Siroj Tungkahotara

A domain decomposition (DD) formulation for solving sparse linear systems of equations resulting from finite element analysis is presented. The formulation incorporates mixed direct and iterative equation solving strategies and other novel algorithmic ideas that are optimized to take advantage of sparsity and exploit modern computer architecture, such as memory and parallel computing. The most time consuming part of the formulation is identified and the critical roles of direct sparse and iterative solvers within the framework of the formulation are discussed. Experiments on several computer platforms using real and complex test matrices are conducted using software based on the formulation. Small-scale structural examples are used to validate the steps in the formulation and large-scale (1,000,000+ unknowns) duct acoustic examples are used to evaluate the parallel performance of the formulation. Results are presented using 64 SUN 10000, 8 SGI ORIGIN 2000 processors, and a cluster of 6 PCs (running under the Windows environment). Statistics show that the formulation is efficient in both sequential and parallel computing environments and that the formulation is significantly faster and consumes less memory than that based on one of the best available commercialized parallel sparse solvers.

Comparing two sequences by using dynamic programming algorithms is studied. Both serial and (multiple processor) parallel computer algorithms are discussed. Numerical performance of the developed software is validated through small to large-scale applications. Results (based upon comparing 2 large sequences with 40,000 and 36,000 character length, respectively, and using 2-24 parallel processors) indicate that the developed software is reliable and highly efficient.

Details of parallel-sparse Domain Decomposition (DD) with multi-point constraints (MPC) formulation are explained. Major computational components of the DD formulation are identified. Critical roles of parallel (direct) sparse and iterative solvers with MPC are discussed within the framework of DD formulation. Both symmetrical and unsymmetrical system of simultaneous linear equations (SLE) can be handled by the developed DD formulation. For symmetrical SLE, option for imposing MPC equations is also provided. Large-scale (up to 25 million unknowns involving complex numbers) structural and acoustic Finite Element (FE) analysis are used to evaluate the parallel computational performance of the proposed DD implementation using different parallel computer platforms. Numerical examples show that the authors' MPI/FORTRAN code is significantly faster than the commercial parallel sparse solver. Furthermore, the developed software can also conveniently and efficiently solve large SLE with MPCs, a feature not available in almost all commercial parallel sparse solvers.

MPI/FORTRAN finite element analysis software based on Domain Decomposition (DD) formulas has been developed in this work. Efficient input data storage/data communication schemes, domain partitioning, fast symbolical and numerical sparse assembly, symmetrical/unsymmetrical sparse solver and robust symmetrical/unsymmetrical iterative solvers algorithms are all incorporated into the developed code. Parallel Precondition Conjugated Gradient (PCG) and Flexible Generalized Minimum Residual (FGMRES) are developed. Efficient computational techniques used in the developed code are explained. Numerical performance and the accuracy of the developed code are conducted on acoustic examples with medium to large grid sizes. The results obtained from ODU Wilbur cluster (under parallel processing computer environments) have revealed the super-linear speedup in 3-D symmetrical acoustic examples. The robustness and the minimum in-core memory usage of the code are also observed.