Efficient fast direct method of solving Poisson’s equation on a parallelepiped and its implementation in an array processor. (English) Zbl 0825.65077
Summary: The paper treats problems of adjusting the structure of the computational algorithms to the architecture of a computer system with an array processor. The authors suggest a method of simulating the computational algorithms. Simulation makes it possible to determine the parameters of efficient implementation of the algorithm for the a priori prescribed level of performance of a specific computer system. As an example of the implementation of the method suggested, algorithms are analysed for the realization of a new fast direct method of solving Poisson’s equation on a parallelepiped. The results of numerical experiments are presented.
MSC:
65N06 | Finite difference methods for boundary value problems involving PDEs |
65Y10 | Numerical algorithms for specific classes of architectures |
65Y20 | Complexity and performance of numerical algorithms |
68M01 | General theory of computer systems |
35J05 | Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation |