Advanced Topics in Computational Partial Differential Equations

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.

Klappentext

A gentle introduction to advanced topics such as 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 - 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 to discretization methods, algorithms, software design, verification, and computational examples. Suitable for readers with a background in basic finite element and finite difference methods for partial differential equations.

Inhalt

X. Cai, E. Acklam, H. P. Langtangen, A. Tveito: Parallel Computing.- X. Cai: Overlapping Domain Decomposition Methods.- K.-A. Mardal, G. W. Zumbusch, H. P. Langtangen: Software Tools for Multigrid Methods.- K.-A. Mardal, H. P. Langtangen: Mixed Finite Elements.- K.-A. Mardal, J. Sundnes, H. P. Langtangen, A. Tveito: Systems of PDEs and Block Preconditioning.- Å. Ødegård, H. P. Langtangen, A. Tveito: Object-Oriented Implementation of Fully Implicit Methods for Systems of PDEs.- H. P. Langtangen, H. Osnes: Stochastic Partial Differential Equations.- H. P. Langtangen and K.-A. Mardal: Using Diffpack from Python Scripts.- X. Cai, A. M. Bruaset, H. P. Langtangen, G. T. Lines, K. Samuelsson, W. Shen, A. Tveito, G. Zumbusch: Performance Modeling of PDE Solvers.- J. Sundnes, G.T. Lines, P. Grøttum, A. Tveito: Numerical Methods and Software for Modeling the Electrical Activity in the Human Heart.- O. Skavhaug, B. F. Nielsen, A. Tveito: Mathematical Models of Financial Derivatives.- O. Skavhaug, B. F. Nielsen, A. Tveito: Numerical Methods for Financial Derivatives.- T. Thorvaldsen, H. P. Langtangen, H. Osnes: Finite Element Modeling of Elastic Structures.- K. M. Okstad, T. Kvamsdal: Simulation of Aluminum Extrusion.- A. Kjeldstad, H. P. Langtangen, J. Skogseid, K. Bjørlykke: Simulation of Deformations, Fluid Flow and HeatTransfer in Sedimentary Basins