Dissertations / Theses on the topic 'PDE'
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1
Ugail, Hassan. "On the spine of a PDE surface." Springer, 2003. http://hdl.handle.net/10454/2687.
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yesThe spine of an object is an entity that can characterise the object¿s topology and describes the object by a lower dimension. It has an intuitive appeal for supporting geometric modelling operations. The aim of this paper is to show how a spine for a PDE surface can be generated. For the purpose of the work presented here an analytic solution form for the chosen PDE is utilised. It is shown that the spine of the PDE surface is then computed as a by-product of this analytic solution. This paper also discusses how the of a PDE surface can be used to manipulate the shape. The solution technique adopted here caters for periodic surfaces with general boundary conditions allowing the possibility of the spine based shape manipulation for a wide variety of free-form PDE surface shapes.
2
Öhrnell, Carl. "Lie Groups and PDE." Thesis, Uppsala universitet, Analys och sannolikhetsteori, 2020. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-420706.
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Tsui, Ka Cheung. "A networked PDE solving environment /." View Abstract or Full-Text, 2003. http://library.ust.hk/cgi/db/thesis.pl?MATH%202003%20TSUI.
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Thesis (M. Phil.)--Hong Kong University of Science and Technology, 2003.Includes bibliographical references (leaves 56-58). Also available in electronic version. Access restricted to campus users.
4
Ugail, Hassan. "Method of trimming PDE surfaces." Elsevier, 2006. http://hdl.handle.net/10454/2648.
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A method for trimming surfaces generated as solutions to Partial Differential Equations
(PDEs) is presented. The work we present here utilises the 2D parameter
space on which the trim curves are defined whose projection on the parametrically
represented PDE surface is then trimmed out. To do this we define the trim curves
to be a set of boundary conditions which enable us to solve a low order elliptic
PDE on the parameter space. The chosen elliptic PDE is solved analytically, even
in the case of a very general complex trim, allowing the design process to be carried
out interactively in real time. To demonstrate the capability for this technique we
discuss a series of examples where trimmed PDE surfaces may be applicable.
5
Bolzonella, Nicolo' <1989>. "MLPG solution of elliptic PDE." Master's Degree Thesis, Università Ca' Foscari Venezia, 2017. http://hdl.handle.net/10579/10509.
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Meshless methods for the numerical solution of Partial Differential Equations (PDE) are emerging techniques. Nowadays their efficiency is not comparable to Finite Element methods.
Among the ample literature on meshless methods, we focus on Meshless Petrov--Galerkin (MLPG) methods.In many variants they pervade the Research on meshless methods for solving PDE.
This thesis aims at implementing a MATLAB code allowing for the numerical approximation of Poisson problems.
The accuracy and efficiency of the code is tested.
Moreover, strategies for using GPU devices are analyzed, developed and implemented.
A discussion of the their efficiency is conducted on test problems.
6
Ugail, Hassan, and N. Kirmani. "Method of surface reconstruction using partial differential equations." WSEAS, 2006. http://hdl.handle.net/10454/2750.
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Seidel, Cathleen. "Integration externer PDE-Löser in Mathcad." Universitätsbibliothek Chemnitz, 2010. http://nbn-resolving.de/urn:nbn:de:bsz:ch1-201000672.
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Mathcad gilt in den unterschiedlichsten Bereichen, z.B. in den Ingenieurwissenschaften, der Mathematik, der Physik, der Biologie oder sogar der Qualitätssicherung als hervorragendes Werkzeug zur übersichtlichen Darstellung komplexer Berechnungen.
Sollten die enthaltenen Funktionalitäten nicht mehr ausreichen, besteht die Möglichkeit, Mathcad mit Hilfe von User-DLLs zu erweitern. Diese Erweiterung kann perfekt als Schnittstelle zwischen Mathcad und anderen Softwarepaketen genutzt werden. Die von der inuTech GmbH entwickelte Klassenbibliothek Diffpack zur Simulation und numerischen Lösung von Differentialgleichungen aus den verschiedensten Bereichen eignet sich hervorragend, erforderliche Funktionalitäten für Mathcad zu implementieren. Mathcad kann somit zur Parametrisierung, für Berechnungen und zur Darstellung der Ergebnisse verwendet werden, während Diffpack die Lösung der partiellen Differentialgleichung, z.B. mittels FEM, übernimmt.
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Dascaliuc, Radu. "Backward time behavior of dissipative PDE." Texas A&M University, 2005. http://hdl.handle.net/1969.1/4940.
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We study behavior for negative times t of the 2D periodic Navier-Stokes equations
and Burgers' original model for turbulence. Both systems are proved to have
rich sets of solutions that exist for all t - R and increase exponentially as t -> -(Infinity) However, our study shows that the behavior of these solutions as well as the geometrical
structure of the sets of their initial data are very different. As a consequence,
Burgers original model for turbulence becomes the first known dissipative system that
despite possessing a rich set of backward-time exponentially growing solutions, does
not display any similarities, as t -> -(Infinity), to the linear case.
9
Broomé, Sofia, and Jonathan Ridenour. "A PDE PERSPECTIVE ON CLIMATE MODELING." Thesis, KTH, Matematik (Inst.), 2014. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-147765.
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This report will provide an overview of climate modeling from a mathematical perspective, particularly with respect to the use of partial differential equations. A visit to the Swedish Meterological and Hydrological Institute's Rossby Center for climate research in Norrkoping, Sweden, is at the foundation of our investigations. An introduction and a brief history section will be followed by a description of the Navier-Stokes equations, which are at the heart of climate-related mathematics, as well as a survey of many of the popular approximations and modeling techniques in use by climate researchers today. Subsequently, a boundary value problem based on the one dimensional compressible Euler equations will be discussed from an analytical as well as a numerical point of view, especially with concern to the well-posedness of the same.
10
Zhu, Kangping. "Two problems in applications of PDE." Thesis, New York University, 2014. http://pqdtopen.proquest.com/#viewpdf?dispub=3635320.
