Parallel computation for the solution of block bordered nonlinear equations and their applications

Thesis/Dissertation · Sun Jan 01 04:00:00 EST 1989

OSTI ID:5815220

Zhang, Xiaodong

The author discusses a group of parallel algorithms, and their implementation, for solving a special class of nonlinear equations arising in VLSI design, structural engineering and other areas. The class of sparsity occurring in these problems is called block bordered structure. He presents the explicit method and several implicit methods for solving block bordered nonlinear problems, and give some mathematical analysis and comparisons of the two methods. Several variations and globally convergent modifications of the implicit method, and the treatment of singular Jacobian matrices are also described. He presents computational results on a sequential computer that help compare and justify the efficiency of the algorithms. He describes parallel algorithms for solving the block bordered nonlinear equations, and present experimental results on both the Encore Multimax, a shared memory multiprocessor, and the Intel hypercube that show the effectiveness of the parallel implicit algorithms. These experiments include a fairly large circuit simulation that leads to a multi-level block bordered system of nonlinear equations.

• Research Organization: Colorado Univ., Boulder, CO (USA)
• OSTI ID: 5815220
• Country of Publication: United States
• Language: English

Related Subjects

99 GENERAL AND MISCELLANEOUS
990200* -- Mathematics & Computers
ALGORITHMS
ARRAY PROCESSORS
BENCH-SCALE EXPERIMENTS
COMPUTER CALCULATIONS
COMPUTERS
DESIGN
ELECTRONIC CIRCUITS
FUNCTIONS
HYPERCUBE COMPUTERS
INTEGRATED CIRCUITS
JACOBIAN FUNCTION
MATHEMATICAL LOGIC
MICROELECTRONIC CIRCUITS
MULTILEVEL ANALYSIS
PARALLEL PROCESSING
PROGRAMMING
SEQUENTIAL CIRCUITS
SIMULATION