Numerical Solution of Partial Differential Equations on Parallel Computers

Since the dawn of computing, the quest for a better understanding of Nature has been a driving force for technological development. Groundbreaking achievements by great scientists have paved the way from the abacus to the supercomputing power of today. When trying to replicate Nature in the computer's silicon test tube, there is need for precise and computable process descriptions. The scienti?c ?elds of Ma- ematics and Physics provide a powerful vehicle for such descriptions in terms of Partial Differential Equations (PDEs). Formulated as such equations, physical laws can become subject to computational and analytical studies. In the computational setting, the equations can be discreti ed for ef?cient solution on a computer, leading to valuable tools for simulation of natural and man-made processes. Numerical so- tion of PDE-based mathematical models has been an important research topic over centuries, and will remain so for centuries to come. In the context of computer-based simulations, the quality of the computed results is directly connected to the model's complexity and the number of data points used for the computations. Therefore, computational scientists tend to ?ll even the largest and most powerful computers they can get access to, either by increasing the si e of the data sets, or by introducing new model terms that make the simulations more realistic, or a combination of both. Today, many important simulation problems can not be solved by one single computer, but calls for parallel computing.

Contenu
Parallel Computing.- Parallel Programming Models Applicable to Cluster Computing and Beyond.- Partitioning and Dynamic Load Balancing for the Numerical Solution of Partial Differential Equations.- Graphics Processor Units: New Prospects for Parallel Computing.- Parallel Algorithms.- Domain Decomposition Techniques.- Parallel Geometric Multigrid.- Parallel Algebraic Multigrid Methods High Performance Preconditioners.- Parallel Mesh Generation.- Parallel Software Tools.- The Design and Implementation of hypre, a Library of Parallel High Performance Preconditioners.- Parallelizing PDE Solvers Using the Python Programming Language.- Parallel PDE-Based Simulations Using the Common Component Architecture.- Parallel Applications.- Full-Scale Simulation of Cardiac Electrophysiology on Parallel Computers.- Developing a Geodynamics Simulator with PETSc.- Parallel Lattice Boltzmann Methods for CFD Applications.