This book presents parallel algorithms for elliptic, parabolic, and hyperbolic equations, with implementations on hypercube Computers and other architectures. It focuses on a reusable library of distributed vector and matrix operations that hide communication details and enable code to run on both serial and parallel machines without modification.

This edition details how to structure PDE solvers around a portable parallel library, including inner products, matrix transposition, and distributed matrix-vector multiplication. It covers areal matrix distributions, diagonal representations, and Transpose-Split algorithms that adapt to different architectures. The work includes practical performance insights from experiments on the Caltech Hypercube and the Intel iPSC, with timing results and discussions of communication bottlenecks, efficiency, and development costs. The authors also describe a parallel Fast Poisson Solver and a parallel Full Multigrid method, along with a general framework for comparing algorithms across machines and problem sizes.
What you’ll experience

A library-based approach to building scalable PDE solvers for distributed data
Techniques for distributing vectors and matrices, including areal and diagonal forms
Parallel strategies for core operations like inner products, matrix-vector multiply, and transposes
Real-world timing data and architectural guidance for hypercubes and similar systems

Ideal for readers of parallel computing, numerical analysis, and computational fluid dynamics who want portable, scalable algorithms with practical performance guidance.

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