Ciegis / Henty / Kågström Parallel Scientific Computing and Optimization

Advances and Applications
1. Auflage 2008
ISBN: 978-0-387-09707-7
Verlag: Springer-Verlag
Format: PDF
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, 274 Seiten

Autoren/Hrsg.

Ciegis, Raimondas

Henty, David

Kågström, Bo

Žilinskas, Julius

Inhaltsverzeichnis

1;Preface;6
2;Contents;11
3;List of Contributors;19
4;Parallel Algorithms for Matrix Computations;24
4.1;RECSY and SCASY Library Software: Recursive Blocked and Parallel Algorithms for Sylvester- Type Matrix Equations with Some Applications;26
4.1.1;1 Motivation and Background;26
4.1.2;2 Variants of Bartels-Stewart's Schur Method;28
4.1.3;3 Blocking Strategies for Reduced Matrix Equations;29
4.1.3.1;3.1 Explicit Blocked Methods for Reduced Matrix Equations;29
4.1.3.2;3.2 Recursive Blocked Methods for Reduced Matrix Equations;30
4.1.4;4 Parallel Algorithms for Reduced Matrix Equations;32
4.1.4.1;4.1 Distributed Wavefront Algorithms;33
4.1.4.2;4.2 Parallelization of Recursive Blocked Algorithms;34
4.1.5;5 Condition Estimation;34
4.1.5.1;5.1 Condition Estimation in RECSY;36
4.1.5.2;5.2 Condition Estimation in SCASY;36
4.1.6;6 Library Software Highlights;36
4.1.6.1;6.1 The RECSY Library;36
4.1.6.2;6.2 The SCASY Library;37
4.1.7;7 Experimental Results;39
4.1.8;8 Some Control Applications and Extensions;41
4.1.8.1;8.1 Condition Estimation of Subspaces with Specified Eigenvalues;41
4.1.8.2;8.2 Periodic Matrix Equations in CACSD;42
4.1.9;References;45
4.2;Parallelization of Linear Algebra Algorithms Using ParSol Library of Mathematical Objects;48
4.2.1;1 Introduction;48
4.2.2;2 The Principles and Implementation Details of ParSol Library;50
4.2.2.1;2.1 Main Classes of ParSol;50
4.2.2.2;2.2 Implementation of ParSol;52
4.2.3;3 Parallel Algorithm for Simulation of Counter-propagating Laser Beams;52
4.2.3.1;3.1 Invariants of the Solution;53
4.2.3.2;3.2 Finite Difference Scheme;54
4.2.3.3;3.3 Parallel Algorithm;56
4.2.3.4;3.4 Results of Computational Experiments;57
4.2.4;4 Conclusions;57
4.2.5;References;58
4.3;The Development of an Object-Oriented Parallel Block Preconditioning Framework;60
4.3.1;1 Introduction;60
4.3.2;2 Block Preconditioning;62
4.3.3;3 The Performance of the Block Preconditioning Framework;63
4.3.3.1;3.1 Reference Problem : 2D Poisson;63
4.3.3.2;3.2 Non-linear Elasticity;64
4.3.3.3;3.3 Fluid Mechanics;65
4.3.3.4;3.4 Fluid-Structure Interaction;67
4.3.4;4 Conclusions;68
4.3.5;References;68
4.4;A Sparse Linear System Solver Used in a Distributed and Heterogenous Grid Computing Environment;70
4.4.1;1 Introduction;70
4.4.2;2 The Parallel Linear Multisplitting Method Used in the GREMLINS Solver;71
4.4.3;3 Load Balancing of the Direct Multisplitting Method;73
4.4.4;4 Experimental Results;74
4.4.4.1;4.1 Experiments with a Matrix Issued from an Advection- Diffusion Model;74
4.4.4.2;4.2 Results of the Load Balancing;75
4.4.5;5 Conclusions and FutureWork;78
4.4.6;References;79
4.5;Parallel Diagonalization Performance on High- Performance Computers;80
4.5.1;1 Introduction;80
4.5.2;2 Parallel Diagonalization Methods;81
4.5.2.1;2.1 Equations for Matrix Diagonalizations in PRMAT;81
4.5.2.2;2.2 Equations for Matrix Diagonalizations in CRYSTAL;81
4.5.2.3;2.3 Symmetric Eigensolver Methods;82
4.5.2.4;2.4 Eigensolver Parallel Library Routines;83
4.5.3;3 Testing Environment;83
4.5.4;4 Results;84
4.5.5;5 Conclusions;88
4.5.6;References;89
5;Parallel Optimization;90
5.1;Parallel Global Optimization in Multidimensional Scaling;91
5.1.1;1 Introduction;91
5.1.2;2 Global Optimization;92
5.1.3;3 Multidimensional Scaling;94
