larger regions of absolute stability than Adams-Bashforth-Moulton methods of comparable orders in PECE mode. The order and stepsize of these methods are controlled by four local error estimators. When programmed in Matlab, HBO(4-14)3 are superior to Matlab's ode113 in solving several problems often used to test higher order ODE solvers on the basis of the number of function evaluations, CPU time, and maximum global error. It is also superior to the variable-step 3-stage HBO(14)3 of order 14 on some problems. When programmed in C, HBO(4-14)3 is superior to the Dormand-Prince Runge-Kutta nested pair DP(8,7)13M in solving expensive equations over a long period of time. HBO(4-14)3 has been implemented in C. The C program for HBO(4-14)3 is an important contribution of this thesis.
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Zhuang, Yuchuan. "Variable-step variable-order 2-stage Hermite-Birkhoff-Obrechkoff ODE solver of order 3 to 14 with a C program." Thesis, University of Ottawa (Canada), 2008. http://hdl.handle.net/10393/27746.
Full textAbstract:
Variable-step variable-order 2-stage Hermite-Birkhoff-Obrechkoff (HBO) methods, HBO(p)2, of order p = 3 to 14, named HBO(3-14)2, are constructed for solving nonstiff first-order differential equations. Forcing an expansion of the numerical solution to agree with a Taylor expansion of the true solution leads to multistep and Runge-Kutta type order conditions which are reorganized into linear Vandermonde-type systems of HBO type. Fast algorithms are developed for solving these systems in O( p2) operations to obtain Hermite-Birkhoff interpolation polynomials in terms of generalized Lagrange basis functions. The order and step size of these methods are controlled by four local error estimators. For numerical computation the lower order 3 is raised to 4 since HBO(4-14)2 produces better results. When programmed in Matlab, HBO (4-14) 2 is superior to Matlab's ode113 in solving several problems often used to test higher order ODE solvers on the basis of the number of steps, CPU time, and maximum global error. On the other hand, HBO (4-14)2 and the Dormand-Prince 13-stage nested Runge-Kutta pair DP(8,7)13M are programmed in C. In this case, DP(8,7) uses less CPU time, have smaller maximum global error but require a larger number of function evaluations than HBO(4-14)2 on nonexpensive problems. However, for expensive equations, such as the Cubicwave, HBO(4-14)2 is superior. Compared with previous results obtained by the 3-stage HBO(4-14)3 on Van der Pol equations with increasing value of epsilon, the new HBO(4-14)2 finally dominates.
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Schaeffer, Laura M. "Interaction of instructional material order and subgoal labels on learning in programming." Thesis, Georgia Institute of Technology, 2015. http://hdl.handle.net/1853/54459.
Full textAbstract:
Expository instructions, worked examples, and subgoal labels have all been shown to positively impact student learning and performance in computer science education. This study examined whether learning and problem solving performance differed based on the sequence of the instructional materials (expository and worked examples) and the presence of subgoal labels within the instructional materials. Participants were 138 undergraduate college students, age 17-25, who watched two instructional videos on creating an application in the App Inventor programming language before completing several learning assessments. A significant interaction showed that when learners were presented with the worked example followed by the expository instructions containing subgoal labels, the learner was better at outlining the procedure for creating an application. These manipulations did not affect cognitive load, novel problem solving performance, explanations of solutions, or the amount of time spent on instructions and completing the assessments. These results suggest that the order instructional materials are presented have has little impact on problem solving, although some benefit can be gained from presenting the worked example before the expository instructions when subgoal labels are included. This suggests the order the instructions are presented to learners does not impact learning. Previous studies demonstrating an effect of subgoal labels used text instructions as opposed to the video instructions used in the present study. Future research should investigate how these manipulations differ for text instructions and video instructions.
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Tomaro, Robert F. "An implicit higher-order spatially accurate scheme for solving time dependent flows on unstructured meshes." Diss., Georgia Institute of Technology, 1997. http://hdl.handle.net/1853/12264.
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Broman, Karolina. "Chemistry: content, context and choices : towards students' higher order problem solving in upper secondary school." Doctoral thesis, Umeå universitet, Institutionen för naturvetenskapernas och matematikens didaktik, 2015. http://urn.kb.se/resolve?urn=urn:nbn:se:umu:diva-95956.
