On generalized discrete PML optimized for propagative and evanescent waves

We suggest a unified spectrally matched optimal grid approach for finite-difference and finite-element approximation of the PML. The new approach allows to combine optimal discrete absorption for both evanescent and propagative waves.

[1]  Vladimir Druskin,et al.  Gaussian Spectral Rules for the Three-Point Second Differences: I. A Two-Point Positive Definite Problem in a Semi-Infinite Domain , 1999, SIAM J. Numer. Anal..

[2]  R. Varga Scientific Computations on Mathematical Problems and Conjectures , 1987 .

[3]  Murthy N. Guddati,et al.  On Optimal Finite-Difference Approximation of PML , 2003, SIAM J. Numer. Anal..

[4]  Vladimir Druskin,et al.  Three-point finite-difference schemes, Padé and the spectral Galerkin method. I. One-sided impedance approximation , 2001, Math. Comput..

[5]  E. Lindman “Free-space” boundary conditions for the time dependent wave equation , 1975 .

[6]  Vladimir Druskin,et al.  Gaussian spectral rules for second order finite-difference schemes , 2000, Numerical Algorithms.

[7]  M. Guddati,et al.  Continued fraction absorbing boundary conditions for convex polygonal domains , 2006 .

[8]  Jean-Pierre Berenger,et al.  A perfectly matched layer for the absorption of electromagnetic waves , 1994 .

[9]  John L. Tassoulas,et al.  CONTINUED-FRACTION ABSORBING BOUNDARY CONDITIONS FOR THE WAVE EQUATION , 2000 .

[10]  A. Majda,et al.  Radiation boundary conditions for acoustic and elastic wave calculations , 1979 .

[11]  Murthy N. Guddati,et al.  Padded continued fraction absorbing boundary conditions for dispersive waves , 2006 .

[12]  Vladimir Druskin,et al.  Optimal finite difference grids and rational approximations of the square root I. Elliptic problems , 2000 .

[13]  Vladimir Druskin,et al.  Application of the Difference Gaussian Rules to Solution of Hyperbolic Problems , 2000 .

[14]  Vladimir Druskin,et al.  Application of the difference Gaussian rules to solution of hyperbolic problems: global expansion , 2002 .

[15]  V. Druskin,et al.  Optimal grids for anisotropic problems , 2006 .