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

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...

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Main Authors Trobec, Roman, Kosec, Gregor
Format eBook Book
LanguageEnglish
Published Cham Springer 2015
Springer International Publishing AG
Springer International Publishing
Edition1
SeriesSpringerBriefs 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
Online AccessGet full text
ISBN3319170724
9783319170725
ISSN2191-5768
2191-5776
DOI10.1007/978-3-319-17073-2

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Abstract 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 detail, with a description of the required algorithms and the methods that are needed for the design of an efficient computer program. Most of the details are demonstrated on solutions of practical problems, from basic to more complicated ones. This book will be a useful tool for any reader interested in solving complex problems in real computational domains.
AbstractList 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 detail, with a description of the required algorithms and the methods that are needed for the design of an efficient computer program. Most of the details are demonstrated on solutions of practical problems, from basic to more complicated ones. This book will be a useful tool for any reader interested in solving complex problems in real computational domains.
Author Kosec, Gregor
Trobec, Roman
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ISBN 3319170724
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Notes Includes bibliographical references (p. 99-104) and index
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Snippet This book is concentrated on the synergy between computer science and numerical analysis. It is written to provide a firm understanding of the described...
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SubjectTerms 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
TableOfContents 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
Title Parallel scientific computing : theory, algorithms, and applications of mesh based and meshless methods
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