Parametric finite elements, exact sequences and perfectly matched layers
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- Matuszyk, P.J. & Demkowicz, L.F. Comput Mech (2013) 51: 35. doi:10.1007/s00466-012-0702-1
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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.