Publications of Frank Schmidt

Theses
  1. F. Schmidt. Solution of Interior-Exterior Helmholtz-Type Problems Based on the Pole Condition Concept: Theory and Algorithms. Habilitation thesis, Free University Berlin, Fachbereich Mathematik und Informatik, 2002. [WWW ] [PS ]


  2. F. Schmidt. Ingenieurmäßige Berechnung der Feldausbreitung in optischen Bauelementen der Lichtwellenleitertechnik. PhD thesis, Department of Electrial Engineering - Optical Telecommunication Theory, Humboldt University Berlin, 1989.


  3. F. Schmidt. Untersuchung heteronomer Differentialgleichungen mit Hilfe des Analogrechners. Diploma thesis, Department of Theoretical Electrial Engineering, Technical University Ilmenau, 1986.


Articles in journal or book chapters
  1. Frank Schmidt, Tilmann Friese, Lin Zschiedrich, and Peter Deuflhard. Adaptive Multigrid Methods for the Vectorial Maxwell Eigenvalue Problem for Optical Waveguide Design. In W. Jäger et al., editor, Mathematics - Key Technology for the Future: Joint Problems between Universities and Industry, pages 270-292. Springer, 2003.


  2. Thorsten Hohage, Frank Schmidt, and Lin Zschiedrich. Solving Time-Harmonic Scattering Problems Based on the Pole Condition I:Theory. SIAM J. Math. Anal., 35(1):183-210, 2003.


  3. Thorsten Hohage, Frank Schmidt, and Lin Zschiedrich. Solving Time-Harmonic Scattering Problems Based on the Pole ConditionII: Convergence of the PML Method. SIAM J. Math. Anal., 35(3):547-560, 2003.


  4. F. Schmidt, T. Friese, and D. Yevick. Transparent Boundary Conditions for Split-Step Padé Approximations of the One-Way Helmholtz equation. J. Comp. Phys, 170:696-719, 2001.


  5. D. Yevick, T. Friese, and F. Schmidt. A Comparison of Transparent Boundary Conditions for the Fresnel Equation. J. Comput. Phys., 168(2):433-444, 2001.


  6. Tilmann Friese, Frank Schmidt, and David Yevick. Transparent boundary conditions for a wide-angle approximation of the one-way Helmholtz equation. J. Comput. Phys., 165(2):645-659, 2000.


  7. F. Schmidt. Construction of Discrete Transparent Boundary Conditions for Schrödinger-Type equations. Surv. Math. Ind., 9:87-100, 1999.


  8. F. Schmidt. Computation of Discrete Transparent Boundary Conditions for the 2D Helmholtz equation. Optical and Quantum Electronics, 30(5,6):427-441, 1998.


  9. F. Schmidt and D. Yevick. Discrete Transparent Boundary Conditions for Schrödinger-Type Equations. J. Comput. Phys., 134:96-107, 1997.


  10. D. Yevick, J. Yu, and F. Schmidt. Analytic Studies of Absorbing and Impedance-Matched Boundary Layers. IEEE Photonics Technology Letters, 9:73-75, 1997.


  11. F. Schmidt and R. März. On the Reference Wave Vector of Paraxial Helmholtz Equations. IEEE Journal of Lightwave Technology, 14:2395-2400, 1996.


  12. F. Schmidt and P. Deuflhard. Discrete Transparent Boundary Conditions for the Numerical Solution of Fresnel's Equation.. Computers Math. Applic., 29:53-76, 1995.


  13. F. Schmidt. An Adaptive Approach to the Numerical Solution of Fresnel's Wave Equation.. IEEE Journal of Lightwave Technology, 11(9):1425-1435, 1993.


  14. F. Schmidt and K. Gottschling. Improved Method of Mode Determination in Planar Optical Waveguides Using Line Transmission Approach. J. Opt. Commun., 12(3):112-114, 1992.


  15. F. Schmidt and H. P. Nolting. Adaptive Multilevel Beam Propagation Method.. IEEE Photonics Technology Letter, 4:1381-1383, 1992.


  16. F. Schmidt. Simulation und Herstellung von Faserschleifkopplern. Wissenschaftliche Zeitschrift der Humboldt-Universität zu Berlin, R. Math./Naturwiss., 39(2):115-118, 1990.


Conference articles
  1. S. Burger, R. Klose, R. März, A. Schädle, F. Schmidt, and L. Zschiedrich. Efficient Finite Element Methods for the Design of Microoptical Components. In Proc. Microoptics Conf. 2004, pages J8, 2004.


  2. S. Burger, R. Klose, A. Schädle, F. Schmidt, and L. Zschiedrich. Adaptive FEM solver for the computation of electromagnetic eigenmodes in 3D photonic crystal structures. In Proc. Sci. Comp. Electr. Eng. 2004, 2004.


