A Comparison of Transparent Boundary Conditions for the Fresnel Equation
Please always quote using this URN: urn:nbn:de:0297-zib-5738
- We establish the relationship between the transparent boundary condition (BPP) of Baskakov and Popov [Wave Motion 14 (1991) 121-128] and Pakpadakis et. al. [J. Acoust. Soc. Am. 92 (1992) 2030-2038] and a second boundary condition (SDY) introduced by Schmidt and Deuflhard [Comp. Math. Appl. 29 (1995) 53-76] and Schmidt and Yevick [J. Compu. Phys. 134 (1997) 96-107], that is explicitly tailored to the form of the underlying numerical propagation scheme. Our analysis demonstrates that if the domain is first discretized in the propagation direction, the SDY expression can be obtained by applying the exact sequence of steps used to derive the BPP procedure. The BPP method is thus an approximate realization of the computationally far simpler and unconditionally stable SDY boundary condition.
Author: | David Yevick, Tilmann Friese, Frank Schmidt |
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Document Type: | ZIB-Report |
Tag: | Fresnel equation; transparent boundary condition |
MSC-Classification: | 65-XX NUMERICAL ANALYSIS / 65Mxx Partial differential equations, initial value and time-dependent initial- boundary value problems / 65M06 Finite difference methods |
Date of first Publication: | 2000/03/03 |
Series (Serial Number): | ZIB-Report (00-05) |
ZIB-Reportnumber: | 00-05 |
Published in: | Appeared in: J. Comput. Phys. 168 (2001) 433-444 |