PSU Mark
Eberly College of Science Mathematics Department

Meeting Details

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Title:Perfectly Matched Layers and Absorbing Boundary Conditions: Unification of Concepts and Extension to Subsurface Imaging and Molecular Dynamics
Seminar:CCMA PDEs and Numerical Methods Seminar Series
Abstract Link:
Domain truncation techniques are of paramount importance in accurate modeling of wave propagation in unbounded domains. Many techniques were developed in the past thirty years, and are often classified into: a. exact global absorbing boundary conditions or Dirichlet-to-Neumann maps (DtN, e.g. [1]); b. approximate local absorbing boundary conditions (ABC, e.g. [2,3]); and c. perfectly matched layers (PML, [4]). While the three classes are considered conceptually disparate by many researchers, we show that there are close links between them. In this talk, the three classes will be analyzed using a model problem with the goal of illustrating various links. Utilizing these links, we propose boundary conditions that combine the respective advantages of DtN, ABC and PML. The resulting boundary conditions are implemented in various settings including (time-harmonic and transient) acoustics and elastodynamics; numerical results will be presented to illustrate the effectiveness of these implementations. The talk will also outline some advances facilitated by the underlying ideas in the fields of subsurface imaging and molecular dynamics. It will conclude with some thoughts on current limitations and possible extensions to the proposed method. Some of the ideas of the development can be found in references [5-9]. References [1] E.Kausel and J.L.Tassoulas, “Transmitting boundaries – a closed form comparison,” Bulletin of Seismological Society of America, v.71, pp.143-159, 1981. [2] B.Engquist, and A.Majda, “Absorbing boundary-conditions for numerical simulation of waves,” Mathematics of Computation, v.31, pp.629-651, 1977. [3] R.L.Higdon, “Numerical absorbing boundary conditions for the wave equations,” Mathematics of Computation, v.49, pp.65-90, 1987. [4] J.P.Berenger, “A Perfectly Matched Layer for the absorption of electromagnetic waves,” Journal of Computational Physics, v.114, pp.185-200, 1994. [5] M.N.Guddati, “Arbitrarily Wide Angle Wave Equations for Complex Media,” Computer Methods in Applied Mechanics and Engineering, v.195, pp.65-93, 2006. [6] M.N.Guddati and K.W.Lim, “Continued Fraction Absorbing Boundary Conditions for Convex Polygonal Domains,” International Journal for Numerical Methods in Engineering, v. 66, pp. 949-977, 2006. [7] M.A.Zahid and M.N.Guddati, “Padded Continued Fraction Absorbing Boundaries for Dispersive Waves,” Computer Methods in Applied Mechanics and Engineering, in press. [8] S.Asvadurov, V.Druskin, M.N.Guddati and L.Knizhnerman, “On Optimal Finite-Difference Approximation of PML”, SIAM Journal on Numerical Analysis, v.41, pp.287-305, 2003. [9] M.N.Guddati and J.L.Tassoulas, “Continued Fraction Absorbing Boundary Conditions for the Wave Equation,” Journal of Computational Acoustics, v.8, pp.139-156, 2000.

Room Reservation Information

Room Number:MB216
Date:09 / 25 / 2007
Time:01:25pm - 02:15pm