Elliptic Marching Methods and Domain Decomposition [Kõva köide]

Contradicts one of the first venerable truths told to students of partial differential equations: it is impossible to solve elliptic equations by spatial marching. Roache shows how to do it, thus providing a powerful tool for solving problems in fluid dynamics, heat transfer, electrostatics, and other fields. After explaining basic methods for two-dimensional problems, he considers higher-orders, extending the mesh size, vectorization and parallelization, semidirect methods for fluid mechanics, a comparison with multigrid methods, and other aspects. Annotation c. by Book News, Inc., Portland, Or.

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.