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This thesis contains two different parts. For part I, we develop a PDE perspective on a model problem from the machine learning literature. The problem involves ''prediction" via ''regret minimization". Our PDE approach identifies the optimal strategies and the associated outcomes in a scaling limit where the number of time steps tends to 1. While our PDE is very nonlinear, explicit solutions are available in many cases due to a surprising and convenient link to the linear heat equation.
For part II, We consider H–αgradient flow of the Modica-Mortola energy. The evolution law can be viewed as a nonlocal analogue of the Cahn-Hilliard equation for α > 0; the limit as α= 0 is (formally at least) the volume preserving Allen-Cahn flow. When α > ½ , we prove a time-averaged upper bound on the typical length scale, of order t < 1/( 1 +2α) We also argue that for α > ½ the true time scale of the evolution is the original time scale (and that the case α < ½ is different). Finally, we derive the sharp interface limit of the flow using heuristic arguments.
11
Schönlieb, Carola-Bibiane. "Modern PDE techniques for image inpainting." Thesis, University of Cambridge, 2009. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.611552.
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Alqarni, Mohammed Zaidi A. "PRECONDITIONERS FOR PDE-CONSTRAINED OPTIMIZATION PROBLEMS." Kent State University / OhioLINK, 2019. http://rave.ohiolink.edu/etdc/view?acc_num=kent1573148003180191.
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Sabra, Ahmad. "Nonlinear PDE and Optical Surfaces Design." Diss., Temple University Libraries, 2015. http://cdm16002.contentdm.oclc.org/cdm/ref/collection/p245801coll10/id/345398.
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MathematicsPh.D.
We introduce two models to design near field reflectors in R^3 that solve an inverse problem in radiometry, taking into account the inverse square law of irradiance. The problem leads to a Monge-Ampere type inequality. The surfaces in the first model are strictly convex and require to be far from the source to avoid obstruction. In the second model, the reflectors are neither convex nor concave and do not block the rays even if they are close to the source.
Temple University--Theses
14
Ugail, Hassan. "Spine based shape parameterisation for PDE surfaces." Springer, 2009. http://hdl.handle.net/10454/2649.
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The aim of this paper is to show how the spine of a PDE surface can be generated and how it can be used to efficiently parameterise a PDE surface. For the purpose of the work presented here an approximate analytic solution form for the chosen PDE is utilised. It is shown that the spine of the PDE surface is then computed as a by-product of this analytic solution. Furthermore, it is shown that a parameterisation can be introduced on the spine enabling intuitive manipulation of PDE surfaces.
15
Ugail, Hassan, M. I. G. Bloor, and M. J. Wilson. "On interactive design using the PDE method." Vanderbilt University Press, 1998. http://hdl.handle.net/10454/2722.
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Ugail, Hassan, M. I. G. Bloor, and M. J. Wilson. "Manipulation of PDE surfaces using an interactively defined parameterisation." Elsevier, 1999. http://hdl.handle.net/10454/2669.
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NoManipulation of PDE surfaces using a set of interactively defined parameters is considered. The PDE method treats surface design as a boundary-value problem and ensures that surfaces can be defined using an appropriately chosen set of boundary conditions and design parameters. Here we show how the data input to the system, from a user interface such as the mouse of a computer terminal, can be efficiently used to define a set of parameters with which to manipulate the surface interactively in real time.
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Nordén, Markus. "Parallel PDE Solvers on cc-NUMA Systems." Licentiate thesis, Uppsala universitet, Avdelningen för teknisk databehandling, 2004. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-86307.
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The current trend in parallel computers is that systems with a large shared memory are becoming more and more popular. A shared memory system can be either a uniform memory architecture (UMA) or a cache coherent non-uniform memory architecture (cc-NUMA). In the present thesis, the performance of parallel PDE solvers on cc-NUMA computers is studied. In particular, we consider the shared namespace programming model, represented by OpenMP. Since the main memory is physically, or geographically distributed over several multi-processor nodes, the latency for local memory accesses is smaller than for remote accesses. Therefore, the geographical locality of the data becomes important. The questions posed in this thesis are: (1) How large is the influence on performance of the non-uniformity of the memory system? (2) How should a program be written in order to reduce this influence? (3) Is it possible to introduce optimizations in the computer system for this purpose? Most of the application codes studied address the Euler equations using a finite difference method and a finite volume method respectively and are parallelized with OpenMP. Comparisons are made with an alternative implementation using MPI and with PDE solvers implemented with OpenMP that solve other equations using different numerical methods. The main conclusion is that geographical locality is important for performance on cc-NUMA systems. This can be achieved through self optimization provided in the system or through migrate-on-next-touch directives that could be inserted automatically by the compiler. We also conclude that OpenMP is competitive with MPI on cc-NUMA systems if care is taken to get a favourable data distribution.
18
Rees, Tyrone. "Preconditioning iterative methods for PDE constrained optimization." Thesis, University of Oxford, 2010. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.543537.
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Nordén, Markus. "Parallel PDE solvers on cc-NUMA systems /." Uppsala : Univ. : Dept. of Information Technology, Univ, 2004.
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Carton, de Wiart Benjamin Valentin Guillaume. "Wavelet optimised PDE methods for financial derivatives." Thesis, University of Cambridge, 2006. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.613648.
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Kováč, Patrik. "Studie využitelnosti PDE toolboxu MATLABu v mechanice." Master's thesis, Vysoké učení technické v Brně. Fakulta strojního inženýrství, 2021. http://www.nusl.cz/ntk/nusl-443740.
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This thesis deals with the practical usability of the PDE Toolbox in the MATLAB. It brieflydescribes the mathematical fundamentals of solution. The thesis presents the possibilitiesof PDE Toolbox in the creation of the model, geometry, boundary conditions, mesh and displayof results. The PDE Toolbox results from selected tasks from static, modal and transientmechanics and thermomechanics are compared with the analytical solution or with the FEMsimulation from the ANSYS. The main part deals with the evaluation and generalizationof results.
