Fast Solvers for Mesh-Based Computations

Maciej Paszynski, PhD, Department of Computer Science, Electronics and Telecommunications, AGH University of Science and Technology, Kraków, Poland

"The author describes how to design and implement effi�cient parallel multi-frontal direct solver algorithms for mesh-based computations.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.The book's structure follows that 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.In each chapter JAVA or Fortran codes of the parallel sparse direct solver are listed. 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.The book represents 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."~Nicola Mastronardi, Mathematical Reviews, 2017

• Multi-Frontal Direct Solver Algorithm for Tri-Diagonal and Block-Diagonal One-Dimensional Problems. One-Dimensional Non-Stationary Problems. Multi-Frontal Direct Solver Algorithm for Multi-Diagonal One-Dimensional Problems. Multi-Frontal Direct Solver Algorithm for Two-Dimensional Grids with Block Diagonal Structure of the Matrix. Multi-Frontal Direct Solver Algorithm for Three-Dimensional Grids with Block Diagonal Structure of the Matrix. Multi-Frontal Direct Solver Algorithm for Two-Dimensional Isogeometric Finite Element Method. Expressing Partial LU Factorization by BLAS Calls. Multi-Frontal Solver Algorithm for Arbitrary Mesh-Based Computations. Elimination Trees. Reutilization and Reuse of Partial LU Factorizatons. Numerical Experiments.