ИСТИНА

New iterative numerical solver for 3d integral equations of electrodynamics was developed. While the other solvers are based on the collocation method, this one is based on the projective method for integral equations solving. The key feature of this solver is a high degree of parallelism. The computational experiments performed by “Bluegene/P” and “Lomonosov” supercomputers from MSU show that it makes the best use of 128-2048 nodes for calculation at single frequency and single source. The maximum number of the used nodes is 2*max(Nx, Ny), where Nx and Ny are the numbers of model cells in X and Y direction respectively. The main computational challenge of projective approach is in evaluation of coefficients of a corresponding system of linear equations, i.e. the double volumetric integrals of the Green's tensor of the layered media. The Green's tensor components are the improper integrals containing the Bessel functions. While the integration in vertical direction can be performed analytically, the integration over the horizontal domains involves the fifth-order integrals over the fast-oscillating functions. In order to compute these integrals we do the following.Changing the order of integration and making the appropriate substitution allows converting the fifth-order integral to the convolution with the special kernel. Then we compute the spectrum of this kernel and build the quadrature formula based on Shannon's interpolation. It is important to stress that both the nodes and the weights in the obtained formula significantly depend on the integration domains. At the same time their computational cost is independent of the integration domains.