Ebook: 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

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.

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.

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.

Content:
Front Matter....Pages i-xii
Improving Conservation for First-Order System Least-Squares Finite-Element Methods....Pages 1-19
Multiscale Coarsening for Linear Elasticity by Energy Minimization....Pages 21-44
Preconditioners for Some Matrices of Two-by-Two Block Form, with Applications, I....Pages 45-67
A Multigrid Algorithm for an Elliptic Problem with a Perturbed Boundary Condition....Pages 69-79
Parallel Unsmoothed Aggregation Algebraic Multigrid Algorithms on GPUs....Pages 81-102
Aspects of Guaranteed Error Control in CPDEs....Pages 103-119
A Finite Volume Element Method for a Nonlinear Parabolic Problem....Pages 121-136
Multidimensional Sensitivity Analysis of Large-Scale Mathematical Models....Pages 137-156
Structures and Waves in a Nonlinear Heat-Conducting Medium....Pages 157-184
Efficient Parallel Algorithms for Unsteady Incompressible Flows....Pages 185-201
Efficient Solvers for Some Classes of Time-Periodic Eddy Current Optimal Control Problems....Pages 203-216
Robust Algebraic Multilevel Preconditioners for Anisotropic Problems....Pages 217-245
A Weak Galerkin Mixed Finite Element Method for Biharmonic Equations....Pages 247-277
Domain Decomposition Scheme for First-Order Evolution Equations with Nonselfadjoint Operators....Pages 279-302
Spectral Coarse Spaces in Robust Two-Level Schwarz Methods....Pages 303-326
Back Matter....Pages 327-327

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.

Content:
Front Matter....Pages i-xii
Improving Conservation for First-Order System Least-Squares Finite-Element Methods....Pages 1-19
Multiscale Coarsening for Linear Elasticity by Energy Minimization....Pages 21-44
Preconditioners for Some Matrices of Two-by-Two Block Form, with Applications, I....Pages 45-67
A Multigrid Algorithm for an Elliptic Problem with a Perturbed Boundary Condition....Pages 69-79
Parallel Unsmoothed Aggregation Algebraic Multigrid Algorithms on GPUs....Pages 81-102
Aspects of Guaranteed Error Control in CPDEs....Pages 103-119
A Finite Volume Element Method for a Nonlinear Parabolic Problem....Pages 121-136
Multidimensional Sensitivity Analysis of Large-Scale Mathematical Models....Pages 137-156
Structures and Waves in a Nonlinear Heat-Conducting Medium....Pages 157-184
Efficient Parallel Algorithms for Unsteady Incompressible Flows....Pages 185-201
Efficient Solvers for Some Classes of Time-Periodic Eddy Current Optimal Control Problems....Pages 203-216
Robust Algebraic Multilevel Preconditioners for Anisotropic Problems....Pages 217-245
A Weak Galerkin Mixed Finite Element Method for Biharmonic Equations....Pages 247-277
Domain Decomposition Scheme for First-Order Evolution Equations with Nonselfadjoint Operators....Pages 279-302
Spectral Coarse Spaces in Robust Two-Level Schwarz Methods....Pages 303-326
Back Matter....Pages 327-327
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