5.1.4;4 Multidimensional Scaling with City-Block Distances;97
5.1.5;5 Parallel Algorithms for Multidimensional Scaling;99
5.1.6;6 Conclusions;103
5.1.7;References;103
5.2;High-Performance Parallel Support Vector Machine Training;105
5.2.1;1 Introduction;105
5.2.2;2 Interior Point Methods;107
5.2.3;3 Support Vector Machines;108
5.2.3.1;3.1 Binary Classification;108
5.2.3.2;3.2 Linear SVM;108
5.2.3.3;3.3 Non-linear SVM;109
5.2.4;4 Parallel Partial Cholesky Decomposition;110
5.2.5;5 Implementing the QP for Parallel Computation;111
5.2.5.1;5.1 Linear Algebra Operations;112
5.2.5.2;5.2 Performance;112
5.2.6;6 Conclusions;114
5.2.7;References;114
5.3;Parallel Branch and Bound Algorithm with Combination of Lipschitz Bounds over Multidimensional Simplices for Multicore Computers;115
5.3.1;1 Introduction;115
5.3.2;2 Parallel Branch and Bound with Simplicial Partitions;116
5.3.3;3 Results of Experiments;118
5.3.4;4 Conclusions;122
5.3.5;References;124
5.4;Experimental Investigation of Local Searches for Optimization of Grillage- Type Foundations;125
5.4.1;1 Introduction;125
5.4.2;2 Optimization of Grillage-Type Foundations;126
5.4.3;3 Methods for Local Optimization of Grillage-Type Foundations;126
5.4.4;4 Experimental Research;127
5.4.5;5 Conclusions;133
5.4.6;References;134
6;Management of Parallel Programming Models and Data;135
6.1;Comparison of the UK National Supercomputer Services: HPCx and HECToR;136
6.1.1;1 Introduction;136
6.1.2;2 SystemOverview;137
6.1.2.1;2.1 HPCx;137
6.1.2.2;2.2 HECToR;139
6.1.3;3 System Comparison;139
6.1.3.1;3.1 Processors;140
6.1.3.2;3.2 Interconnect;140
6.1.4;4 Applications Performance;141
6.1.4.1;4.1 PDNS3D;142
6.1.4.2;4.2 NAMD;143
6.1.5;5 Conclusions;144
6.1.6;References;144
6.2;DL POLY 3 I/O: Analysis, Alternatives, and Future Strategies;146
6.2.1;1 Introduction;146
6.2.2;2 I/O in DL POLY 3;147
6.2.2.1;2.1 Serial Direct Access I/O;147
6.2.2.2;2.2 Parallel Direct Access I/O;148
6.2.2.3;2.3 MPI-I/O;148
6.2.2.4;2.4 Serial I/O Using NetCDF;149
6.2.3;3 Results and Discussion;149
6.2.4;4 Conclusions;152
6.2.5;References;153
6.3;Mixed Mode Programming on HPCx;154
6.3.1;1 Introduction;154
6.3.2;2 Benchmark Codes;155
6.3.3;3 MixedMode;156
6.3.4;4 Hardware;158
6.3.5;5 Experimental Results;160
6.3.6;6 Conclusions;163
6.3.7;References;164
6.4;A Structure Conveying Parallelizable Modeling Language for Mathematical Programming;165
6.4.1;1 Introduction;165
6.4.2;2 Background ;166
6.4.2.1;2.1 Mathematical Programming;166
6.4.2.2;2.2 Modeling Languages;167
6.4.3;3 Solution Approaches to Structured Problems;169
6.4.3.1;3.1 Decomposition;169
6.4.3.2;3.2 Interior Point Methods;169
6.4.4;4 Structure Conveying Modeling Languages;170
6.4.4.1;4.1 Other Structured Modeling Approaches;171
6.4.4.2;4.2 Design;171
6.4.4.3;4.3 Implementation;173
6.4.5;5 Conclusions;175
6.4.6;References;175
6.5;Computational Requirements for Pulsar Searches with the Square Kilometer Array;177
6.5.1;1 Introduction;177
6.5.2;2 SKA Configuration;178
6.5.2.1;Technical Considerations;178
6.5.3;3 Computational Requirements;179
6.5.3.1;3.1 Beam Forming;179
6.5.3.2;3.2 Data Analysis;181
6.5.4;4 Conclusions;184
6.5.5;References;184
7;Parallel Scientific Computing in Industrial Applications;186
7.1;Parallel Multiblock Multigrid Algorithms for Poroelastic Models;187
7.1.1;1 Introduction;187
7.1.2;2 Mathematical Model and Stabilized Difference Scheme;189
7.1.3;3 Multigrid Methods;190
7.1.3.1;3.1 Box Relaxation;191
7.1.4;4 Numerical Experiments;192
7.1.5;5 Parallel Multigrid;194
7.1.5.1;5.1 Code Implementation;194
7.1.5.2;5.2 Critical Issues Regarding Parallel MG;195
