By Maciej Paszynski
Fast Solvers for Mesh-Based Computations provides an alternate approach of creating multi-frontal direct solver algorithms for mesh-based computations. It additionally describes the way to layout and enforce these algorithms.
The book’s constitution follows these of the matrices, ranging from tri-diagonal matrices caused by one-dimensional mesh-based tools, via multi-diagonal or block-diagonal matrices, and finishing with basic sparse matrices.
Each bankruptcy explains how you can layout and enforce a parallel sparse direct solver particular for a specific constitution of the matrix. all of the solvers awarded are both designed from scratch or in accordance with formerly designed and applied solvers.
Each bankruptcy additionally derives the full JAVA or Fortran code of the parallel sparse direct solver. The exemplary JAVA codes can be utilized as reference for designing parallel direct solvers in additional effective languages for particular architectures of parallel machines.
The writer additionally derives exemplary point frontal matrices for various one-, two-, or third-dimensional mesh-based computations. those matrices can be utilized as references for trying out the built parallel direct solvers.
Based on greater than 10 years of the author’s adventure within the sector, this e-book is a worthy source for researchers and graduate scholars who want to tips on how to layout and enforce parallel direct solvers for mesh-based computations.
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Extra info for Fast solvers for mesh-based computations
5: Dependency plan for the parts of the book describing numerical results. 6: Dependency plan for the parts of the book describing numerical results. ✐ ✐ ✐ ✐ ✐ ✐ “main” — 2015/11/6 — 17:59 — page xxxv — #31 ✐ Preface ✐ xxxv Related Works The solver algorithms presented in this book can be used to compute solutions of systems of linear equations obtained from several mesh-based methods. This includes the finite difference method, the finite element method with linear and hierarchical basis functions, and the isogeometric finite element and collocation methods.
We add suitable indices. 3. Additionally, we shade the dependency graph, in such a way that different shades of gray represent sets of tasks that can be executed concurrently. We can also get an analogous result by employing the trace theory [32, 66]. 2: Construction of the exemplary elimination tree by execution of productions (P 1) − (P 2)1 − (P 2)2 − (P 2)3 − (P 2)4 − (P 3)1 − (P 3)2 − (P 3)3 − (P 3)4 − (P 3)5 − (P 3)6 . 3: Left panel: Dependency graph between tasks. Right panel: Shading of the dependency graph.
I present some particular classes of the two- and three-dimensional grids resulting in a similar structure of the matrix and in a similar structure of the graph-grammar-based solvers as for the case of the one-dimensional mesh-based computations. These are two-dimensional grids with anisotropic edge singularities, two-dimensional grids with point singularities, three-dimensional grids with anisotropic edge singularities, three-dimensional grids with anisotropic face singularities, and three-dimensional grid with point singularities.