22
Liu, Pan. "Variational and PDE Methods for Image Processing." Research Showcase @ CMU, 2017. http://repository.cmu.edu/dissertations/945.
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Hobbs, Graham. "Particles and biomembranes : a variational PDE approach." Thesis, University of Warwick, 2016. http://wrap.warwick.ac.uk/90319/.
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We examine mathematical models for small deformations of membranes. First we review physically well-established models, posed in the Monge gauge, from a mathematical perspective. We produce a variational framework in which well posedness can be studied and finite element methods applied. The methods are used to investigate the effects of point forces, point displacement constraints and point curvature constraints. Such models are suitable for the study of deformations induced by filaments contained in the cell cytoskeleton and by embedded protein inclusions. In particular we study the membrane mediated interactions between filaments and also between inclusions. We then introduce a new linearised model which describes small deformations of closed surfaces that are minimisers of Helfrich-type energies. The deformed surface is described as a graph over the Helfrich minimising undeformed surface. This is the natural generalisation of the Monge gauge to initially curved surfaces. We focus on a Willmore energy which gives rise to spheres and a family of tori as undeformed surfaces and also introduce surface tension on a sphere. Again we study deformations induced by filaments. A variational formulation is produced which is similar to the Monge gauge case and we formulate a numerical method to study membrane mediated interactions. Finally we introduce an abstract splitting method which allows a high order PDE to be solved by an equivalent system of lower order equations. We give conditions which ensure well posedness of the system and produce a finite element method whose solution converges to the solution of the full system. The theory is applied to show convergence for the numerical methods used for the surface deformations model. We provide examples which show the theoretical error estimates are achieved.
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SCODINA, STEFANO. "Observation and control of PDE with disturbances." Doctoral thesis, Università degli Studi di Cagliari, 2012. http://hdl.handle.net/11584/266149.
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In this Thesis, the problem of controlling and Observing some classes of distributed parameter systems is addressed. The particularity of this work is to consider partial differential equations (PDE) under the effect of external unknown disturbances. We consider generalized forms of two popular parabolic and hyperbolic infinite dimensional dynamics, the heat and wave equations. Sliding-mode control is used to achieve the control goals, exploiting the robustness properties of this robust control technique against persistent disturbances and parameter uncertainties.
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Brasco, Lorenzo. "Geodesics and PDE methods in transport models." Phd thesis, Paris 9, 2010. https://bu.dauphine.psl.eu/fileviewer/index.php?doc=2010PA090033.
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Cette thèse est dédiée à l'étude des problèmes de transport optimal, alternative au problème de Monge-Kantorovich : ils apparaissent naturellement dans des applications pratiques, telles que la conception des réseaux de transport optimal ou la modélisation des problèmes de circulation urbaine. En particulier, nous considérons des problèmes où le coût du transport a une dèpendance non linèaire de la masse : typiquement dans ce type de problèmes, le coût pour déplacer une masse m pour une longueur ℓ est φ (m) ℓ, où φ est une fonction assignée, obtenant ainsi un coût total de type Σ φ (m) ℓ. Deux cas importants sont abordés en détail dans ce travail : le cas où la fonction φ est subadditive (transport ramifié), de sorte que la masse a intérêt à voyager ensemble, de manière à réduire le coût total; le cas où φ est superadditive (transport congestionné), où au contraire, la masse tend à diffuser autant que possible. Dans le cas du transport ramifié, nous introduisons deux nouveaux modèles: dans le premièr, le transport est décrit par des courbes de mesures de probabilité que minimisent une fonctionnelle de type géodésique (avec un coefficient que pénalise le mesures qui ne sont pas atomiques). Le second est plus dans l'esprit de la formulation de Benamou et Brenier pour les distances de Wasserstein, en particulier, le transport est décrit par paires de ``courbe de mesures--champ de vitesse'', liées par l'équation de continuité, qui minimisent une énergie adéquate (non convexe). Pour les deux modèles, on démontre l'existence de configurations minimales et l'équivalence avec d'autres formulations existantes dans la littèrature. En ce qui concerne le cas du transport congestionné, nous passons en revue deux modèles déjà existants, afin de prouver leur équivalence: alors que le premier de ces modèles peut être considéré comme une approche Lagrangienne du problème et il a des liens intéressants avec des questions d'équilibre pour la circulation urbaine, le second est un problème d'optimisation convexe avec contraintes de divergence par La preuve de l'équivalence entre les deux modèles constitue le corps principal de la deuxième partie de cette thèse et contient différents éléments d'intérêt, y compris: la théorie des flots des champs de vecteurs peu réguliers (DiPerna-Lions), la construction de Dacorogna et Moser pour les applications de transport et en particulier les résultats de régularité (que nous prouvons ici) pour une équation elliptique très dégénérés, qui ne semble pas avoir été beaucoup étudiéeThis thesis is devoted to to the study of optimal transport problems, alternative to the so called Monge-Kantorovich one: they naturally arise in some real world applications, like in the design of optimal transportation networks or in urban traffic modeling. More precisely, we consider problems where the transport cost has a nonlinear dependence on the mass: typically in this type of problems, to move a mass m for a distance ℓ costs φ (m) ℓ, where φ is a given function, thus giving rise to a total cost of the type Σ φ (m) ℓ. Two interesting cases are widely addressed in this work: the case where φ is subadditive (branched transport), so that masses have the interest to travel together in order to lower the total cost; the case of φ being superadditive (congested transport), where on the contrary the mass tends to be as widespread as possible. In the case of branched transport, we introduce two new dynamical models: in the first one, the transport is described through the employ of curves of probabilty measures