Load-balanced parallel banded-system solvers

Abstract

Solving banded systems is important in the applications of science and engineering. This paper presents a load-balancing strategy for solving banded systems in parallel when the number of processors used is small. An optimization-based load-balancing analysis is given to determine how many loads should be assigned to each processor in order to minimize the time requirement. Some experimentations are carried out on the nCUBE 2E multiprocessor to demonstrate the speedup advantage of the proposed load-balancing strategy. The speedup improvement ratio ranges from $\text{47\%}$ to $\text{66\%}$ (from $\text{12\%}$ to $\text{24\%}$) when using 4 (8) processors.