Advanced Topics in Computational Partial Differential Equations: Numerical Methods and Diffpack Programming

Description

The book is suitable for readers with a background in basic finite element and finite difference methods for partial differential equations who wants gentle introductions to advanced topics like parallel computing, multigrid methods, and special methods for systems of PDEs. The goal of all chapters is to *compute* solutions to problems, hence algorithmic and software issues play a central role. All software examples use the Diffpack programming environment, so to take advantage of these examples some experience with Diffpack is required. There are also some chapters covering complete applications, i.e., the way from a model, expressed as systems of PDEs, through discretization methods, algorithms, software design, verification, and computational examples. Cover Lecture Notes in Computational Science and Engineering 33 Advanced Topics in Computational Partial Differential Equations ISBN 9783540014386 Preface Table of Contents 1 Parallel Computing 2 Overlapping Domain Decomposition Methods 3 Software Tools for Multigrid Methods 4 Mixed Finite Elements 5 Systems of PDEs and Block Preconditioning 6 Fully Implicit Methods for Systems of PDEs 7 Stochastic Partial Differential Equations 8 Using Diffpack from Python Scripts 9 Performance Modeling of PDE Solvers 10 Electrical Activity in the Human Heart 11 Mathematical Models of Financial Derivatives 12 Numerical Methods for Financial Derivatives 13 Finite Element Modeling of Elastic Structures 14 Simulation of Aluminum Extrusion 15 Simulation of Sedimentary Basins Editorial Policy General Remarks