minimizing a length-type functional (with a weight function penalizing non atomic measures). On the other hand, the secon model is much more in the spirit of the celebrated Benamou-Brenier formulation for Wasserstein distances: in particular, the transport is described by means of pairs ``curve of measures--velocity vector field'', satisfying the continuity equation and minimizing a suitable dynamical energy (which is a non convex one, actually). For both models we prove existence of minimal configurations and equivalence with other modelizations existing in literature. Concerning the case of congested transport, we review in great details two already existing models, proving their equivalence: while the first one can be viewed as a Lagrangian approach to the problem and it has some interesting links with traffic equilibrium issues, the second one is a divergence-constrained convex optimization problem. The proof of this equivalence represents the central core of the second part of the work and contains various points of interest: among them, the DiPerna-Lions theory of flows of weakly differentiable vector fields, the Dacorogna-Moser construction for transport maps and, above all, some regularity estimates (that we derive here) for a very degenerate elliptic equation, that seems to be quite unexplored
Questa tesi è dedicata allo studio di problemi di trasporto ottimo, alternativi al cosiddetto problema di Monge-Kantorovich: essi appaiono in modo naturale in alcune applicazioni concrete, come nel disegno di reti ottimali di trasporto o nella modellizzazione di problemi di traffico urbano. In particolare, si considerano problemi in cui il costo di trasporto ha una dipendenza non lineare dalla massa: tipicamente in questo tipo di problemi, muovere una massa m per un tratto di lunghezza ℓ costa φ (m) ℓ, dove φ è una funzione assegnata, dando perciò luogo ad un costo totale del tipo Σ φ (m) ℓ. Due casi significativi vengono ampiamente trattati in questo lavoro: il caso in cui la funzione φ è subadditiva (trasporto ramificato), ragion per cui le masse hanno maggiore interesse a viaggiare insieme, in modo da diminuire il costo totale; il caso in cui φ è superadditiva (trasporto congestionato), dove al contrario la massa tende a diffondersi quanto più possibile. Nel caso del trasporto ramificato, si introducono due nuovi modelli dinamici: nel primo il trasporto è descritto da curve di misure di probabilità che minimizzano un funzionale di tipo geodetico (con un coefficiente penalizzante le misure non atomiche). Il secondo invece è maggiormente nello spirito della formulazione data da Benamou e Brenier per le distanze di Wasserstein: in particolare, il trasporto è descritto per mezzo di coppie ``curva di misure--campo di velocità'', legate dall'equazione di continuità, che minimizzano un'opportuna energia (non convessa). Per entrambi i modelli, si mostra l'esistenza di configurazioni minimali e si prova l'equivalenza con altre formulazioni esistenti in letteratura. Per quanto riguarda il caso del trasporto congestionato, si rivedono in dettaglio due modelli già esistenti, provandone l'equivalenza: mentre il primo di questi modelli può essere visto come un approccio Lagrangiano al problema ed ha interessanti legami con questioni di equilibrio per il traffico urbano, il secondo è un problema di ottimizzazione convessa con vincolo di divergenza. La dimostrazione dell'equivalenza tra i due modelli costituisce il corpo centrale della seconda parte del lavoro e contiene vari elementi di interesse, tra questi: la teoria dei flussi di campi vettoriali poco regolari di DiPerna e Lions, la costruzione di Dacorogna e Moser per mappe di trasporto e soprattutto dei risultati di regolarità (che quivi ricaviamo) per un'equazione ellittica molto degenere, che non sembra essere stata molto studiata
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Brasco, Lorenzo. "Geodesics and PDE methods in transport models." Phd thesis, Université Paris Dauphine - Paris IX, 2010. http://tel.archives-ouvertes.fr/tel-00578447.
Full textAbstract:
Cette thèse est dédiée à l'étude des problèmes de transport optimal, alternatifs au problème de Monge-Kantorovich : ils apparaissent naturellement dans des applications pratiques, telles que la conception des réseaux de transport optimal ou la modélisation des problèmes de circulation urbaine. En particulier, nous considérons des problèmes où le coût du transport a une dèpendance non linèaire de la masse : typiquement dans ce type de problèmes, le côut pour déplacer une masse $m$ pour une longueur $\ell$ est $\varphi(m)\, \ell$, où $\varphi$ est une fonction assignée, obtenant ainsi un coût total de type $\sum\varphi(m) \ell$. \par Deux cas importants sont abordés en détail dans ce travail : le cas où la fonction $\varphi$ est subadditive (transport branché), de sorte que la masse a intérêt à voyager ensemble, de manière à réduire le coût total; le cas où $\varphi$ est superadditive (transport congestionné), où au contraire, la masse tend à diffuser autant que possible. \par Dans le cas du transport branché, nous introduisons deux nouveaux modèles: dans le premièr, le transport est décrit par des courbes de mesures de probabilité que minimisent une fonctionnelle de type géodésique (avec un coefficient que pénalise le mesures qui ne sont pas atomiques). Le second est plus dans l'esprit de la formulation de Benamou et Brenier pour les distances de Wasserstein : en particulier, le transport est décrit par paires de ``courbe de mesures--champ de vitesse'', liées par l'équation de continuité, qui minimisent une énergie adéquate (non convexe). Pour les deux modèles, on démontre l'existence de configurations minimales et l'équivalence avec d'autres formulations existantes dans la littèrature. \par En ce qui concerne le cas du transport congestionné, nous passons en revue deux modèles déjà existants, afin de prouver leur équivalence: alors que le premier de ces modèles peut être considéré comme une approche Lagrangienne du problème et il a des liens intéressants avec des questions d'équilibre pour la circulation urbaine, le second est un problème d'optimisation convexe avec contraintes de divergence. \par La preuve de l'équivalence entre les deux modèles constitue le corps principal de la deuxième partie de cette thèse et contient différents éléments d'intérêt, y compris: la théorie des flots des champs de vecteurs peu réguliers (DiPerna-Lions), la construction de Dacorogna et Moser pour les applications de transport et en particulier les résultats de régularité (que nous prouvons ici) pour une équation elliptique très dégénérés, qui ne semble pas avoir été beaucoup étudiée.
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Ugail, Hassan. "Time-dependent shape parameterisation of complex geometry using PDE surfaces." Nashboro Press, 2004. http://hdl.handle.net/10454/2686.
