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 H 1 -, H (curl)-, H (div)-, and L 2 -conforming elements, and the corresponding PML comp...

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Bibliographic Details
Published in:Computational mechanics 2013, Vol.51 (1), p.35-45
Main Authors: Matuszyk, Pawel J., Demkowicz, Leszek F.
Format: Article
Language:English
Subjects:
Absorption
Analogies
Boundary layers
Classical and Continuum Physics
Computational Science and Engineering
Energy use
Engineering
Finite element method
Mathematical analysis
Original Paper
Perfectly matched layers
Stretching
Theoretical and Applied Mechanics
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Summary: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 H 1 -, H (curl)-, H (div)-, and L 2 -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.
ISSN:0178-7675
1432-0924
DOI:10.1007/s00466-012-0702-1