7.1.6;6 Conclusions;197
7.1.7;References;197
7.2;A Parallel Solver for the 3D Simulation of Flows Through Oil Filters;199
7.2.1;1 Introduction;199
7.2.2;2 Mathematical Model and Discretization;200
7.2.2.1;2.1 Time Discretization;201
7.2.2.2;2.2 Finite Volume Discretization in Space;202
7.2.2.3;2.3 Subgrid Approach;203
7.2.3;3 Parallel Algorithms;203
7.2.3.1;3.1 DD Parallel Algorithm;203
7.2.3.2;3.2 OpenMP Parallel Algorithm;207
7.2.4;4 Conclusions;208
7.2.5;References;208
7.3;High-Performance Computing in Jet Aerodynamics;210
7.3.1;1 Introduction;210
7.3.2;2 Numerical Background ;212
7.3.2.1;2.1 HYDRA and FLUXp;212
7.3.2.2;2.2 Boundary and Initial Conditions;213
7.3.2.3;2.3 Ffowcs Williams Hawkings Surface;213
7.3.3;3 Computing Facilities;214
7.3.4;4 Code Parallelization and Scalability;215
7.3.5;5 Axisymmetric Jet Results ;216
7.3.5.1;5.1 Problem Set Up and Mesh;216
7.3.5.2;5.2 Results;217
7.3.6;6 Complex Geometries;217
7.3.6.1;6.1 Mesh and Initial Conditions;217
7.3.6.2;6.2 Results;220
7.3.7;7 Conclusions;222
7.3.8;References;222
7.4;Parallel Numerical Solver for the Simulation of the Heat Conduction in Electrical Cables;224
7.4.1;1 Introduction;224
7.4.2;2 The Model of Heat Conduction in Electrical Cables and Discretization;225
7.4.3;3 Parallel Algorithm;228
7.4.4;4 Conclusions;229
7.4.5;References;229
7.5;Orthogonalization Procedure for Antisymmetrization of J- shell States;230
7.5.1;1 Introduction;230
7.5.2;2 Antisymmetrization of Identical Fermions States;231
7.5.3;3 Calculations and Results;234
7.5.4;4 Conclusions;237
7.5.5;References;238
7.6;Parallel Direct Numerical Simulation of an Annular Gas - Liquid Two- Phase Jet with Swirl;239
7.6.1;1 Introduction;239
7.6.2;2 Governing Equations;240
7.6.3;3 Computational Methods ;242
7.6.3.1;3.1 Time Advancement, Discretization, and Parallelization;242
7.6.3.2;3.2 Boundary and Initial Conditions;243
7.6.4;4 Results and Discussion;245
7.6.4.1;4.1 Instantaneous Flow Data;245
7.6.4.2;4.2 Time-Averaged Data, Velocity Histories, and Energy Spectra;248
7.6.5;5 Conclusions;250
7.6.6;References;251
7.7;Parallel Numerical Algorithm for the Traveling Wave Model;253
7.7.1;1 Introduction;253
7.7.2;2 Mathematical Model;256
7.7.3;3 Finite Difference Scheme;258
7.7.3.1;3.1 Discrete Transport Equations for Optical Fields;259
7.7.3.2;3.2 Discrete Equations for Polarization Functions;260
7.7.3.3;3.3 Discrete Equations for the Carrier Density Function;260
7.7.3.4;3.4 Linearized Numerical Algorithm;260
7.7.4;4 Parallelization of the Algorithm;262
7.7.4.1;4.1 Parallel Algorithm;262
7.7.4.2;4.2 Scalability Analysis;263
7.7.4.3;4.3 Computational Experiments;264
7.7.5;5 Conclusions;266
7.7.6;References;266
7.8;Parallel Algorithm for Cell Dynamics Simulation of Soft Nano- Structured Matter;268
7.8.1;1 Introduction;268
7.8.2;2 The Cell Dynamics Simulation;269
7.8.3;3 Parallel Algorithm of CDS Method;271
7.8.3.1;3.1 The Spatial Decomposition Method;271
7.8.3.2;3.2 Parallel Platform and Performance Tuning;273
7.8.3.3;3.3 Performance Analysis and Results;274
7.8.4;4 Conclusions;277
7.8.5;References;277
7.9;Docking and Molecular Dynamics Simulation of Complexes of High and Low Reactive Substrates with Peroxidases;278
7.9.1;1 Introduction;278
7.9.2;2 Experimental ;280
7.9.2.1;2.1 Ab Initio Molecule Geometry Calculations;280
7.9.2.2;2.2 Substrates Docking in Active Site of Enzyme;280
7.9.2.3;2.3 Molecular Dynamics of Substrate-Enzyme Complexes;281
7.9.3;3 Results and Discussion;282
7.9.3.1;3.1 Substrate Docking Modeling;282
7.9.3.2;3.2 Molecular Dynamics Simulation;283
7.9.4;4 Conclusions;285
7.9.5;References;285
8;Index;287