Introduction / 1.: |
Parallel Computers / 1.1: |
Measurements for Algorithms' Performance / 1.2: |
Vector Computers / 1.3: |
Summary / 1.4: |
Exercises / 1.5: |
References / 1.6: |
Storage Schemes for the Coefficient Stiffness Matrix / 2.: |
Full Matrix / 2.1: |
Symmetrical Matrix / 2.3: |
Banded Matrix / 2.4: |
Variable Banded Matrix / 2.5: |
Skyline Matrix / 2.6: |
Sparse Matrix / 2.7: |
Detailed Procedures For Determining The Mapping Between 2-D Array and 1-D Array in Skyline Storage Scheme / 2.8: |
Determination of the Column Height (ICOLH) of a Finite Element Model / 2.9: |
Computer Implementation For Determining Column Heights / 2.10: |
Parallel Algorithms for Generation and Assembly of Finite Element Matrices / 2.11: |
Conventional Algorithm to Generate and Assemble Element Matrices / 3.1: |
Node-by-Node Parallel Generation and Assembly Algorithms / 3.3: |
Additional Comments on Baddourah-Nguyen's (Node-by-Node) Parallel Generation and Assembly (GandA) Algorithm / 3.4: |
Application of Baddourah-Nguyen's Parallel GandA Algorithm / 3.5: |
Qin-Nguyen's GandA Algorithm / 3.6: |
Applications of Qin-Nguyen's Parallel GandA Algorithm / 3.7: |
Parallel-Vector Skyline Equation Solver on Shared Memory Computers / 3.8: |
Choleski-based Solution Strategies / 4.1: |
Factorization / 4.3: |
Basic sequential skyline Choleski factorization: computer code (version 1) / 4.3.1: |
Improved basic sequential skyline Choleski factorization: computer code (version 2) / 4.3.2: |
Parallel-vector Choleski factorization (version 3) / 4.3.3: |
Parallel-vector (with "few" synchronization checks) Choleski factorization (version 4) / 4.3.4: |
Parallel-vector enhancement (vector unrolling) Choleski factorization (version 5) / 4.3.5: |
Parallel-vector (unrolling) skyline Choleski factorization (version 6) / 4.3.6: |
Solution of Triangular Systems / 4.4: |
Forward solution / 4.4.1: |
Backward solution / 4.4.2: |
Force: A Portable, Parallel FORTRAN Language / 4.5: |
Evaluation of Methods on Example Problems / 4.6: |
Skyline Equation Solver Computer Program / 4.7: |
Parallel-Vector Variable Bandwidth Equation Solver on Shared Memory Computers / 4.8: |
Data Storage Schemes / 5.1: |
Basic Sequential Variable Bandwidth Choleski Method / 5.3: |
Vectorized Choleski Code with Loop Unrolling / 5.4: |
More on Force: A Portable, Parallel FORTRAN Language / 5.5: |
Parallel-Vector Choleski Factorization / 5.6: |
Relations Amongst the Choleski, Gauss and LDL[superscript T] Factorizations / 5.7: |
Choleski (U[superscript T]U) factorization / 5.8.1: |
Gauss (with diagonal terms L[subscript ii]=1) LU factorization / 5.8.2: |
Gauss (LU) factorization with diagonal terms U[subscript ii]=1 / 5.8.3: |
LDL[superscript T] factorization with diagonal term L[subscript ii]=1 / 5.8.4: |
Similarities of Choleski and Gauss methods / 5.8.5: |
Factorization Based Upon "Look Backward" Versus "Look Forward" Strategies / 5.9: |
Evaluation of Methods For Structural Analyses / 5.10: |
High speed research aircraft / 5.10.1: |
Space shuttle solid rocket booster (SRB) / 5.10.2: |
Descriptions of Parallel-Vector Subroutine PVS / 5.11: |
Parallel-Vector Equation Solver Subroutine PVS / 5.12: |
Parallel-Vector Variable Bandwidth Out-of-Core Equation Solver / 5.13: |
Out-of-Core Parallel/Vector Equation Solver (version 1) / 6.1: |
Memory usage and record length / 6.2.1: |
A synchronous input/output on Cray computers / 6.2.2: |
Brief summary for parallel-vector incore equation solver on the Cray Y-MP / 6.2.3: |
Parallel-vector out-of-core equation solver on the Cray Y-MP / 6.2.4: |
Out-of-Core Vector Equation Solver (version 2) / 6.3: |
Memory usage / 6.3.1: |
Vector out-of-core equation solver on the Cray Y-MP / 6.3.2: |
Out-of-Core Vector Equation Solver (version 3) / 6.4: |
Application / 6.5: |
