On numerical solution of the complex Helmholtz equation

In this paper we consider numerical methods for solving three-dimensional mixed boundary value problems for the complex Helmholtz equation describing electromagnetic fields with a harmonic time dependence. We propose nondivergent finite volume approximations on parallelepiped and tetrahedral grids, which are based on elementwise technologies calculating local balance matrices and assembling a global matrix. For the iterative solution of the obtained real system of linear algebraic equations (SLAE) with a nonsymmetric sparse high-order matrix we describe a preconditioned semi-conjugate residual method.We give results of numerical experiments for a set of model problems on a sequence of denser grids, which demonstrate the second order of accuracy of grid solutions and a high rate of convergence of iterative processes.