Numerical Analysis and Mathematical Modelling PDF Download

Author: Jan Krzysztof Kowalski
Publisher:
ISBN:
Category : Mathematical models
Languages : en
Pages : 312

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Author: Alexandre Ern
Publisher: Springer Nature
ISBN: 3030563413
Category : Mathematics
Languages : en
Pages : 325

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Book Description
This book is the first volume of a three-part textbook suitable for graduate coursework, professional engineering and academic research. It is also appropriate for graduate flipped classes. Each volume is divided into short chapters. Each chapter can be covered in one teaching unit and includes exercises as well as solutions available from a dedicated website. The salient ideas can be addressed during lecture, with the rest of the content assigned as reading material. To engage the reader, the text combines examples, basic ideas, rigorous proofs, and pointers to the literature to enhance scientific literacy. Volume I is divided into 23 chapters plus two appendices on Banach and Hilbert spaces and on differential calculus. This volume focuses on the fundamental ideas regarding the construction of finite elements and their approximation properties. It addresses the all-purpose Lagrange finite elements, but also vector-valued finite elements that are crucial to approximate the divergence and the curl operators. In addition, it also presents and analyzes quasi-interpolation operators and local commuting projections. The volume starts with four chapters on functional analysis, which are packed with examples and counterexamples to familiarize the reader with the basic facts on Lebesgue integration and weak derivatives. Volume I also reviews important implementation aspects when either developing or using a finite element toolbox, including the orientation of meshes and the enumeration of the degrees of freedom.

Author: Arnaud Ducrot
Publisher: Editions Publibook
ISBN: 2748346319
Category : Differential operators
Languages : en
Pages : 119

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Author: Vinicio C Boffi
Publisher: World Scientific
ISBN: 9814554456
Category :
Languages : en
Pages : 284

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Book Description
Contents: Mathematical Biology and Kinetic Theory Evolution of the Dominance in a Population of Interacting Organisms (N Bellomo & M Lachowicz)Formation of Maxwellian Tails (A V Bobylev)On Long Time Asymptotics of the Vlasov-Poisson-Boltzmann System (J Dolbeault)The Classical Limit of a Self-Consistent Quantum-Vlasov Equation in 3-D (P A Markowich & N J Mauser)Simple Balance Methods for Transport in Stochastic Mixtures (G C Pomraning)Knudsen Layer Analysis by the Semicontinuous Boltzmann Equation (L Preziosi)Remarks on a Self Similar Fluid Dynamic Limit for the Broadwell System (M Slemrod & A E Tzavaras)On Extended Kinetic Theory with Chemical Reaction (C Spiga)Stability and Exponential Convergence in Lp for the Spatially Homogeneous Boltzmann Equation (B Wennberg)and other papers Readership: Applied mathematicians. keywords:Proceedings;Workshop;Rapallo (Italy);Kinetic Theory;Hyperbolic Systems;Nonlinear Kinetic Theory

Author: Bernardo Cockburn
Publisher: Springer Science & Business Media
ISBN: 3642597211
Category : Mathematics
Languages : en
Pages : 468

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Book Description
A class of finite element methods, the Discontinuous Galerkin Methods (DGM), has been under rapid development recently and has found its use very quickly in such diverse applications as aeroacoustics, semi-conductor device simula tion, turbomachinery, turbulent flows, materials processing, MHD and plasma simulations, and image processing. While there has been a lot of interest from mathematicians, physicists and engineers in DGM, only scattered information is available and there has been no prior effort in organizing and publishing the existing volume of knowledge on this subject. In May 24-26, 1999 we organized in Newport (Rhode Island, USA), the first international symposium on DGM with equal emphasis on the theory, numerical implementation, and applications. Eighteen invited speakers, lead ers in the field, and thirty-two contributors presented various aspects and addressed open issues on DGM. In this volume we include forty-nine papers presented in the Symposium as well as a survey paper written by the organiz ers. All papers were peer-reviewed. A summary of these papers is included in the survey paper, which also provides a historical perspective of the evolution of DGM and its relation to other numerical methods. We hope this volume will become a major reference in this topic. It is intended for students and researchers who work in theory and application of numerical solution of convection dominated partial differential equations. The papers were written with the assumption that the reader has some knowledge of classical finite elements and finite volume methods.

Author: Houman Owhadi
Publisher: Cambridge University Press
ISBN: 1108484360
Category : Mathematics
Languages : en
Pages : 491

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Book Description
Presents interplays between numerical approximation and statistical inference as a pathway to simple solutions to fundamental problems.

Author: Thierry Goudon
Publisher: John Wiley & Sons
ISBN: 111937118X
Category : Mathematics
Languages : en
Pages : 478

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Book Description
This book provides the mathematical basis for investigating numerically equations from physics, life sciences or engineering. Tools for analysis and algorithms are confronted to a large set of relevant examples that show the difficulties and the limitations of the most naïve approaches. These examples not only provide the opportunity to put into practice mathematical statements, but modeling issues are also addressed in detail, through the mathematical perspective.

Author: Harbir Antil
Publisher: Springer
ISBN: 1493986368
Category : Mathematics
Languages : en
Pages : 435

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Book Description
This volume provides a broad and uniform introduction of PDE-constrained optimization as well as to document a number of interesting and challenging applications. Many science and engineering applications necessitate the solution of optimization problems constrained by physical laws that are described by systems of partial differential equations (PDEs)​. As a result, PDE-constrained optimization problems arise in a variety of disciplines including geophysics, earth and climate science, material science, chemical and mechanical engineering, medical imaging and physics. This volume is divided into two parts. The first part provides a comprehensive treatment of PDE-constrained optimization including discussions of problems constrained by PDEs with uncertain inputs and problems constrained by variational inequalities. Special emphasis is placed on algorithm development and numerical computation. In addition, a comprehensive treatment of inverse problems arising in the oil and gas industry is provided. The second part of this volume focuses on the application of PDE-constrained optimization, including problems in optimal control, optimal design, and inverse problems, among other topics.

Author: Alain Bensoussan
Publisher: Elsevier
ISBN: 0080931006
Category : Mathematics
Languages : en
Pages : 743

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Book Description
Mathematical finance is a prolific scientific domain in which there exists a particular characteristic of developing both advanced theories and practical techniques simultaneously. Mathematical Modelling and Numerical Methods in Finance addresses the three most important aspects in the field: mathematical models, computational methods, and applications, and provides a solid overview of major new ideas and results in the three domains. - Coverage of all aspects of quantitative finance including models, computational methods and applications - Provides an overview of new ideas and results - Contributors are leaders of the field

Author: Filippo Santambrogio
Publisher: Birkhäuser
ISBN: 3319208284
Category : Mathematics
Languages : en
Pages : 376

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Book Description
This monograph presents a rigorous mathematical introduction to optimal transport as a variational problem, its use in modeling various phenomena, and its connections with partial differential equations. Its main goal is to provide the reader with the techniques necessary to understand the current research in optimal transport and the tools which are most useful for its applications. Full proofs are used to illustrate mathematical concepts and each chapter includes a section that discusses applications of optimal transport to various areas, such as economics, finance, potential games, image processing and fluid dynamics. Several topics are covered that have never been previously in books on this subject, such as the Knothe transport, the properties of functionals on measures, the Dacorogna-Moser flow, the formulation through minimal flows with prescribed divergence formulation, the case of the supremal cost, and the most classical numerical methods. Graduate students and researchers in both pure and applied mathematics interested in the problems and applications of optimal transport will find this to be an invaluable resource.