Fourier Analysis of Numerical Algorithms for the Maxwell Equations

摘要: The Fourier method is used to analyze the dispersive, dissipative, and isotropy errors of various spatial time discretizations applied Maxwell equations on multi-dimensional grids. Both Cartesian grids non-Cartesian based hexagons tetradecahedra are studied compared. numerical quantitatively determined in terms phase speed, wavenumber, propagation direction, gridspacings, CFL number. study shows that centered schemes more efficient accurate than upwind yield superior ones. For schemes, staggered produce less unstaggered A new algorithm which has all best properties introduced. Using an optimization technique determine nodal weights, provides highest accuracy among discussed. also demonstrates a proper choice discretization can reduce overall due discretization.