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Numerical Solution of Partial Differential Equations: Theory, Algorithms, and Their Applications

In Honor of Professor Raytcho Lazarov's 40 Years of Research in Computational Methods and Applied Mathematics

  • Conference proceedings
  • © 2013

Overview

Editors:
  1. Oleg P. Iliev

    1. , Dept. of Flow and Material Simulation, Fraunhofer Institute for Industrial Math, Kaiserslautern, Germany

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  2. Svetozar D. Margenov

    1. Institute for Parallel Processing, Bulgarian Academy of Sciences, Sofia, Bulgaria

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  3. Peter D Minev

    1. , Dept. of Mathematical and Statistical Sc, University of Alberta, Edmonton, Canada

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  4. Panayot S. Vassilevski

    1. Center for Applied Scientific Computing, Lawrence Livermore National Laboratory, Livermore, USA

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  5. Ludmil T Zikatanov

    1. , Department of Mathematics, Pennsylvania State University, University Park, USA

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  • Provides a broad spectrum of numerical techniques and real life applications of these techniques
  • All fundamentally important aspects of numerical modeling of physical phenomena described by partial differential equations are covered
  • Additionally, some state-of-the-art numerical multiscale discretization and solution techniques are presented ?
  • Includes supplementary material: sn.pub/extras

Part of the book series: Springer Proceedings in Mathematics & Statistics (PROMS, volume 45)

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Table of contents (15 papers)

  1. Front Matter

    Pages i-xii
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  2. Improving Conservation for First-Order System Least-Squares Finite-Element Methods

    • J. H. Adler, P. S. Vassilevski
    Pages 1-19

  3. Multiscale Coarsening for Linear Elasticity by Energy Minimization

    • Marco Buck, Oleg Iliev, Heiko Andrä
    Pages 21-44

  4. Preconditioners for Some Matrices of Two-by-Two Block Form, with Applications, I

    • Owe Axelsson
    Pages 45-67

  5. A Multigrid Algorithm for an Elliptic Problem with a Perturbed Boundary Condition

    • Andrea Bonito, Joseph E. Pasciak
    Pages 69-79

  6. Parallel Unsmoothed Aggregation Algebraic Multigrid Algorithms on GPUs

    • James Brannick, Yao Chen, Xiaozhe Hu, Ludmil Zikatanov
    Pages 81-102

  7. Aspects of Guaranteed Error Control in CPDEs

    • C. Carstensen, C. Merdon, J. Neumann
    Pages 103-119

  8. A Finite Volume Element Method for a Nonlinear Parabolic Problem

    • P. Chatzipantelidis, V. Ginting
    Pages 121-136

  9. Multidimensional Sensitivity Analysis of Large-Scale Mathematical Models

    • Ivan Dimov, Rayna Georgieva
    Pages 137-156

  10. Structures and Waves in a Nonlinear Heat-Conducting Medium

    • Stefka Dimova, Milena Dimova, Daniela Vasileva
    Pages 157-184

  11. Efficient Parallel Algorithms for Unsteady Incompressible Flows

    • Jean-Luc Guermond, Peter D. Minev
    Pages 185-201

  12. Efficient Solvers for Some Classes of Time-Periodic Eddy Current Optimal Control Problems

    • Michael Kolmbauer, Ulrich Langer
    Pages 203-216

  13. Robust Algebraic Multilevel Preconditioners for Anisotropic Problems

    • J. Kraus, M. Lymbery, S. Margenov
    Pages 217-245

  14. A Weak Galerkin Mixed Finite Element Method for Biharmonic Equations

    • Lin Mu, Junping Wang, Yanqiu Wang, Xiu Ye
    Pages 247-277

  15. Domain Decomposition Scheme for First-Order Evolution Equations with Nonselfadjoint Operators

    • Petr Vabishchevich, Petr Zakharov
    Pages 279-302

  16. Spectral Coarse Spaces in Robust Two-Level Schwarz Methods

    • J. Willems
    Pages 303-326

  17. Back Matter

    Pages 327-327
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Keywords

About this book

One of the current main challenges in the area of scientific computing​ is the design and implementation of accurate numerical models for complex physical systems which are described by time dependent coupled systems of nonlinear PDEs. This volume integrates the works of experts in computational mathematics and its applications, with a focus on modern algorithms which are at the heart of accurate modeling: adaptive finite element methods, conservative finite difference methods and finite volume methods, and multilevel solution techniques. Fundamental theoretical results are revisited in survey articles and new techniques in numerical analysis are introduced. Applications showcasing the efficiency, reliability and robustness of the algorithms in porous media, structural mechanics and electromagnetism are presented. 

 

Researchers and graduate students in  numerical analysis and numerical solutions of PDEs and their scientific computing applications will find this book useful. 

Editors and Affiliations

  • , Dept. of Flow and Material Simulation, Fraunhofer Institute for Industrial Math, Kaiserslautern, Germany

    Oleg P. Iliev

  • Institute for Parallel Processing, Bulgarian Academy of Sciences, Sofia, Bulgaria

    Svetozar D. Margenov

  • , Dept. of Mathematical and Statistical Sc, University of Alberta, Edmonton, Canada

    Peter D Minev

  • Center for Applied Scientific Computing, Lawrence Livermore National Laboratory, Livermore, USA

    Panayot S. Vassilevski

  • , Department of Mathematics, Pennsylvania State University, University Park, USA

    Ludmil T Zikatanov

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