Algorithms for Elliptic Problems: Efficient Sequential and Parallel Solvers: 58 (Mathematics and its Applications) - Tapa dura

'Et moi, ... , si j'avait su comment. One service mathematics has ren­ en revenir, je n'y serais point alle'. dered the human race. It has put common sense back where it be­ Jules Verne longs, on the topmost shelf next to the dusty canister labelIed 'discard­ The series is divergent; therefore we ed nonsense'. may be able to do something with Eric T. Bell it. O. Heaviside Mathematics is a tool for thought. A highly necessary tool in a world where both feedback and nonlinearities abound. Similarly, all kinds of parts of mathematics serve as tools for other parts and for other sciences. Applying a simple rewriting rule to the quote on the right above one finds such statements as: 'One service topology has rendered mathema­ tical physics ... '; 'One service logic has rendered computer science ... '; 'One service category theory has rendered mathematics ... '. All ar­ guably true. Alld all statements obtainable this way form part of the raison d 'etre of this serics.

This volume deals with problems of modern effective algorithms for the numerical solution of the most frequently occurring elliptic partial differential equations. From the point of view of implementation, attention is paid to algorithms for both classical sequential and parallel computer systems.
The first two chapters are devoted to fast algorithms for solving the Poisson and biharmonic equation. In the third chapter, parallel algorithms for model parallel computer systems of the SIMD and MIMD types are described. The implementation aspects of parallel algorithms for solving model elliptic boundary value problems are outlined for systems with matrix, pipeline and multiprocessor parallel computer architectures. A modern and popular multigrid computational principle which offers a good opportunity for a parallel realization is described in the next chapter. More parallel variants based in this idea are presented, whereby methods and assignments strategies for hypercube systems are treated in more detail. The last chapter presents VLSI designs for solving special tridiagonal linear systems of equations arising from finite-difference approximations of elliptic problems.
For researchers interested in the development and application of fast algorithms for solving elliptic partial differential equations using advanced computer systems.