Parallel scientific computing : theory, algorithms, and applications of mesh based and meshless methods

• Main Authors: Trobec, Roman, Kosec, Gregor
• Format: eBook Book
• Language: English
• Published: Cham Springer 2015; Springer International Publishing AG; Springer International Publishing
• Edition: 1
• Series: SpringerBriefs in Computer Science
• Subjects: Computer Science; Numerical analysis; Numerical analysis > Data processing; Parallel computers; Parallel processing (Electronic computers); Partial Differential Equations; Programming Techniques; Science; Science > Data processing; Simulation and Modeling; System Performance and Evaluation
• ISBN: 3319170724; 9783319170725
• ISSN: 2191-5768; 2191-5776
• DOI: 10.1007/978-3-319-17073-2

This book is concentrated on the synergy between computer science and numerical analysis. It is written to provide a firm understanding of the described approaches to computer scientists, engineers or other experts who have to solve real problems. The meshless solution approach is described in more...

Table of Contents:

• 7.2 Computational Fluid Dynamics -- 7.2.1 Problem Definition -- 7.2.2 Convergence -- 7.2.3 Stability and Execution Time -- 7.3 Semiconductor Simulation -- 7.3.1 Problem Definition -- 7.3.2 Solution Accuracy and Convergence -- 8 Parallel Implementation -- 8.1 Multicore Parallelization -- 8.2 GPU Parallelization -- 8.3 Parallelization on Distributed Computers -- 9 Final Remarks and Conclusions -- References -- Index
• Intro -- Preface -- Contents -- 1 Introduction -- 1.1 Overview and Motivation -- 1.2 Why Solve PDEs? -- 1.3 The Background of the Numerical Solution -- 1.4 Related Work -- 2 Discretization and Formulation of Solution Approaches -- 2.1 Background -- 2.2 Strong Form -- 2.3 Weak Form -- 2.4 Discretization of Time -- 2.5 Summary of Solution Methodology -- 3 Supporting Algorithms -- 3.1 Domain Discretization -- 3.1.1 Mesh Topology -- 3.1.2 Mesh Generation -- 3.1.3 Mesh Enhancement -- 3.1.4 Mesless Discretization -- 3.1.5 Complexity of Discretization Algorithms -- 3.2 Determining Local Support Domain -- 3.2.1 Strategies for Determining Support Nodes -- 3.2.2 kD Tree -- 3.2.3 Computational Complexity of Determining the Support Domain -- 3.3 Interpolation and Approximation -- 3.3.1 Interpolation -- 3.3.2 Moving Least Squares Approximation -- 3.3.3 Accuracy of MLS -- 3.3.4 Computational Complexity of MLS -- 3.4 Numerical Quadrature -- 3.4.1 Computational Complexity of Numerical Integration -- 3.5 Solution of Linear System of Equations -- 3.5.1 Computational Complexity of Solving a Linear System of Equations -- 4 Mesh-Based Methods -- 4.1 Finite Difference Method -- 4.2 Finite Element Method -- 4.2.1 FEM Weak System -- 4.2.2 FEM Complexity -- 5 Meshless Methods -- 5.1 Meshless Local Strong Form Method -- 5.1.1 MLSM Complexity -- 5.2 Meshless Local Petrov Galerkin Method -- 5.2.1 MLPG1 Weak System -- 5.2.2 MLPG1 Complexity -- 6 Assessment of Described Solution Methods -- 6.1 Diffusion Equation -- 6.2 Test Conditions -- 6.3 Solution Approaches -- 6.3.1 FDM -- 6.3.2 FEM -- 6.3.3 MLSM -- 6.3.4 MLPG1 -- 6.4 Experimental Comparison of Convergence and Execution Time -- 6.4.1 Convergence -- 6.4.2 Execution Time -- 7 Test Cases -- 7.1 Mechanics of Cantilever Beam -- 7.1.1 Governing Equations -- 7.1.2 Closed Form Solution -- 7.1.3 Convergence and Runtime