A second order discretization of Maxwell’s equations in the quasi-static regime on OcTree grids. (English) Zbl 1232.65019
Summary: We consider adaptive mesh refinement for the solution of Maxwell’s equations in the quasi-static or diffusion regime. We propose a new finite volume OcTree discretization for the problem and show how to construct second order stencils on Yee grids, extending the known first order discretization stencils. We then develop an effective preconditioner to the problem. We show that our preconditioner performs well for discontinuous conductivities as well as for a wide range of frequencies.
MSC:
65D05 | Numerical interpolation |
65D25 | Numerical differentiation |
65F10 | Iterative numerical methods for linear systems |
65F50 | Computational methods for sparse matrices |
65G30 | Interval and finite arithmetic |
65M06 | Finite difference methods for initial value and initial-boundary value problems involving PDEs |
65M12 | Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs |
65M15 | Error bounds for initial value and initial-boundary value problems involving PDEs |
65M55 | Multigrid methods; domain decomposition for initial value and initial-boundary value problems involving PDEs |
65M50 | Mesh generation, refinement, and adaptive methods for the numerical solution of initial value and initial-boundary value problems involving PDEs |