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Strzodka, Robert. "Hardware efficient PDE solvers in quantized image processing." [S.l.] : [s.n.], 2004. http://deposit.ddb.de/cgi-bin/dokserv?idn=974954594.
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Nordén, Markus. "Multithreaded PDE Solvers on Non-Uniform Memory Architectures." Doctoral thesis, Uppsala universitet, Avdelningen för teknisk databehandling, 2006. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-7149.
Full textAbstract:
A trend in parallel computer architecture is that systems with a large shared memory are becoming more and more popular. A shared memory system can be either a uniform memory architecture (UMA) or a cache coherent non-uniform memory architecture (cc-NUMA). In the present thesis, the performance of parallel PDE solvers on cc-NUMA computers is studied. In particular, we consider the shared namespace programming model, represented by OpenMP. Since the main memory is physically, or geographically distributed over several multi-processor nodes, the latency for local memory accesses is smaller than for remote accesses. Therefore, the geographical locality of the data becomes important. The focus of the present thesis is to study multithreaded PDE solvers on cc-NUMA systems, in particular their memory access pattern with respect to geographical locality. The questions posed are: (1) How large is the influence on performance of the non-uniformity of the memory system? (2) How should a program be written in order to reduce this influence? (3) Is it possible to introduce optimizations in the computer system for this purpose? The main conclusion is that geographical locality is important for performance on cc-NUMA systems. This is shown experimentally for a broad range of PDE solvers as well as theoretically using a model involving characteristics of computer systems and applications. Geographical locality can be achieved through migration directives that are inserted by the programmer or — possibly in the future — automatically by the compiler. On some systems, it can also be accomplished by means of transparent, hardware initiated migration and replication. However, a necessary condition that must be fulfilled if migration is to be effective is that the memory access pattern must not be "speckled", i.e. as few threads as possible shall make accesses to each memory page. We also conclude that OpenMP is competitive with MPI on cc-NUMA systems if care is taken to get a favourable data distribution.
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Calatroni, Luca. "New PDE models for imaging problems and applications." Thesis, University of Cambridge, 2016. https://www.repository.cam.ac.uk/handle/1810/256139.
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Variational methods and Partial Differential Equations (PDEs) have been extensively employed for the mathematical formulation of a myriad of problems describing physical phenomena such as heat propagation, thermodynamic transformations and many more. In imaging, PDEs following variational principles are often considered. In their general form these models combine a regularisation and a data fitting term, balancing one against the other appropriately. Total variation (TV) regularisation is often used due to its edgepreserving and smoothing properties. In this thesis, we focus on the design of TV-based models for several different applications. We start considering PDE models encoding higher-order derivatives to overcome wellknown TV reconstruction drawbacks. Due to their high differential order and nonlinear nature, the computation of the numerical solution of these equations is often challenging. In this thesis, we propose directional splitting techniques and use Newton-type methods that despite these numerical hurdles render reliable and efficient computational schemes. Next, we discuss the problem of choosing the appropriate data fitting term in the case when multiple noise statistics in the data are present due, for instance, to different acquisition and transmission problems. We propose a novel variational model which encodes appropriately and consistently the different noise distributions in this case. Balancing the effect of the regularisation against the data fitting is also crucial. For this sake, we consider a learning approach which estimates the optimal ratio between the two by using training sets of examples via bilevel optimisation. Numerically, we use a combination of SemiSmooth (SSN) and quasi-Newton methods to solve the problem efficiently. Finally, we consider TV-based models in the framework of graphs for image segmentation problems. Here, spectral properties combined with matrix completion techniques are needed to overcome the computational limitations due to the large amount of image data. Further, a semi-supervised technique for the measurement of the segmented region by means of the Hough transform is proposed.
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Nordén, Markus. "Multithreaded PDE solvers on non-uniform memory architectures /." Uppsala : Acta Universitatis Upsaliensis, 2006. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-7149.
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Johansson, Henrik. "Performance characterization and evaluation of parallel PDE solvers." Licentiate thesis, Uppsala : Department of Information Technology, Uppsala University, 2006. http://www.it.uu.se/research/publications/lic/2006-010/2006-010.pdf.
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Sajadini, Sadna. "Essays in Finance Related Problems with PDE Approach." Doctoral thesis, KTH, Matematik (Avd.), 2013. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-134786.
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This thesis is comprised of three scientific articles, all in PDE problems related to finance. The first two papers address problems concerning bonds and the third one treat s asymmetry problem in the mean field game theory. We investigate the free boundary for the problem of valuation of American type convertible bond with extra call feature, in paper one. In this case the free boundary behaviour is of interest since it shows the optimal conversion strategy. We study the regularity of the free boundary and also the solution to the pricing of this special financial derivative. The touching point of the free boundary and fixed boundary is discussed, as well. The second paper is devoted to the study of bonds with call feature and conversion. Further, it is shown that the price of a Bermudan type bond tends to that of an American one on condition that the conversion time goes to the whole life-span of the bond. Our main goal in the third paper is to investigate a symmetry case regarding the stationary problem in mean field game of Lasry-Lions. Starting with a priori unknown ring-'shaped region, taking the boundaries as level sets and admitting harmonic solutions, it is implied that the region has spherical symmetry. Moreover, therein we attempt to state the model to an higher dimensional case.QC 20131129
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Brandvik, Tobias. "The implementation of PDE solvers on parallel processors." Thesis, University of Cambridge, 2012. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.609958.
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Eswaran, Akilesh. "Wavelet based PDE valuation of swaps and swaptions." Thesis, University of Cambridge, 2002. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.620182.
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Pearson, John W. "Fast iterative solvers for PDE-constrained optimization problems." Thesis, University of Oxford, 2013. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.581405.
