This page is a copy of research/scientific_computing/former/pml (Wed, 31 Aug 2022 15:00:52)
Perfectly Matched absorbing Layers
for wave propagation problems
Participants
- Gunilla Kreiss
- Kenneth Duru, PhD 2012
- Anna Nissen, PhD 2011
Numerical simulation of propagating waves in unbounded spatial domains is a challenge common to many branches of engineering and applied sciences. Relevant application areas are electromagnetism, seismology, acoustics, aerodynamics, oceanography, quantum mechanics. In numerical simulations unbounded domains must be replaced by smaller computational domains. An efficient and reliable domain truncation therefore becomes a vital tool in a numerical wave simulator.
The perfectly matched layer (PML) has proved to be flexible and accurate, for simulating the absorption of waves and provides an alternative to absorbing or non-reflecting boundary conditions (ABC). The PML consists of extending the computational domain to a layer (buffer zone), where the underlying equations are modified such that waves decay rapidly in the layer. The modified equations are perfectly matched to the original equations in the interior. That is, there are no reflections as waves propagate across the interface, into the PML. This approach is analogous to the physical treatment of the walls of the anechoic chambers.
The project
The goal of this project is to construct and analysis PML models for various wave propagation problems.
Applications
Completed work
The PML is usually derived by assuming a homogeneous medium and an infinite domain in all directions. In a domain with physical boundaries, in order to avoid unwanted reflection from the interface, the underlying boundary conditions must be accurately extended from the interior into the PML. These type of problems are important in many applications areas, including seismic, optical and gravitational waves. Examples include glancing waves and surface waves in electromagnetic and elastic wave propagation problems. We are currently extending the PML to these problems and our preliminary results are quite promising.
Future or recently started work includes developing the PML technique for:
Non-linear flow problems modeled by the Euler equations and the Navier-Stokes equations,
underwater acoustics, where we aim at designing absorbing layers that model the open boundary below the seafloor. We are also considering quantum molecular dynamics, where we solve the time dependent Schrödinger equation. This is part of an effort of developing efficient methods for simulating chemical reactions.
Articles
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Numerical interaction of boundary waves with perfectly matched layers in two space dimensional elastic waveguides
. In Wave motion, volume 51, pp 445-465, 2014. (DOI
).
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Efficient and stable perfectly matched layer for CEM
. In Applied Numerical Mathematics, volume 76, pp 34-47, 2014. (DOI
).
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Discrete stability of perfectly matched layers for anisotropic wave equations in first and second order formulation
. In BIT Numerical Mathematics, volume 53, pp 641-663, 2013. (DOI
).
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On the accuracy and stability of the perfectly matched layer in transient waveguides
. In Journal of Scientific Computing, volume 53, pp 642-671, 2012. (DOI
).
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A well-posed and discretely stable perfectly matched layer for elastic wave equations in second order formulation
. In Communications in Computational Physics, volume 11, pp 1643-1672, 2012. (DOI
).
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An optimized perfectly matched layer for the Schrödinger equation
. In Communications in Computational Physics, volume 9, pp 147-179, 2011. (DOI
).
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Error control for simulations of a dissociative quantum system
. In Numerical Mathematics and Advanced Applications: 2009, pp 523-531, Springer-Verlag, Berlin, 2010. (DOI
).
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Stable perfectly matched layers for the Schrödinger equations
. In Numerical Mathematics and Advanced Applications: 2009, pp 287-295, Springer-Verlag, Berlin, 2010. (DOI
).
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A perfectly matched layer applied to a reactive scattering problem
. In Journal of Chemical Physics, volume 133, pp 054306:1-11, 2010. (DOI
).
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Application of a perfectly matched layer to the nonlinear wave equation
. In Wave motion, volume 44, pp 531-548, 2007. (DOI
).
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Perfectly matched layers for hyperbolic systems: General formulation, well-posedness, and stability
. In SIAM Journal on Applied Mathematics, volume 67, pp 1-23, 2006. (DOI
).
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A new absorbing layer for elastic waves
. Daniel Appelö and Gunilla Kreiss. In Journal of Computational Physics, volume 215, pp 642-660, 2006.
Theses
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Perfectly Matched Layers and High Order Difference Methods for Wave Equations
. Ph.D. thesis, Digital Comprehensive Summaries of Uppsala Dissertations from the Faculty of Science and Technology nr 931, Acta Universitatis Upsaliensis, Uppsala, 2012. (fulltext
).
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High Order Finite Difference Methods with Artificial Boundary Treatment in Quantum Dynamics
. Ph.D. thesis, Digital Comprehensive Summaries of Uppsala Dissertations from the Faculty of Science and Technology nr 864, Acta Universitatis Upsaliensis, Uppsala, 2011. (fulltext
).
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Perfectly matched layers for second order wave equations
. Licentiate thesis, IT licentiate theses / Uppsala University, Department of Information Technology nr 2010-004, Uppsala University, 2010. (fulltext
).
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Absorbing boundary techniques for the time-dependent Schrödinger equation
. Licentiate thesis, IT licentiate theses / Uppsala University, Department of Information Technology nr 2010-001, Uppsala University, 2010. (fulltext
).
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Absorbing Layers and Non-Reflecting Boundary Conditions for Wave Propagation Problems
. Daniel Appelö. Ph.D. thesis, Trita-NA / Royal Institute of Technology, Department of Numerical Analysis and Computing Science nr 0534, 2005.
Contact: , Gunilla Kreiss