Parallel-Vector Equation Solvers for Finite Element Engineering Applications

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.