Efficient and stable perfectly matched layer for CEM

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• 作者：Kenneth Duru ; Gunilla Kreiss
• 关键词：Maxwell始s equations ; Fourier analysis ; Perfectly matched layers ; Energy estimates ; Well-posedness ; Stability ; High order accuracy ; Efficiency
• 刊名：Applied Numerical Mathematics
• 出版年：February, 2014
• 年：2014
• 卷：76
• 期：Complete
• 页码：34-47
• 全文大小：1010 K

文摘

An efficient unsplit perfectly matched layer for numerical simulation of electromagnetic waves in unbounded domains is derived via a complex change of variables. In order to surround a Cartesian grid with the PML, the time-dependent PML requires only one (scalar) auxiliary variable in two space dimensions and six (scalar) auxiliary variables in three space dimensions. It is therefore cheap and straightforward to implement. We use Fourier and energy methods to prove the stability of the PML. We extend the stability result to a semi-discrete PML approximated by central finite differences of arbitrary order of accuracy and to a fully discrete problem for the 鈥楲eap-Frog鈥?schemes. This makes precise the usefulness of the derived PML model for longtime simulations. Numerical experiments are presented, illustrating the accuracy and stability of the PML.