Version 1 performance / 6.5.1: |
Version 2 performance / 6.5.2: |
Version 3 performance / 6.5.3: |
Parallel-Vector Skyline Equation Solver for Distributed Memory Computers / 6.6: |
Parallel-Vector Symmetrical Equation Solver / 7.1: |
Basic symmetrical equation solver / 7.2.1: |
Parallel-vector performance improvement in decomposition / 7.2.2: |
Communication performance improvement in factorization / 7.2.3: |
Forward/backward elimination / 7.2.4: |
Numerical Results and Discussions / 7.3: |
FORTRAN Call Statement to Subroutine Node / 7.4: |
Parallel-Vector Unsymmetrical Equation Solver / 7.5: |
Parallel-Vector Unsymmetrical Equation Solution Algorithms / 8.1: |
Basic unsymmetric equation solver / 8.2.1: |
Detailed derivation for the [L] and [U] matrices / 8.2.2: |
Basic algorithm for decomposition of "full" bandwidth/column heights unsymmetrical matrix / 8.2.3: |
Basic algorithm for decomposition of "variable" bandwidths/column heights unsymmetrical matrix / 8.2.4: |
Algorithms for decomposition of "variable" bandwidths/column heights unsymmetrical matrix with unrolling strategies / 8.2.5: |
Parallel-vector algorithm for factorization / 8.2.6: |
Forward solution phase [L]{y}={b} / 8.2.7: |
Backward solution phase [U] {x{ = {y{ / 8.2.8: |
Numerical Evaluations / 8.3: |
A Few Remarks On Pivoting Strategies / 8.4: |
A FORTRAN Call Statement to Subroutine UNSOLVER / 8.5: |
A Tridiagonal Solver for Massively Parallel Computers / 8.6: |
Basic Sequential Solution Procedures for Tridiagonal Equations / 9.1: |
Cyclic Reduction Algorithm / 9.3: |
Parallel Tridiagonal Solver by Using Divided and Conquered Strategies / 9.4: |
Parallel Factorization Algorithm for Tridiagonal System of Equations Using Separators / 9.5: |
Forward and Backward Solution Phases / 9.6: |
Forward solution phase: [L] {z} = {y} / 9.6.1: |
Backward solution phase: [U] {x} = {z} / 9.6.2: |
Comparisons between Different Algorithms / 9.7: |
Numerical Results / 9.8: |
A FORTRAN Call Statement To Subroutine Tridiag / 9.9: |
Sparse Equation Solver with Unrolling Strategies / 9.10: |
Basic Equation Solution Algorithms / 10.1: |
Choleski algorithm / 10.2.1: |
LDL[superscript T] algorithm / 10.2.2: |
Reordering Algorithms / 10.3: |
Sparse Symbolic Factorization / 10.5: |
Sparse Numerical Factorization / 10.6: |
Forward and Backward Solutions / 10.7: |
Forward substitution phase / 10.7.1: |
Backward substitution phase / 10.7.2: |
Sparse Solver with Improved Strategies / 10.8: |
Finding master (or super) degree-of-freedom (dof) / 10.8.1: |
Sparse matrix (with unrolling strategies) times vector / 10.8.2: |
Modifications for the chained list array ICHAINL (-) / 10.8.3: |
Sparse numerical factorization with unrolling strategies / 10.8.4: |
Out-of-core sparse equation solver with unrolling strategies / 10.8.5: |
Numerical Performance of the Developed Sparse Equation Solver / 10.9: |
FORTRAN Call Statement to SPARSE Equation Solver / 10.10: |
Algorithms for Sparse-Symmetrical-Indefinite and Sparse-Unsymmetrical System of Equations / 10.11: |
Basic Formulation for Indefinite System of Linear Equations / 11.1: |
Rotation Matrix [R] Strategies / 11.3: |
Natural 2 x 2 Pivoting / 11.4: |
Switching Row(s) and Column(s) During Factorization / 11.5: |
Simultaneously Performing Symbolic and Numerical Factorization / 11.6: |
Restart Memory Managements / 11.7: |
Major Step-by-Step Procedures for Mixed Look Forward/Backward, Sparse LDL[superscript T] Factorization, Forward and Backward Solution With 2x2 Pivoting Strategies / 11.8: |
Some Remarks on Unsymmetrical-Sparse System of Linear Equations / 11.9: |
Index / 11.11: |
Introduction / 1.: |
Parallel Computers / 1.1: |
Measurements for Algorithms' Performance / 1.2: |
Vector Computers / 1.3: |
Summary / 1.4: |
Exercises / 1.5: |