The Barycentric Finite Volume Method for3D Helmholtz Complex Equation
A. V. Petukhov
Institute of Computational Mathematics and Mathematical Geophysics, SB RAS Novosibirsk, Russia, E-mail: mnu@ngs.ru
Pages: 182-191
Abstract
Numerical methods for solving 3D mixed boundary-value problems for a Helmholtz complex equation describing electromagnetic fields with the time-harmonic dependence are presented. Divergence-free barycentric finite volume approximations on tetrahedral grids are proposed. Computation of the local balance matrices and assembling of the global matrix are based on element-by-element technologies. A preconditioned semi-conjugate residual method is described for iterative solving the resulting real system of linear algebraic equations with a nonsymmetric sparse high-order matrix. Results of numerical experiments for a series of model problems on a sequence of refined grids are presented. The results demonstrate the second-order accuracy of the grid solutions and the high convergence rate of the iterative processes
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