Block algorithm for the joint difference solution of the d’Alembert and Maxwell’s equations

Abstract

A characteristic feature of mathematical modeling at the present stage of development is the consideration of the architecture of the computer system, not only for stage of compiling a computer program, but also during the development of a numerical method and synthesis of the mathematical model. This method significantly broadens the researcher's ability to search for the optimal mapping of the numerical method to the mentioned architecture, in the sense of accelerating computations. In this paper, this idea is illustrating by examples of the basic mathematical model of computational electrodynamics and optics, Maxwell's equations, and the FDTD. This modification allows to reducing the data exchange rate between the operational and cache memory due to the greater number of arithmetic operations per one grid function in solving the d'Alembert equation. On the other hand, freely use the technologies FDTD method and ready-made software implementations for setting the incident wave, imposing the absorbing layers, taking into account the dispersion of the medium.

Research of parallel algorithms for solving three-diagonal systems of linear algebraic equations on a graphical computing device using various types of memory

“…The applicability of systems of linear equations of tridiagonal form is very extensive [1]. Tridiagonal matrices have an extremely important role in difference methods of solving problems of mathematical physics [2]. In addition, many linear algebra problems, such as solving equations and finding eigenvalues, are solved through transformations of matrices of general form to tridiagonal ones [3].…”