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COMPUTATIONAL METHODS FOR ACOUSTICS PROBLEMS
Edited by: F. Magoulès
Perfectly Matched Discrete Layers for Unbounded Domain Modeling
M.N. Guddati1, K.W. Lim2 and M.A. Zahid3
1North Carolina State University, Raleigh NC, United States of America
M.N. Guddati, K.W. Lim, M.A. Zahid, "Perfectly Matched Discrete Layers for Unbounded Domain Modeling", in F. Magoulès, (Editor), "Computational Methods for Acoustics Problems", Saxe-Coburg Publications, Stirlingshire, UK, Chapter 3, pp 69-98, 2008. doi:10.4203/csets.18.3
Keywords: absorbing boundary conditions, non-reflecting boundary conditions, perfectly matched layers, wave propagation, finite elements, finite differences.
Perfectly Matched Layers (PML) have been very successful in modeling unbounded domains, but suffer from two disadvantages: (a) they are no longer perfectly matched when discretized and (b) significant care is needed to design the stretching function to minimize the reflections. This chapter outlines a simple variant of PML that eliminates these disadvantages. It is shown that the use of linear discretization with midpoint integration makes the layers perfectly matched even after discretization. Called perfectly matched discrete layers (PMDL), they are also linked to the continued fraction approximation of the exact impedance operator, and thus to all the existing local absorbing boundary conditions (ABCs). By relating PML and local ABCs, PMDL combines the computational efficiency of local ABCs with the broader applicability of PML. This chapter contains the basic ideas behind PMDL as well as the illustration of its effectiveness using various numerical examples.
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