A platform for research: civil engineering, architecture and urbanism
A platform for research: civil engineering, architecture and urbanism
Perfectly Matched Layers for Time-Harmonic Second Order Elliptic Problems
Abstract The main goal of this work is to give a review of the Perfectly Matched Layer (PML) technique for time-harmonic problems. Precisely, we focus our attention on problems stated in unbounded domains, which involve second order elliptic equations writing in divergence form and, in particular, on the Helmholtz equation at low frequency regime. Firstly, the PML technique is introduced by means of a simple porous model in one dimension. It is emphasized that an adequate choice of the so called complex absorbing function in the PML yields to accurate numerical results. Then, in the two-dimensional case, the PML governing equation is described for second order partial differential equations by using a smooth complex change of variables. Its mathematical analysis and some particular examples are also included. Numerical drawbacks and optimal choice of the PML absorbing function are studied in detail. In fact, theoretical and numerical analysis show the advantages of using non-integrable absorbing functions. Finally, we present some relevant real life numerical simulations where the PML technique is widely and successfully used although they are not covered by the standard theoretical framework.
Perfectly Matched Layers for Time-Harmonic Second Order Elliptic Problems
Abstract The main goal of this work is to give a review of the Perfectly Matched Layer (PML) technique for time-harmonic problems. Precisely, we focus our attention on problems stated in unbounded domains, which involve second order elliptic equations writing in divergence form and, in particular, on the Helmholtz equation at low frequency regime. Firstly, the PML technique is introduced by means of a simple porous model in one dimension. It is emphasized that an adequate choice of the so called complex absorbing function in the PML yields to accurate numerical results. Then, in the two-dimensional case, the PML governing equation is described for second order partial differential equations by using a smooth complex change of variables. Its mathematical analysis and some particular examples are also included. Numerical drawbacks and optimal choice of the PML absorbing function are studied in detail. In fact, theoretical and numerical analysis show the advantages of using non-integrable absorbing functions. Finally, we present some relevant real life numerical simulations where the PML technique is widely and successfully used although they are not covered by the standard theoretical framework.
Perfectly Matched Layers for Time-Harmonic Second Order Elliptic Problems
Bermúdez, A. (author) / Hervella-Nieto, L. (author) / Prieto, A. (author) / Rodríguez, R. (author)
2010
Article (Journal)
Electronic Resource
English
Time harmonic analysis of dam-foundation systems by perfectly matched layers
| British Library Online Contents | 2014
Parametric finite elements, exact sequences and perfectly matched layers
| British Library Online Contents | 2013
Efficient Unsplit Perfectly Matched Layers for Finite-Element Time-Domain Modeling of Elastodynamics
| Online Contents | 2016
Elliptic Harbor Wave Model with Perfectly Matched Layer and Exterior Bathymetry Effects
| British Library Online Contents | 2016
Efficient Unsplit Perfectly Matched Layers for Finite-Element Time-Domain Modeling of Elastodynamics
| Online Contents | 2016