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Transparent Boundary Conditions for Split-Step Pade Approximations of the One-Way Helmholtz Equation
Please always quote using this URN: urn:nbn:de:0297-zib-4353
- In this paper, we generalize the nonlocal discrete transparent boundary condition introduced by Schmidt and Deuflhard {[}Comp. Math. Appl. 29 (1995) 53-76{]} and Schmidt and Yevick {[}J. Comput. Phys. 134 (1997) 96-107{]} to propagation methods based on arbitrary Pad\'e approximations to the two-dimensional one-way Helmholtz equation. Our approach leads to a recursive formula for the coefficients appearing in the nonlocal condition which then yields an unconditionally stable propagation method.
Author: | Frank Schmidt, Tilmann Friese, David Yevick |
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Document Type: | ZIB-Report |
Tag: | Finite-element method; Helmholtz equation; Pad/'e split step approximation; Transparent boundary conditions; Wide-angle approximation |
MSC-Classification: | 65-XX NUMERICAL ANALYSIS / 65Mxx Partial differential equations, initial value and time-dependent initial- boundary value problems / 65M55 Multigrid methods; domain decomposition |
65-XX NUMERICAL ANALYSIS / 65Mxx Partial differential equations, initial value and time-dependent initial- boundary value problems / 65M60 Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods | |
Date of first Publication: | 1999/12/16 |
Series (Serial Number): | ZIB-Report (SC-99-46) |
ZIB-Reportnumber: | SC-99-46 |
Published in: | Appeared in: J. Comput. Phys. 170 (2001) 696-719 |