Parametric finite elements, exact sequences and perfectly matched layers

The paper establishes a relation between exact sequences, parametric finite elements, and perfectly matched layer (PML) techniques. We illuminate the analogy between the Piola-like maps used to define parametric H1-, H(curl)-, H(div)-, and L2-conforming elements, and the corresponding PML complex coordinates stretching for the same energy spaces. We deliver a method for obtaining PML-stretched bilinear forms (constituting the new weak formulation for the original problem with PML absorbing boundary layers) directly from their classical counterparts.

[1]  Qing Huo Liu,et al.  PERFECTLY MATCHED LAYERS FOR ELASTODYNAMICS: A NEW ABSORBING BOUNDARY CONDITION , 1996 .

[2]  Jin-Fa Lee,et al.  A perfectly matched anisotropic absorber for use as an absorbing boundary condition , 1995 .

[3]  Yibing Zheng,et al.  Anisotropic Perfectly Matched Layers for Elastic Waves in Cartesian and Curvilinear Coordinates , 2002 .

[4]  Maciej Paszyński,et al.  Computing with hp-ADAPTIVE FINITE ELEMENTS: Volume II Frontiers: Three Dimensional Elliptic and Maxwell Problems with Applications , 2007 .

[5]  Leszek Demkowicz,et al.  Improving the performance of perfectly matched layers by means of hp‐adaptivity , 2007, Numerical Methods for Partial Differential Equations.

[6]  Weng Cho Chew,et al.  A 3D perfectly matched medium from modified maxwell's equations with stretched coordinates , 1994 .

[7]  J. Vilotte,et al.  The Newmark scheme as velocity–stress time-staggering: an efficient PML implementation for spectral element simulations of elastodynamics , 2005 .

[8]  Qing Huo Liu,et al.  The perfectly matched layer for acoustic waves in absorptive media , 1997 .

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

[10]  Fernando L. Teixeira,et al.  General closed-form PML constitutive tensors to match arbitrary bianisotropic and dispersive linear media , 1998 .

[11]  W. Chew,et al.  Complex space approach to perfectly matched layers: a review and some new developments , 2000 .

[12]  Peter Monk,et al.  The Perfectly Matched Layer in Curvilinear Coordinates , 1998, SIAM J. Sci. Comput..

[13]  Qing Huo Liu,et al.  The application of the perfectly matched layer in numerical modeling of wave propagation in poroelastic media , 2001 .

[14]  Yibing Zheng,et al.  New anisotropic perfectly matched layer boundary condition for elastic waves in solids , 2002 .

[15]  L. Demkowicz.  One and two dimensional elliptic and Maxwell problems , 2006 .

[16]  Leszek Demkowicz,et al.  Polynomial Exact Sequences and Projection-Based Interpolation with Application to Maxwell Equations , 2008 .

[17]  Patrick Joly,et al.  Stability of perfectly matched layers, group velocities and anisotropic waves , 2003 .

[18]  E. Michielssen,et al.  Complex coordinate system as a generalized absorbing boundary condition , 1997, IEEE Antennas and Propagation Society International Symposium 1997. Digest.

[19]  Weng Cho Chew,et al.  Analytical derivation of a conformal perfectly matched absorber for electromagnetic waves , 1998 .

[20]  W. Chew,et al.  Systematic derivation of anisotropic PML absorbing media in cylindrical and spherical coordinates , 1997 .