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In this thesis, we develop preconditioned iterative methods for the solution of matrix systems arising from PDE-constrained optimization problems. In order to do this, we exploit saddle point theory, as this is the form of the matrix systems we wish to solve. We utilize well-known results on saddle point systems to motivate preconditioners based on effective approximations of the (1,1)-block and Schur complement of the matrices involved. These preconditioners are used in conjunction with suitable iterative solvers, which include MINRES, non-standard Conjugate Gradients, GMRES and BiCG. The solvers we use are selected based on the particular problem and preconditioning strategy employed. We consider the numerical solution of a range of PDE-constrained optimization problems, namely the distributed control, Neumann boundary control and subdomain control of Poisson's equation, convection-diffusion control, Stokes and Navier-Stokes control, the optimal control of the heat equation, and the optimal control of reaction-diffusion problems arising in chemical processes. Each of these problems has a special structure which we make use of when developing our preconditioners, and specific techniques and approximations are required for each problem. In each case, we motivate and derive our preconditioners, obtain eigenvalue bounds for the preconditioners where relevant, and demonstrate the effectiveness of our strategies through numerical experiments. The goal throughout this work is for our iterative solvers to be feasible and reliable, but also robust with respect to the parameters involved in the problems we consider.
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Lee, Hock Seng. "An ODE/MOL PDE Template For Soil Physics." Thesis, Griffith University, 2003. http://hdl.handle.net/10072/365588.
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The aim of the thesis is to find a method, in conjunction with the ordinary differential equation (ODE) based method of lines (MOL) solution of Richards’ equation, to model the steep wetting front infiltration in very dry soils, accurately and efficiently. Due to the steep pressure head or steep water volumetric content gradients, highly nonlinear soil hydraulic properties and the rapid movement of the wetting front, accurate solutions for infiltration into a dry soil are usually difficult to obtain. Additionally, such problems often require very small time steps and large computation times. As an enhancement to the used ODE/MOL approach, Higher Order Finite Differencing, Varying Order Finite Differencing, Vertical Scaling, Adaptive Schemes and Non-uniform Stretching Techniques have been implemented and tested in this thesis. Success has been found in the ability of Vertical Scaling to simulate very steep moving front solution for the Burgers’ equation. Unfortunately, the results also show that Vertical Scaling needs significant research and improvement before their full potential in routine applications for difficult nonlinear problems, such as Richard’s equation with very steep moving front solution, can be realized. However, we have also shown that the use of the composed form of RE and a 2nd order finite differencing for the first order derivative approximation is conducive for modelling steep moving front problem in a very dry soil. Additionally, with the combination of an optimal influx value at the edges of the inlet, the ODE/MOL approach is able to model a 2-D infiltration in very dry soils, effectively and accurately. Furthermore, one of the strengths of this thesis is the use of a MATLAB PDE template. Implementing the ODE/MOL approach via a MATLAB PDE template has shown to be most suitable for modelling of partial differential equations. The plug and play mode of modifying the PDE template for solving time-dependent partial differential equations is user-friendly and easy, as compared to more conventional approaches using Pascal, Fortran, C or C++. The template offers greater modularity, flexibility, versatility, and efficiency for solving PDE problems in both 1-D and 2-D spatial dimensions. Moreover, the 2-D PDE template has been extended for irregular shaped domains.Thesis (PhD Doctorate)
Doctor of Philosophy (PhD)
Australian School of Environmental Studies
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GOMES, Fabiana Oliveira dos Santos. "Avaliação dos efeitos do inibidor de fosfodiesterase-5 (Sildenafil) em um modelo de prostatite experimental." Universidade Federal de Pernambuco, 2015. https://repositorio.ufpe.br/handle/123456789/17363.
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FACEPE
O Sildenafil é um inibidor potente e seletivo da fosfodiesterase-5 (PDE5). Este fármaco foi aprovado para uso terapêutico na disfunção erétil e, atualmente, vem sendo usado também no tratamento da hipertensão pulmonar. Embora mantenha um excelente nível de segurança e perfil de tolerabilidade, poucos estudos avaliaram os possíveis efeitos colaterais do tratamento crônico com Sildenafil sobre o sistema reprodutor masculino, especialmente na próstata visando o relaxamento da uretra e alívio dos Sintomas do Trato Urinário Inferior (STUI). Desta forma, avaliamos o efeito do tratamento, em camundongos C57Bl/6, através de análise morfológica, ultraestrutural e expressão molecular de guanilato ciclase solúvel-sGC, Óxido nítrico sintase endotelial-eNOS, Antígeno prostático específico-PSA e Fator de crescimento transformador beta-TGF- no tecido prostático. Foi-se observado que o tratamento com Sildenafil não induz danos evidentes na próstata. Além disso, tem sido demonstrado que Sildenafil tem eficácia terapêutica em doenças inflamatórias crônicas, podendo apresentar uma eficácia terapêutica potencial em diferentes doenças. Entre elas, uma atenção especial tem sido dada para as patologias relacionadas ao trato urogenital masculino, como a Hiperplasia Prostática Benigna (HPB), Câncer de próstata e Prostatites. A inflamação tem sido considerada como um fator etiológio da HPB e STUI. Assim, foi proposto um modelo de lesão prostática com injeção intrauretral de LPS (1mg/ml), em camundongos machos Swiss e C57Bl/6, desenvolvido durante 3, 7, 10 e 14 dias. A análise dos resultados mostrou que a indução intrauretral com lipopolisacarideo-LPS atua como importante agente da HPB, além de promover o aumento de fatores de crescimento (FGF-7 e FGF- β), α-actina e citocinas pró-inflamatórias (IL-1, IL-6, IL-17), tanto no estroma como no epitélio. Uma vez que o Sildenafil tem potencial anti-inflamatório, este estudo se propôs a analisar a ação do Sildenafil em um modelo de lesão prostática experimental, induzido por injeção intrauretral de LPS em camundongos C57BL/6. O tratamento com Sildenafil (25mg/kg) dos animais com prostatite apresentaram redução significativa de -actina, COX-2, NFK- B, IL-6, IL-17 e FGF-7. Por não induzir danos na próstata , o Sildenafil, por não induzir a longo prazo danos evidentes na próstata pode representar uma estratégia farmacológica para o tratamento de doenças inflamatórias crônicas do trato urogenital.
