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

✍ Scribed by X. Cai, E. Acklam, H. P. Langtangen (auth.), Hans Petter Langtangen, Aslak Tveito (eds.)

• Publisher: Springer-Verlag Berlin Heidelberg
• Year: 2003
• Tongue: English
• Leaves: 684
• Series: Lecture Notes in Computational Science and Engineering 33
• Edition: 1
• Category: Library

✦ Synopsis

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.

✦ Table of Contents

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