Fast Solvers for Mesh-Based Computations

Maciej Paszynski

December 1, 2015 by CRC Press
Reference - 309 Pages - 154 B/W Illustrations
ISBN 9781498754194 - CAT# K27391
Series: Advances in Applied Mathematics

USD$89.95

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Features

  • Introduces a new paradigm for designing direct solvers based on the structure of the computational mesh
  • Presents how to construct a workflow for the parallel solver using basic atomic tasks and how to obtain an efficient parallel implementation of the solver based on the coloring of the workflow graph
  • Derives parallel multi-frontal solver algorithms delivering logarithmic O(logN) computational cost for different mesh-based methods
  • Derives specific parallel multi-frontal solver algorithms delivering logarithmic O(logN) computational cost for two- and three-dimensional grids with singularities
  • Introduces general methodology for designing and building general mesh-based solvers for sparse matrices
  • Shows how to construct efficient elimination trees based on the structure of the computational mesh

Summary

Fast Solvers for Mesh-Based Computations presents an alternative way of constructing multi-frontal direct solver algorithms for mesh-based computations. It also describes how to design and implement those algorithms.

The book’s structure follows those of the matrices, starting from tri-diagonal matrices resulting from one-dimensional mesh-based methods, through multi-diagonal or block-diagonal matrices, and ending with general sparse matrices.

Each chapter explains how to design and implement a parallel sparse direct solver specific for a particular structure of the matrix. All the solvers presented are either designed from scratch or based on previously designed and implemented solvers.

Each chapter also derives the complete JAVA or Fortran code of the parallel sparse direct solver. The exemplary JAVA codes can be used as reference for designing parallel direct solvers in more efficient languages for specific architectures of parallel machines.

The author also derives exemplary element frontal matrices for different one-, two-, or three-dimensional mesh-based computations. These matrices can be used as references for testing the developed parallel direct solvers.

Based on more than 10 years of the author’s experience in the area, this book is a valuable resource for researchers and graduate students who would like to learn how to design and implement parallel direct solvers for mesh-based computations.