Sildenafil is a potent and selective inhibitor of phosphodiesterase-5 (PDE5). This drug has been approved for therapeutic use in erectile dysfunction and currently has been also used to treat pulmonary hypertension. While maintaining an excellent level of safety and tolerability profile, few studies have evaluated the possible side effects of chronic treatment with Sildenafil on the male reproductive system, especially in prostate aimed at relaxing the urethra and relief of symptoms of Lower Urinary Tract (LUTS). Therefore, we assessed the treatment effect in C57Bl/6 mice, using morphological analysis, ultrastructural and molecular expression of soluble guanylate cyclase-sGC, endothelial nitric oxide synthase, eNOS, prostate-specific antigen PSA and transforming growth factor beta TGF- in prostate tissue. It is observed that the treatment with sildenafil does not induce apparent damage to the prostate. Furthermore, Sildenafil has been shown to have therapeutic efficacy in chronic inflammatory diseases, which have a potential therapeutic efficacy in various diseases. Among them, special attention has been given to the pathologies related to the male urogenital tract, such as Benign Prostatic Hyperplasia (BPH), prostate cancer and Prostatitis. Inflammation has been considered as a factor etiológio of BPH and LUTS. Thus, it has been proposed a prostatic intraurethral injection injury model of LPS (1mg/ml) in male Swiss mice and C57Bl /6 developed for 3, 7, 10 and 14 days. The results showed that the intraurethral induction with lipopolysaccharide-LPS acts as an important agent of HPB, and to promote the increase of growth factors (FGF-7 and FGF- ), -actin and proinflammatory cytokines (IL- 1, IL-6, IL-17), both in the stroma and the epithelium. Since Sildenafil has potential anti-inflammatory, this study aimed to analyze the action of Sildenafil in an experimental prostate injury model induced by intraurethral injection of LPS in C57Bl/6 mice. Treatment with sildenafil (25 mg/kg) of animals with prostatitis showed a significant reduction of -actin, COX-2 NFK-kB, IL-6, IL-17 and FGF-7. By not induce damage to the prostate, Sildenafil, not to induce long term damage evident in the prostate may represent a pharmacologic strategy for the treatment of chronic inflammatory diseases of the urogenital tract.
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Arnarson, Teitur. "PDE methods for free boundary problems in financial mathematics." Doctoral thesis, KTH, Matematik (Inst.), 2008. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-4777.
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We consider different aspects of free boundary problems that have financial applications. Papers I–III deal with American option pricing, in which case the boundary is called the early exercise boundary and separates the region where to hold the option from the region where to exercise it. In Papers I–II we obtain boundary regularity results by local analysis of the PDEs involved and in Paper III we perform local analysis of the corresponding stochastic representation. The last paper is different in its character as we are dealing with an optimal switching problem, where a switching of state occurs when the underlying process crosses a free boundary. Here we obtain existence and regularity results of the viscosity solutions to the involved system of variational inequalities.QC 20100630
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Löf, Henrik. "Iterative and Adaptive PDE Solvers for Shared Memory Architectures." Doctoral thesis, Uppsala universitet, Avdelningen för teknisk databehandling, 2006. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-7136.
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Scientific computing is used frequently in an increasing number of disciplines to accelerate scientific discovery. Many such computing problems involve the numerical solution of partial differential equations (PDE). In this thesis we explore and develop methodology for high-performance implementations of PDE solvers for shared-memory multiprocessor architectures. We consider three realistic PDE settings: solution of the Maxwell equations in 3D using an unstructured grid and the method of conjugate gradients, solution of the Poisson equation in 3D using a geometric multigrid method, and solution of an advection equation in 2D using structured adaptive mesh refinement. We apply software optimization techniques to increase both parallel efficiency and the degree of data locality. In our evaluation we use several different shared-memory architectures ranging from symmetric multiprocessors and distributed shared-memory architectures to chip-multiprocessors. For distributed shared-memory systems we explore methods of data distribution to increase the amount of geographical locality. We evaluate automatic and transparent page migration based on runtime sampling, user-initiated page migration using a directive with an affinity-on-next-touch semantic, and algorithmic optimizations for page-placement policies. Our results show that page migration increases the amount of geographical locality and that the parallel overhead related to page migration can be amortized over the iterations needed to reach convergence. This is especially true for the affinity-on-next-touch methodology whereby page migration can be initiated at an early stage in the algorithms. We also develop and explore methodology for other forms of data locality and conclude that the effect on performance is significant and that this effect will increase for future shared-memory architectures. Our overall conclusion is that, if the involved locality issues are addressed, the shared-memory programming model provides an efficient and productive environment for solving many important PDE problems.
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Rehurek, Adam. "Stable Numerical Methods for PDE Models of Asian Options." Thesis, Högskolan i Halmstad, Tillämpad matematik och fysik (MPE-lab), 2011. http://urn.kb.se/resolve?urn=urn:nbn:se:hh:diva-16367.
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Asian options are exotic financial derivative products which price must be calculated by numerical evaluation. In this thesis, we study certain ways of solving partial differential equations, which are associated with these derivatives. Since standard numerical techniques for Asian options are often incorrect and impractical, we discuss their variations, which are efficiently applicable for handling frequent numerical instabilities reflected in form of oscillatory solutions. We will show that this crucial problem can be treated and eliminated by adopting flux limiting techniques, which are total variation dimishing.
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Ljungberg, Malin. "Handling of curvilinear coordinates in a PDE solver framework." Licentiate thesis, Uppsala universitet, Avdelningen för teknisk databehandling, 2003. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-86138.
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By the use of object-oriented analysis and design combined with variability modeling a highly flexible software model for the metrics handling functionality of a PDE solver framework was obtained. This new model was evaluated in terms of usability, particularly with respect to efficiency and flexibility. The efficiency of a pilot implementation is similar to, or even higher than that of a pre-existing application-specific reference code. With regards to flexibility it is shown that the new software model performs well for a set of four change scenarios selected by an expert user group.
