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.