Full textAbstract:
Chemistry is often claimed to be difficult, irrelevant, and uninteresting to school students. Even students who enjoy doing science often have problems seeing themselves as being scientists. This thesis explores and challenges the negative perception of chemistry by investigating upper secondary students’ views on the subject. Based on students’ ideas for improving chemistry education to make the subject more interesting and meaningful, new learning approaches rooted in context-based learning (CBL) are presented. CBL approaches are applied in several countries to enhance interest, de-emphasise rote learning, and improve students’ higher order thinking. Students’ views on upper secondary school chemistry classes in combination with their problem- solving strategies and application of chemistry content knowledge when solving context-based chemistry tasks were investigated using a mixed methods approach. Questionnaire responses, written solutions to chemistry problems, classroom observations, and think-aloud interviews with upper secondary students at the Natural Science Programme and with experts working on context- based chemistry tasks were analysed to obtain a general overview and explore specific issues in detail. Several students were identified who had positive feelings about chemistry, found it interesting, and chose to continue with it beyond the compulsory level, mainly with the aim of future university studies or simply because they enjoyed it. Their suggestions for improving school chemistry by connecting it to everyday life prompted an exploration of CBL approaches. Studies on the cognitive learning outcomes arising from the students’ work on context-based tasks revealed that school chemistry heavily emphasises the recall of memorised facts. However, there is evidence of higher order thinking when students’ problem-solving processes are scaffolded using hints based on the Model of Hierarchical Complexity in Chemistry (MHC-C). In addition, the contextualisation of problems is identified as something that supports learning rather than distracting students. To conclude, the students in this thesis are interested in chemistry and enjoy chemistry education, and their motives for choosing to study chemistry at the post-compulsory level are related to their aspirations; students’ identity formation is important for their choices. Because students are accustomed to recalling facts and solving chemistry problems that have “one single correct answer”, they find more open problems that demand higher order thinking (e.g. knowledge transfer) unfamiliar and complex, suggesting that such processes should be practiced more often in school chemistry.Kemi är ett skolämne som generellt anses vara både svårt, irrelevant och ointressant för ungdomar. Trots att det ändå finns ungdomar som uppskattar naturvetenskap i allmänhet och kemi i synnerhet, har de ofta problem att se sig själva som naturvetare eller kemister. Denna avhandling undersöker och ifrågasätter den negativa bilden av kemiämnet genom att till en början studera gymnasieelevers syn på kemi. Med utgångspunkt från naturvetarelevers förslag för att förbättra kemiundervisningen och göra ämnet mer intressant och meningsfullt, anknyter avhandlingen därefter till kontextbaserad kemi. Kontextbaserade kurser används i flera länder för att öka elevernas intresse, minska fokuseringen på utantillkunskaper och utveckla elevernas mer avancerade tänkande; med andra ord med målet att uppnå ett meningsfullt lärande. Vid kontextbaserade angreppssätt utgår man från ett sammanhang (kontexten), ofta något personligt eller samhälleligt, som ska vara relevant och intressant. Från dessa kontexter koncentreras därefter undervisningen på de ämneskunskaper man behöver ha för att förstå sammanhanget (s.k. need-to-know). Syftet med avhandlingen är att undersöka naturvetarelevers syn på gymnasiekemin, både deras intresse för ämnet och deras skäl att välja det naturvetenskapliga programmet på gymnasiet, samt elevernas problemlösningsförmåga och användande av ämneskunskaper när de löser kontextbaserade kemiuppgifter. Skälet att studera naturvetarelever på gymnasiet är att dessa elever uppfattas som möjliga framtida naturvetare eftersom de själva har valt naturvetenskaplig inriktning efter den obligatoriska grundskolan. Med hjälp av olika metoder (enkäter, klassrums- observationer, skriftliga lösningar till kemiuppgifter och intervjuer med både elever och experter som löser kemiuppgifter) har analyser genomförts för att dels får en allmän överblick, dels för att utforska specifika delar i detalj både gällande kognitiva och affektiva aspekter av lärande. Resultaten visar att flertalet elever har en positiv inställning till kemi, många tycker att ämnet är intressant och har valt