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Löf, Henrik. "Iterative and adaptive PDE solvers for shared memory architectures /." Uppsala : Acta Universitatis Upsaliensis, 2006. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-7136.
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Bentley, P. W. "Regularity and inverse SDE representations of some stochastic PDE." Thesis, University of Warwick, 1999. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.343150.
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Qian, Elizabeth Yi. "A certified reduced basis approach to PDE-constrained optimization." Thesis, Massachusetts Institute of Technology, 2017. http://hdl.handle.net/1721.1/108932.
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Thesis: S.M. in Aerospace Engineering, Massachusetts Institute of Technology, Department of Aeronautics and Astronautics, 2017.Cataloged from PDF version of thesis.
Includes bibliographical references (pages 65-67).
Parameter optimization problems constrained by partial differential equations (PDEs) appear in many science and engineering applications. The PDE usually describes the underlying system or component behavior, while the parameters identify a particular configurations of the component, such as boundary and initial conditions, material properties, and geometry. Solving these optimization problems may require a prohibitively large number of computationally expensive PDE solves, particularly if the parameter dimension is high. It is therefore advantageous to replace expensive high-dimensional PDE solvers (e.g., finite element) with lower-dimension surrogate models. This work builds on the reduced basis (RB) method, a model reduction method that allows efficient and reliable reduced order approximations for a large class of parametrized PDEs. Traditionally, RB models are generated during a computationally expensive offline phase for a certain admissible parameter space. The optimization problem can then be solved efficiently during the online phase. However, since the RB model is only evaluated along the optimization trajectory, building an RB model for the entire admissible parameter set incurs superfluous offline costs. In this thesis, we break from the traditional RB offline/online decomposition and use a trust region framework to adaptiviely build the RB model along the optimization trajectory only. Novel a posteriori error bounds on the RB cost and cost gradient for quadratic cost functionals (e.g., least squares) are presented, and used to guarantee convergence to the optimum of the high-fidelity model. The proposed certified RB trust region approach uses high-fidelity solves to update the RB model only if the approximation is no longer sufficiently accurate, reducing the number of full-fidelity solves required. We consider problems governed by elliptic and parabolic PDEs and present numerical results for a thermal fin model problem in which we are able to reduce the number of full solves necessary for the optimization by up to 86%.
by Elizabeth Yi Qian.
S.M. in Aerospace Engineering
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Banholzer, Stefan [Verfasser]. "ROM-Based Multiobjective Optimization with PDE Constraints / Stefan Banholzer." Konstanz : KOPS Universität Konstanz, 2021. http://nbn-resolving.de/urn:nbn:de:bsz:352-2-1g98y1ic7inp29.
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McDonald, Eleanor. "All-at-once solution of time-dependent PDE problems." Thesis, University of Oxford, 2016. https://ora.ox.ac.uk/objects/uuid:60f2985b-6071-47ae-97a9-7813db0194ae.
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In this thesis, we examine the solution to a range of time-dependent Partial Differential Equation (PDE) problems. Throughout, we focus on the development of preconditioners for the all-at-once system, which solves for all time-steps in a single coupled computation. The preconditioners developed are used with existing iterative methods and, due to their specific block structure, could be applied in parallel over time. We first develop solvers for the heat equation and the transient convection-diffusion equation. For both of these forward problems, the all-at-once system is non-symmetric. Despite this, in certain cases, we are able to provide rigorous termination bounds for non-symmetric iterative methods, contrary to what is generally possible for non-symmetric systems. The ideas developed for evolutionary PDEs are extended to develop preconditioners for time-dependent optimal control problems. By incorporating the methods designed for the forward problem, we are able to develop block diagonal Schur complement based preconditioners, which also could be implemented in parallel over time. We provide extensive eigenvalue analysis for each preconditioner and demonstrate their effectiveness through numerical computations for a variety of problems. We are able to describe solvers that are robust to various parameters, including the mesh size and number of time-steps.
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Moldenhauer, Marian [Verfasser]. "Adaptive Algorithms in Optimization under PDE Constraints / Marian Moldenhauer." Berlin : Freie Universität Berlin, 2021. http://d-nb.info/1236573064/34.
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Funke, Simon. "The automation of PDE-constrained optimisation and its applications." Thesis, Imperial College London, 2013. http://hdl.handle.net/10044/1/11079.
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This thesis is concerned with the automation of solving optimisation problems constrained by partial differential equations (PDEs). Gradient-based optimisation algorithms are the key to solve optimisation problems of practical interest. The required derivatives can be efficiently computed with the adjoint approach. However, current methods for the development of adjoint models often require a significant amount of effort and expertise, in particular for non-linear time-dependent problems. This work presents a new high-level reinterpretation of algorithmic differentiation to develop adjoint models. This reinterpretation considers the discrete system as a sequence of equation solves. Applying this approach to a general finite-element framework results in an automatic and robust way of deriving and solving adjoint models. This drastically reduces the development effort compared to traditional methods. Based on this result, a new framework for rapidly defining and solving optimisation problems constrained by PDEs is developed. The user specifies the discrete optimisation problem in a compact high-level language that resembles the mathematical structure of the underlying system. All remaining steps, including parameter updates, PDE solves and derivative computations, are performed without user intervention. The framework can be applied to a wide range of governing PDEs, and interfaces to various gradient-free and gradient-based optimisation algorithms. The capabilities of this framework are demonstrated through the application to two PDE-constrained optimisation problems. The first is concerned with the optimal layout of turbines in tidal stream farms; this optimisation problem is one of the main challenges facing the marine renewable energy industry. The second application applies data assimilation to reconstruct the profile of tsunami waves based on inundation observations. This provides the first step towards the general reconstruction of tsunami signals from satellite information.
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Lyne, O. D. "Probability and analysis for a hyperbolic coupled PDE system." Thesis, University of Bath, 1996. https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.319202.
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