Paperback : £128.00
Despite the ample number of articles on parallel-vector computational algorithms published over the last 20 years, there is a lack of texts in the field customized for senior undergraduate and graduate engineering research. Parallel-Vector Equation Solvers for Finite Element Engineering Applications aims to fill this gap, detailing both the theoretical development and important implementations of equation-solution algorithms. The mathematical background necessary to understand their inception balances well with descriptions of their practical uses. Illustrated with a number of state-of-the-art FORTRAN codes developed as examples for the book, Dr. Nguyen's text is a perfect choice for instructors and researchers alike.
Preface. Acknowledgments. Disclaimer of Warranty. 1. Introduction. 2. Storage Schemes for the Coefficient Stiffness Matrix. 3. Parallel Algorithms for Genreation and Assembly of Finite Element Matrices. 4. Parallel-Vector Skyline Equation Solver on Shared memory Computers. 5. Parallel-Vector Variable Bandwidth Equation Solver on Shared Memory Computers. 6. Parallel-Vector Variable Bandwidth Out-of-Core Equation Solver. 7. Parallel-Vector Skyline Equation Solver for Distributed Memory Computers. 8. Parallel-Vector Unsymmetrical Equation Solver. 9. A Tridiagonal Solver for Massively Parallel Computers. 10. Sparse Equation Solver with Unrolling Strategies. 11. Algorithms for Sparse-Symmetrical-Indefinite and Sparse-Unsymmetrical System of Equations. Index.
Show moreDespite the ample number of articles on parallel-vector computational algorithms published over the last 20 years, there is a lack of texts in the field customized for senior undergraduate and graduate engineering research. Parallel-Vector Equation Solvers for Finite Element Engineering Applications aims to fill this gap, detailing both the theoretical development and important implementations of equation-solution algorithms. The mathematical background necessary to understand their inception balances well with descriptions of their practical uses. Illustrated with a number of state-of-the-art FORTRAN codes developed as examples for the book, Dr. Nguyen's text is a perfect choice for instructors and researchers alike.
Preface. Acknowledgments. Disclaimer of Warranty. 1. Introduction. 2. Storage Schemes for the Coefficient Stiffness Matrix. 3. Parallel Algorithms for Genreation and Assembly of Finite Element Matrices. 4. Parallel-Vector Skyline Equation Solver on Shared memory Computers. 5. Parallel-Vector Variable Bandwidth Equation Solver on Shared Memory Computers. 6. Parallel-Vector Variable Bandwidth Out-of-Core Equation Solver. 7. Parallel-Vector Skyline Equation Solver for Distributed Memory Computers. 8. Parallel-Vector Unsymmetrical Equation Solver. 9. A Tridiagonal Solver for Massively Parallel Computers. 10. Sparse Equation Solver with Unrolling Strategies. 11. Algorithms for Sparse-Symmetrical-Indefinite and Sparse-Unsymmetrical System of Equations. Index.
Show more1. Introduction.- 1.1 Parallel Computers.- 1.2 Measurements for Algorithms’ Performance.- 1.3 Vector Computers.- 1.4 Summary.- 1.5 Exercises.- 1.6 References.- 2. Storage Schemes for the Coefficient Stiffness Matrix.- 2.1 Introduction.- 2.2 Full Matrix.- 2.3 Symmetrical Matrix.- 2.4 Banded Matrix.- 2.5 Variable Banded Matrix.- 2.6 Skyline Matrix.- 2.7 Sparse Matrix.- 2.8 Detailed Procedures For Determining The Mapping Between 2-D Array and 1-D Array in Skyline Storage Scheme.- 2.9 Determination of the Column Height (ICOLH) of a Finite Element Model.- 2.10 Computer Implementation For Determining Column Heights.- 2.11 Summary.- 2.12 Exercises.- 2.13 References.- 3. Parallel Algorithms for Generation and Assembly of Finite Element Matrices.- 3.1 Introduction.- 3.2 Conventional Algorithm to Generate and Assemble Element Matrices.- 3.3 Node-by-Node Parallel Generation and Assembly Algorithms.- 3.4 Additional Comments on Baddourah-Nguyen’s (Node-by-Node) Parallel Generation and Assembly (G&A) Algorithm.