Ebook: Algorithms for Elliptic Problems: Efficient Sequential and Parallel Solvers

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.

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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.

Content:
Front Matter....Pages i-xix
Fast methods for solving the Poisson equation....Pages 1-52
Fast serial algorithms for solving biharmonic equation....Pages 53-86
Parallel algorithms for solving certain elliptic boundary value problems....Pages 87-133
Implementation of parallel algorithms on specialized computers....Pages 134-202
Parallel multigrid algorithms....Pages 203-251
VLSI elliptic solvers....Pages 252-287
Back Matter....Pages 288-292

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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.

Content:
Front Matter....Pages i-xix
Fast methods for solving the Poisson equation....Pages 1-52
Fast serial algorithms for solving biharmonic equation....Pages 53-86
Parallel algorithms for solving certain elliptic boundary value problems....Pages 87-133
Implementation of parallel algorithms on specialized computers....Pages 134-202
Parallel multigrid algorithms....Pages 203-251
VLSI elliptic solvers....Pages 252-287
Back Matter....Pages 288-292
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