Improvement of Numerical Techniques in BEM : Simultaneous Linear Equation

Abstract

The boundary element method requires only discretization on the boundary but demands a memory capacity equivalent to the square of the total degrees of freedom and a computation time proportional to the cube of the total degrees of freedom. For a large-scale problem, since much time is consumed by communication between the main computer and an external memory device, the elapsed time is much longer than the CPU time. With the aim of reducing the elapsed time, we propose herein a new"diagonal escalation"method, which enables solving of simultaneous linear equations using about 1/4 of the normally required memory capacity. We also explored the possibility of using the present method to optimize the solution to both contact and eigenvalue problems, and cited examples of computations that demonstrate the present method's efficiency.