@misc{YevickFrieseSchmidt, author = {Yevick, David and Friese, Tilmann and Schmidt, Frank}, title = {A Comparison of Transparent Boundary Conditions for the Fresnel Equation}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-5738}, number = {00-05}, abstract = {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.}, language = {en} } @misc{FrieseSchmidtYevick, author = {Friese, Tilman and Schmidt, Frank and Yevick, David}, title = {Transparent Boundary Conditions for a Wide-Angle Approximation of the One-Way Helmholtz Equation}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-4345}, number = {SC-99-45}, abstract = {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.}, language = {en} } @misc{SchmidtFrieseYevick, author = {Schmidt, Frank and Friese, Tilmann and Yevick, David}, title = {Transparent Boundary Conditions for Split-Step Pade Approximations of the One-Way Helmholtz Equation}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-4353}, number = {SC-99-46}, abstract = {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.}, language = {en} } @misc{SchmidtYevick, author = {Schmidt, Frank and Yevick, David}, title = {Discrete Transparent Boundary Conditions for Schr{\"o}dinger-Type Equations}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-2289}, number = {SC-96-17}, abstract = {We present a general technique for constructing nonlocal transparent boundary conditions for one-dimensional Schr{\"o}dinger-type equations. Our method supplies boundary conditions for the \$\theta\$-family of implicit one-step discretizations of Schr{\"o}dinger's equation in time. The use of Mikusi\'nski's operator approach in time avoids direct and inverse transforms between time and frequency domains and thus implements the boundary conditions in a direct manner.}, language = {en} } @article{SchmidtFrieseYevick2001, author = {Schmidt, Frank and Friese, T. and Yevick, David}, title = {Transparent Boundary Conditions for Split-Step Pad{\´e} Approximations of the One-Way Helmholtz equation}, series = {J. Comp. Phys}, volume = {170}, journal = {J. Comp. Phys}, pages = {696 -- 719}, year = {2001}, language = {en} } @article{FrieseSchmidtYevick2000, author = {Friese, T. and Schmidt, Frank and Yevick, David}, title = {Transparent boundary conditions for a wide-angle approximation of the one-way Helmholtz equation}, series = {J. Comput. Phys.}, volume = {165}, journal = {J. Comput. Phys.}, number = {2}, doi = {10.1006/jcph.2000.6637}, pages = {645 -- 659}, year = {2000}, language = {en} } @article{YevickFrieseSchmidt2001, author = {Yevick, David and Friese, T. and Schmidt, Frank}, title = {A Comparison of Transparent Boundary Conditions for the Fresnel Equation}, series = {J. Comput. Phys.}, volume = {168}, journal = {J. Comput. Phys.}, number = {2}, pages = {433 -- 444}, year = {2001}, language = {en} } @article{YevickYuSchmidt1997, author = {Yevick, David and Yu, J. and Schmidt, Frank}, title = {Analytic Studies of Absorbing and Impedance-Matched Boundary Layers}, series = {IEEE Photonics Technology Letters}, volume = {9}, journal = {IEEE Photonics Technology Letters}, doi = {10.1109/68.554499}, pages = {73 -- 75}, year = {1997}, language = {en} } @article{SchmidtYevick1997, author = {Schmidt, Frank and Yevick, David}, title = {Discrete Transparent Boundary Conditions for Schr{\"o}dinger-Type Equations}, series = {J. Comput. Phys.}, volume = {134}, journal = {J. Comput. Phys.}, number = {1}, doi = {10.1006/jcph.1997.5675}, pages = {96 -- 107}, year = {1997}, language = {en} } @inproceedings{SchmidtYevick1997, author = {Schmidt, Frank and Yevick, David}, title = {Discrete Transparent Boundary Conditions for the Fresnel Equation}, series = {Proceedings of the 8th European Conference on Integrated Optics}, booktitle = {Proceedings of the 8th European Conference on Integrated Optics}, address = {Royal Institute of Technology, Stockholm, Sweden}, pages = {222 -- 225}, year = {1997}, language = {en} }