One of the first things a student of partial differential equations learns is that it is impossible to solve elliptic equations by spatial marching. This new book describes how to do exactly that, providing a powerful tool for solving problems in fluid dynamics, heat transfer, electrostatics, and other fields characterized by discretized partial differential equations. Elliptic Marching Methods and Domain Decomposition demonstrates how to handle numerical instabilities (i.e., limitations on the size of the problem) that appear when one tries to solve these discretized equations with marching methods. The book also shows how marching methods can be superior to multigrid and pre-conditioned conjugate gradient (PCG) methods, particularly when used in the context of multiprocessor parallel computers. Techniques for using domain decomposition together with marching methods are detailed, clearly illustrating the benefits of these techniques for applications in engineering, applied mathematics, and the physical sciences.Chapter 6 PERFORMANCE OF THE 2D GEM CODE 6.1 Introduction The present chapter describes timing and accuracy tests  on a ... 62 Uses and Users Elliptic and mixed equations with nonseparable coefficients arise in a variety of applications in heat transfer, fluid dynamics, ... The simplest second-order finite- difference discretization then leads to a 9-point nonseparable stencil. ... The user is simply provided with documented FORTRAN subroutines and some example problems.
|Title||:||Elliptic Marching Methods and Domain Decomposition|
|Author||:||Patrick J. Roache|
|Publisher||:||CRC Press - 1995-06-29|