Numerical Solution of Partial Differential Equations: Theory, Algorithms, and Their Applications, 1st Edition

  • Published By:
  • ISBN-10: 1461471729
  • ISBN-13: 9781461471721
  • DDC: 515.353
  • Grade Level Range: College Freshman - College Senior
  • 327 Pages | eBook
  • Original Copyright 2013 | Published/Released June 2014
  • This publication's content originally published in print form: 2013

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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. 

Table of Contents

Front Cover.
Other Frontmatter.
Other Frontmatter.
Title Page.
Copyright Page.
1: Improving Conservation for First-Order System Least-Squares Finite-Element Methods.
2: Multiscale Coarsening for Linear Elasticity by Energy Minimization.
3: Preconditioners for Some Matrices of Two-by-Two Block Form, with Applications, I.
4: A Multigrid Algorithm for an Elliptic Problem with a Perturbed Boundary Condition.
5: Parallel Unsmoothed Aggregation Algebraic Multigrid Algorithms on GPUs.
6: Aspects of Guaranteed Error Control in CPDEs.
7: A Finite Volume Element Method for a Nonlinear Parabolic Problem.
8: Multidimensional Sensitivity Analysis of Large-Scale Mathematical Models.
9: Structures and Waves in a Nonlinear Heat-Conducting Medium.
10: Efficient Parallel Algorithms for Unsteady Incompressible Flows.
11: Efficient Solvers for Some Classes of Time-Periodic Eddy Current Optimal Control Problems.
12: Robust Algebraic Multilevel Preconditioners for Anisotropic Problems.
13: A Weak Galerkin Mixed Finite Element Method for Biharmonic Equations.
14: Domain Decomposition Scheme for First-Order Evolution Equations with Nonselfadjoint Operators.
15: Spectral Coarse Spaces in Robust Two-Level Schwarz Methods.
About the Editors.