Fast solvers for mesh-based computations. (2016)

• Record Type: Book
• Further Information: Note: Maciej Paszynski.
• Authors: Paszynski, Maciej
• Contents: Multi-Frontal Direct Solver Algorithm for Tri-Diagonal and Block-Diagonal One-Dimensional Problems; Derivation of the Linear System for One-Dimensional Finite Difference Method; Algebraic Algorithm of the Multi-Frontal Solver; Graph-Grammar Based Model of Concurrency of the Multi-Frontal Solver Algorithm; One-Dimensional Finite Element Method with Linear Basis Functions; One-Dimensional Isogeometric Collocation Method with Quadratic B-Splines; One-Dimensional Finite Element Method with Buble Basis Functions; ; One-Dimensional Non-Stationary Problems; Euler Scheme with Respect to Time Mixed with Finite Element Method with Linear; Basis Functions with Respect to Space; α-Scheme with Respect to Time Mixed with Method with Linear Basis Functions; for Space; ; Multi-Frontal Direct Solver Algorithm for Multi-Diagonal One-Dimensional Problems; One-Dimensional Collocation Method with Higher Order B-Splines ; One-Dimensional Isogeometric Finite Element Method; ; Multi-Frontal Direct Solver Algorithm for Two-Dimensional Grids with Block Diagonal; Structure of the Matrix; Two-Dimensional Projection Problem with Linear Basis Functions; Two-Dimensional Mesh with Anisotropic Edge Singularity; Two-Dimensional Mesh with Point Singularity; ; Multi-Frontal Direct Solver Algorithm for Three-Dimensional Grids with Block Diagonal Structure of the Matrix; Three-Dimensional Projection Problem with Linear Basis Functions; Three-Dimensional Mesh with Anisotropic Face Singularity; Three-Dimensional Mesh with Anisotropic Edge Singularity; Three-Dimensional Mesh with Point Singularity; ; Multi-Frontal Direct Solver Algorithm for Two-Dimensional Isogeometric Finite; Element Method; Isogeometric Finite Element Method for Two-Dimensional Problems; Graph-Grammar for Generation of the Elimination Tree; Graph-Grammar Productions for the Solver Algorithm; ; Expressing Partial LU Factorization by BLAS Calls; LU Factorization of A(1, 1); Multiplication of A(1, 2) by the Inverse of A(1, 1); Multiplication of b(1) by the Inverse of A(1, 1); Matrix Multiplication and Subtraction A(2, 2)=A(2, 2)-A(2, 1)A(1, 2); Matrix Vector Multiplication and Subtraction b(2)=b, 2)-A(2, 1)b(1); Example; ; Multi-Frontal Solver Algorithm for Arbitrary Mesh-Based Computations; Multi-Frontal Solver Algorithm for Arbitrary Grids; Hypermatrix Module; Elimination Tree Module; Supernodes System Module; Interface; Structure of Matrices for Different Two-Dimensional Methods; ; Elimination Trees; Elimination Trees and Multi-Frontal Solvers; Quasi-Optimal Elimination Tree for Two-Dimensional Mesh with Point Singularity; Quasi-Optimal Elimination Tree for Two-Dimensional Mesh with Edge Singularity; Nested-Dissection Elimination Tree for Two-Dimensional Mesh with Edge Singularity; Minimum Degree Tree for Two-Dimensional Mesh with Edge Singularity; Estimation of the Number of Floating Point Operations and Memory Usage; Elimination Trees for Three-Dimensional Grids; ; Reutilization and Reuse of Partial LU Factorizatons; Idea of the Reutilization Algorithm; Exemplary Implementation of the Reutilization Algorithm; Idea of the Reuse Algorithm; Exemplary Implementation of the Reuse Algorithm; ; Numerical Experiments; Measuring the Solver Performance by Means of Execution Time; Measuring the Solver Performance by Means of the Number of Floating Point Operations (FLOPs); Measuring the Solver Performance by Means of the Efficiency and Speedup; Graph-Grammar Based Multi-Thread GALOIS Solver for Two-Dimensional Grids with Singularities; Graph-Grammar Based Multi-Thread GALOIS Solver for Three-Dimensional Grids with Singularities; Graph-Grammar Based GPU Solver for One-Dimensional Isogoemetric Finite Element Method; Graph-Grammar Based GPU Solver for Two-Dimensional Isogoemetric Finite Element Method; Graph-Grammar Based Solver for Two-Dimensional Adaptive Finite Element Method; Graph-Grammar Based Solver for Three-Dimensional Adaptive Finite Element; Method
• Edition: 1st
• Publisher Details: Boca Raton : CRC Press
• Publication Date: 2016
• Extent: 1 online resource, illustrations (black and white)
• Subjects: 005.1; Computer algorithms
• Languages: English
• ISBNs: 9781498754200
• Related ISBNs: 9781498754194
• Notes: Note: Description based on CIP data; item not viewed.
• Access Rights: Legal Deposit; Only available on premises controlled by the deposit library and to one user at any one time; The Legal Deposit Libraries (Non-Print Works) Regulations (UK).
• Access Usage: Restricted: Printing from this resource is governed by The Legal Deposit Libraries (Non-Print Works) Regulations (UK) and UK copyright law currently in force.