Transparent Boundary Conditions for a Wide-Angle Approximation of the One-Way Helmholtz Equation
Please always quote using this URN: urn:nbn:de:0297-zib-4345
- We present nonlocal discrete transparent boundary conditions for a fourth-order wide-angle approximation of the two-dimensional Helmholtz equation. The boundary conditions are exact in the sense that they supply the same discrete solution on a bounded interior domain as would be obtained by considering the problem on the entire unbounded domain with zero boundary conditions at infinity. The proposed algorithm results in an unconditionally stable propagation method. Numerical examples from optics illustrate the efficiency of our approach.
Author: | Tilman Friese, Frank Schmidt, David Yevick |
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Document Type: | ZIB-Report |
Tag: | Finite-element method; Helmholtz equation; 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-99-45) |
ZIB-Reportnumber: | SC-99-45 |
Published in: | Appeared in: J. Comput. Phys. 165 (2000) 645-659 |