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

Front Matter....Pages I-XIX
Parallel Computing....Pages 1-55
Overlapping Domain Decomposition Methods....Pages 57-95
Software Tools for Multigrid Methods....Pages 97-151
Mixed Finite Elements....Pages 153-197
Systems of PDEs and Block Preconditioning....Pages 199-236
Fully Implicit Methods for Systems of PDEs....Pages 237-256
Stochastic Partial Differential Equations....Pages 257-320
Using Diffpack from Python Scripts....Pages 321-360
Performance Modeling of PDE Solvers....Pages 361-399
Electrical Activity in the Human Heart....Pages 401-449
Mathematical Models of Financial Derivatives....Pages 451-482
Numerical Methods for Financial Derivatives....Pages 483-506
Finite Element Modeling of Elastic Structures....Pages 507-576
Simulation of Aluminum Extrusion....Pages 577-609
Simulation of Sedimentary Basins....Pages 611-658
Back Matter....Pages 659-663

✦ Subjects

Computational Science and Engineering; Partial Differential Equations