Numerical computation of large partial differential equations on memory hierarchy

Abstract

AbstractOften, partial differential equations for the case of numerical computation are solved. However, to solve partial differential equations whose order of dimensions are more than 2, main memory is not large enough even in the main frame or super computers, not to mention workstations or personal computers. Thus, we have to use external memory to solve large partial differential equations numerically. This paper proposes an algorithm to solve numerically by explicit methods, large partial differential equations which are time‐dependent and have fixed boundary conditions. In this algorithm, neighbor mesh points are placed together in main memory. Also, even partially, they are computed toward the time axis as far as possible. In other words, this method computes mesh points toward the time axis with priority, reusing computed data in main memory. The proposed algorithm is unique in this point. It is faster than conventional methods in proportion to D√P where P is the bulk of the main memory and D is the order of dimensions.