att fortsätta läsa kemi efter den obligatoriska grundskolan främst med målet att studera vidare på universitetsnivå, men också eftersom de specifikt uppskattar kemi. Gymnasieeleverna lyfter fram lärarna som viktiga och lärarstyrda kemilektioner anses positivt, speciellt om lärarna är strukturerade i sin undervisning. Ett vanligt skäl till att välja naturvetenskapsprogrammet är också att man aktivt väljer utbildning med utgångspunkt från vilken skola man vill gå på, något som i denna avhandling tolkas som ett identitetsskapande. Elevernas förslag för att förbättra skolkemin genom att anknyta kemin till vardagen låg till grund för avhandlingens fortsatta inriktning mot kontextbaserade angreppssätt. Analyser av elevernas kognitiva resultat när de löser kontextbaserade kemiuppgifter visar att dagens skolkemi tydligt fokuserar på att memorera faktakunskaper. Eleverna är vana att använda utantillkunskaper när de löser kemiuppgifter eftersom uppgifterna, enligt eleverna, efterfrågar ”det rätta svaret”. Däremot visar studierna också att ett mer avancerat tänkande kan uppnås när elevernas problemlösning stöds av hjälp och ledtrådar som baseras på ett specifikt ramverk, MHC-C (Model of Hierarchical Complexity in Chemistry). När det gäller ämneskunskaperna som krävs för att lösa de kontextbaserade kemiuppgifterna är vissa kemibegrepp viktiga tröskelbegrepp (sk. threshold concepts). Med hjälp av medvetenhet om tröskelbegrepp, som exempelvis polaritet och elektronegativitet för löslighetsuppgifter inom den organiska kemin, kan en större helhetsförståelse för övergripande begrepp (crosscutting disciplinary concepts) som förhållandet mellan kemiska ämnens struktur och egenskaper förhoppningsvis uppnås. När det gäller affektiva resultat anser eleverna att kontexterna i uppgifterna både var intressanta och relevanta, främst när en personlig anknytning var tydlig. Dessutom visade sig kontexterna i uppgifterna vara positiva för lärandet, inte en distraktionsfaktor. Sammanfattningsvis konstateras att svenska elever på naturvetenskaps- programmet är intresserade av kemi och uppskattar kemiundervisningen, speciellt om kemin knyts till vardagen och att lärarna har en tydlig struktur i sin undervisning. Elevernas skäl att välja fortsatta kemistudier efter den obligatoriska grundskolan kan knytas till deras utbildningssträvan men också att elevers identitetsskapande är viktigt för deras gymnasieval. Med hjälp av kontextbaserade angreppssätt kan kemiundervisningen göras mer intressant och relevant samtidigt som elevernas problemlösningsförmåga kan utvecklas. När eleverna möter mer öppna frågor som kräver förklaringar och resonemang är de ovana vid detta och uppfattar uppgifterna komplicerade, samtidigt som de uppskattar denna typ av uppgifter eftersom de uppfattas relevanta och intressanta. Slutsatsen blir att elevernas förmåga till problemlösning av öppna frågor som både kräver faktakunskaper men också förklaringar och resonemang måste tränas oftare inom ramen för skolans kemi för att utveckla elevernas meningsfulla lärande.
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Underwood, Tyler Carroll. "Performance Comparison of Higher-Order Euler Solvers by the Conservation Element and Solution Element Method." The Ohio State University, 2014. http://rave.ohiolink.edu/etdc/view?acc_num=osu1399017583.
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Wurst, Michael [Verfasser]. "Development of a high-order Discontinuous Galerkin CFD solver for moving bodies / Michael Wurst." München : Verlag Dr. Hut, 2017. http://d-nb.info/1135596670/34.
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Zhao, Qiuying. "Towards Improvement of Numerical Accuracy for Unstructured Grid Flow Solver." University of Toledo / OhioLINK, 2012. http://rave.ohiolink.edu/etdc/view?acc_num=toledo1353107603.
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Niegemann, Jens [Verfasser], and K. [Akademischer Betreuer] Busch. "Higher-Order Methods for Solving Maxwell's Equations in the Time-Domain / Jens Niegemann. Betreuer: K. Busch." Karlsruhe : KIT-Bibliothek, 2009. http://d-nb.info/1014099129/34.
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Luo, BiYong. "Shooting method-based algorithms for solving control problems associated with second-order hyperbolic partial differential equations." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 2001. http://www.collectionscanada.ca/obj/s4/f2/dsk3/ftp05/NQ66358.pdf.
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Bilyeu, David L. "A HIGHER-ORDER CONSERVATION ELEMENT SOLUTION ELEMENT METHOD FOR SOLVING HYPERBOLIC DIFFERENTIAL EQUATIONS ON UNSTRUCTURED MESHES." The Ohio State University, 2014. http://rave.ohiolink.edu/etdc/view?acc_num=osu1396877409.
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