Engineering Commons^™

Efficient Domain Decomposition Algorithms And Applications In Transportation And Structural Engineering, Paul W. Johnson Iii

Civil & Environmental Engineering Theses & Dissertations

Domain decomposition is a divide-and-conquer strategy. In the first part of this dissertation, a new/simple/efficient domain decomposition partitioning algorithm is proposed to break a large domain into smaller sub-domains, in such a way as to minimize the number of system boundary nodes and to balance the work load for each sub-domain. This new domain decomposition algorithm is based on the network’s shortest path solution. Numerical results indicate that the new Shortest Distance Decomposition Algorithm outperformed the most widely used METIS algorithm in 21 out of 27 tested (transportation) examples. In the second part of this dissertation, another new/simple and highly …

Efficient Stand-Alone Generalized Inverse Algorithms And Software For Engineering/Sciences Applications: Research And Education, Subhash Chandra Bose S V Kadiam

Civil & Environmental Engineering Theses & Dissertations

Efficient numerical procedures for finding the generalized (or pseudo) inverse of a general (square/rectangle, symmetrical/unsymmetrical, non-singular/singular, real/complex numbers) matrix and solving systems of Simultaneous Linear Equations (SLE) are formulated and explained. The developed procedures and its associated computer software (under MATLAB computer environment) have been based on "special Cholesky factorization schemes" (for a singular matrix), the generalized inverse of the matrix product, and were further enhanced by the Domain Decomposition (DD) formulation.

Test matrices from different fields of applications have been chosen, tested and compared with other existing algorithms. The results of the numerical tests have indicated that the developed …

Parallel Mpi/Fortran Finite Element Symmetrical/Unsymmetrical Domain Decomposition, Siroj Tungkatara

Civil & Environmental Engineering Theses & Dissertations

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 …