
Author(s)  Vajtersic, Maián 

Title  Algorithms for Elliptic Problems. Efficient sequential and Parallel Solvers 
Publisher  Kluwer Academic Publishers 
Year of publication  1993 
Reviewed by  VALERII V.TROFIMOV 
The book under review elucidates the modern effective numerical methods used in engineering and scientific design practices. These algorithms concern with the fast numerical solution of the elliptic partial differential equations and parallel computer systems as well. The Poisson equation <formula> and the biharmonic equation <formula> are the subjects of much current interest and two chapters of the book are devoted to numerical solution of these fundamental equations of the nature.
The following topics are covered in the book under review. First chapter, Fast Methods for Solving the Poisson Equation, presents some fast direct and iterative algorithms for solving the Poisson equation with Dirichlet, Neumann and periodic boundary conditions. The second chapter, Fast Serial Algorithms for Solving Biharmonic Equation, examines some algorithms for solving biharmonic equation. The third chapter, Parallel Algorithms for Solving Certain Elliptic Boundary Value Problems, describes the parallel algorithms for model parallel computer systems of the SIMD (Single Instruction Multiple Data) and MIMD (Multiple Instruction Multiple Data) types. The fourth chapter, Implementatlon of Parallel Algorithms on Specialized Computers, deals with the implementation aspects of parallel algorithms for systems with matrix, pipeline and multiprocessor parallel computer architectures. The fifth chapter, Parallel Multigrid Algorithms, introduces the multigrid methods for the approximate solution of boundary value problems for elliptic partial differential equations. The sixth chapter, VLSI Elliptic Solvers, gives VLSI (Very Large Scale Integration) algorithms for realization of some fast elliptic solvers studied in the preceding chapters.
All in all, Algorithms for Elliptic Problems, provides a comprehensive description of the technology for solving of the elliptic problems and one shall be of interest to researchers and graduate students. I can recommend the purchase this book for students, experts, and libraries alike.