Department of Applied Mathematics, Okayama University of Science
Abstract
The paper presents a numerical method for solving an initial-boundary value problem of heat equations. The boundary matrix method, which is a kind of boundary element method, is formulated for the one-dimensional problem. The solution procedure is applied to two-and three-dimensional problems with the local one-dimensional method. Although the present method is a kind of implicit method, it is easy to describe it with an explicit form. It means that it is unnecessary to solve a large linear system to proceed the numerical time integration. The present algorithm suits a vector computer since two-and three-dimensional problems are reduced to one-dimensional problems. We show some numerical examples to verify the method, numerically and discuss the ratio of vectorization on the supercomputer VP30E. Consequently, we develop the program whichi has 99.6% vectorization
