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Optimizing perfectly matched layers in discrete contexts
Author(s) -
Modave A.,
Delhez E.,
Geuzaine C.
Publication year - 2014
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.4690
Subject(s) - function (biology) , mathematics , harmonic , finite element method , mathematical optimization , computer science , mathematical analysis , physics , engineering , acoustics , structural engineering , evolutionary biology , biology
SUMMARY Perfectly matched layers (PMLs) are widely used for the numerical simulation of wave‐like problems defined on large or infinite spatial domains. However, for both time‐dependent and time‐harmonic cases, their performance critically depends on the so‐called absorption function. This paper deals with the choice of this function when classical numerical methods are used (based on finite differences, finite volumes, continuous finite elements and discontinuous finite elements). After reviewing the properties of the PMLs at the continuous level, we analyze how they are altered by the different spatial discretizations. In the light of these results, different shapes of absorption function are optimized and compared by means of both one‐dimensional and two‐dimensional representative time‐dependent cases. This study highlights the advantages of the so‐called shifted hyperbolic function, which is efficient in all cases and does not require the tuning of a free parameter, by contrast with the widely used polynomial functions. Copyright © 2014 John Wiley & Sons, Ltd.