- 3.5 Application of Baddourah-Nguyen’s Parallel G&A Algorithm.- 3.6 Qin-Nguyen’s G&A Algorithm.- 3.7 Applications of Qin-Nguyen’s Parallel G&A Algorithm.- 3.8 Summary.- 3.9 Exercises.- 3.10 References.- 4. Parallel-Vector Skyline Equation Solver on Shared Memory Computers.- 4.1 Introduction.- 4.2 Choleski-based Solution Strategies.- 4.3 Factorization.- 4.4 Solution of Triangular Systems.- 4.5 Force: A Portable, Parallel FORTRAN Language.- 4.6 Evaluation of Methods on Example Problems.- 4.7 Skyline Equation Solver Computer Program.- 4.8 Summary.- 4.9 Exercises.- 4.10 References.- 5. Parallel-Vector Variable Bandwidth Equation Solver on Shared Memory Computers.- 5.1 Introduction.- 5.2 Data Storage Schemes.- 5.3 Basic Sequential Variable Bandwidth Choleski Method.- 5.4Vectorized Choleski Code with Loop Unrolling.- 5.5 More on Force: A Portable, Parallel FORTRAN Language.- 5.6 Parallel-Vector Choleski Factorization.- 5.7 Solution of Triangular Systems.- 5.8 Relations Amongst the Choleski, Gauss and LDLT Factorizations.- 5.9 Factorization Based Upon “Look Backward” Versus “Look Forward” Strategies.- 5.10 Evaluation of Methods For Structural Analyses.- 5.11 Descriptions of Parallel-Vector Subroutine PVS.- 5.12 Parallel-Vector Equation Solver Subroutine PVS.- 5.13 Summary.- 5.14 Exercises.- 5.15 References.- 6. Parallel-Vector Variable Bandwidth Out-of-Core Equation Solver.- 6.1 Introduction.- 6.2 Out-of-Core Parallel/Vector Equation Solver (version 1).- 6.3 Out-of-Core Vector Equation Solver (version 2).- 6.4 Out-of-Core Vector Equation Solver (version 3).- 6.5 Application.- 6.6 Summary.- 6.7 Exercises.- 6.8 References.- 7. Parallel-Vector Skyline Equation Solver for Distributed Memory Computers.- 7.1 Introduction.- 7.2 Parallel-Vector Symmetrical Equation Solver.- 7.3 Numerical Results and Discussions.- 7.4 FORTRAN Call Statement to Subroutine Node.- 7.5 Summary.- 7.6 Exercises.- 7.7 References.- 8. Parallel-Vector Unsymmetrical Equation Solver.- 8.1 Introduction.- 8.2 Parallel-Vector Unsymmetrical Equation Solution Algorithms.- 8.3 Numerical Evaluations.- 8.4 A Few Remarks On Pivoting Strategies.- 8.5 A FORTRAN Call Statement to Subroutine UNSOLVER.- 8.6 Summary.- 8.7 Exercises.- 8.8 References.- 9. A Tridiagonal Solver for Massively Parallel Computers.- 9.1 Introduction.- 9.2 Basic Sequential Solution Procedures for Tridiagonal Equations.- 9.3 Cyclic Reduction Algorithm.- 9.4 Parallel Tridiagonal Solver by Using Divided and Conquered Strategies.- 9.5 Parallel Factorization Algorithm for Tridiagonal System of Equations UsingSeparators.- 9.6 Forward and Backward Solution Phases.- 9.7 Comparisons between Different Algorithms.- 9.8 Numerical Results.- 9.9 A FORTRAN Call Statement To Subroutine Tridiag.- 9.10 Summary.- 9.11 Exercises.- 9.12 References.- 10. Sparse Equation Solver with Unrolling Strategies.- 10.1 Introduction.- 10.2 Basic Equation Solution Algorithms.- 10.3 Storage Schemes for the Coefficient Stiffness Matrix.- 10.4 Reordering Algorithms.- 10.5 Sparse Symbolic Factorization.- 10.6 Sparse Numerical Factorization.- 10.7 Forward and Backward Solutions.- 10.8 Sparse Solver with Improved Strategies.- 11. Algorithms for Sparse-Symmetrical-Indefinite and Sparse-Unsymmetrical System of Equations.- 11.1 Introduction.- 11.2 Basic Formulation for Indefinite System of Linear Equations.- 11.3 Rotation Matrix [R] Strategies.- 11.4 Natural 2x2 Pivoting.- 11.5 Switching Row(s) and Column(s) During Factorization.- 11.6 Simultaneously Performing Symbolic and Numerical Factorization.- 11.7 Restart Memory Managements.- 11.8 Major Step-by-Step Procedures for Mixed Look Forward/ Backward, Sparse LDLT Factorization, Forward and Backward Solution With 2x2 Pivoting Strategies.- 11.9 Numerical Evaluations.- 11.10 Some Remarks on Unsymmetrical-Sparse System of Linear Equations.- 11.11 Summary.- 11.12 Exercises.- 11.13 References.
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