  3. S. Burger, F. Schmidt, and L. Zschiedrich. A fast and efficient Finite-Element Solver for 2D and 3D Photonic Band-Gap Problems. In Dig. LEOS/IEEE 2003 Summer Topicals, pages 75, 2003.


  4. F. Schmidt. Discrete Nonreflecting Boundary Conditions for the Helmholtz equation. In A. Bermúdez, D. Gómez, C. Hazard, P. Joly, and J. E. Roberts, editors, Fifth International Conference on Mathematical and Numerical Aspects of Wave Propagation, Waves 2000, Santiago de Compostella, Spain, pages 921-925, 2000.


  5. T. Friese, P. Deuflhard, and F. Schmidt. A Multigrid Method for the Complex Helmholtz Eigenvalue Problem. In C.-H. Lai, P. E. Bjorstad, M. Cross, and O. B. Widlund, editors, Procs. Eleventh International Conference on Domain Decomposition Methods in Sciences and Engineering (DD11), UK, pages 19-26, 1999. DDM.org.


  6. F. Schmidt. Simulation of Scattering and Reflection Problems via Solution ofthe 2D Helmholtz Equation. In Integrated Photonics Research, volume 4 of OSA Technical Digest Series, pages 408-410, 1998.


  7. F. Schmidt and D. Yevick. Discrete Transparent Boundary Conditions for the Fresnel Equation. In Proceedings of the 8th European Conference on Integrated Optics, Royal Institute of Technology, Stockholm, Sweden, pages 222-225, 2-4 April 1997.


  8. P. Deuflhard, T. Friese, F. Schmidt, R. März, and H.-P. Nolting. Effiziente Eigenmodenberechnung für den Entwurf integriert--optischer Chips. In K. -H. Hoffmann, W. Jäger, Th. Lohmann, and H. Schunck, editors, Mathematik--Schlüsseltechnologie für die Zukunft, pages 267-279, 1996. Springer Verlag.


  9. F. Schmidt. Phase-adaptive basis functions for a multilevel finite element solution of the paraxial wave equation. In D. Yevick G. C. Righini, editor, Euro-Opto Series: Linear and Nonlinear Integrated Optics., Lindau, Germany, pages 57-61, April,11-13 1994.


  10. F. Schmidt and P. Deuflhard. Discrete Transparent Boundary Conditions for Fresnel's Equation. In Integrated Photonics Research, San Francisco, California, USA, pages 45-47, February, 17-19 1994.


  11. F. Schmidt and H.-P. Nolting. An Adaptive Approach to a Beam Propagation Method. In Integrated Photonics Research, New Orleans, Louisiana, USA, pages 302-303, April 13-16 1992.


  12. E. Philippow and F. Schmidt. Besondere Lösungen in harmonisch erregten Ferroresonanz-Kreisen. In 4. Internationales Symposium Theoretische Elektrotechnik Ilmenau, volume 2, pages 26-32, 1987.


Internal reports
  1. Lin Zschiedrich, Roland Klose, Achim Schädle, and Frank Schmidt. A new finite element realization of the Perfectly Matched Layer Method for Helmholtz scattering problems on polygonal domains in 2D. Technical report 03-44, ZIB, 2003. [PDF ] [PS ]


  2. T. Hohage and F. Schmidt. On the Numerical Solution of Nonlinear Schrödinger equations in fiber optics. Technical report 02-04, ZIB, 2002. [PDF ] [PS ]


  3. Thorsten Hohage, Frank Schmidt, and Lin Zschiedrich. A new method for the solution of scattering problems. Technical report 02-01, Konrad-Zuse-Zentrum Berlin, 2002. [WWW ] [PDF ] [PS ]


  4. Thorsten Hohage, Frank Schmidt, and Lin Zschiedrich. Solving time-harmonic scattering problems based on the pole condition:Convergence of the PML method. Technical report ZR-01-23, Konrad-Zuse-Zentrum (ZIB), 2001. [WWW ] [PDF ] [PS ]


  5. Thorsten Hohage, Frank Schmidt, and Lin Zschiedrich. Solving time-harmonic scattering problems based on the pole condition:Numerical algorithms. Technical report, Konrad-Zuse-Zentrum (ZIB), 2001.


  6. Thorsten Hohage, Frank Schmidt, and Lin Zschiedrich. Solving time-harmonic scattering problems based on the pole condition:Theory. Technical report 01-01, Konrad-Zuse-Zentrum (ZIB), 2001. [WWW ] [PDF ] [PS ]


  7. D. Yevick, T. Friese, and F. Schmidt. A Comparison of Transparent Boundary Conditions for the Fresnel Equation. Technical report, Department of Physics, University of Waterloo, 2000.


  8. T. Friese, F. Schmidt, and D. Yevick. Transparent Boundary Conditions for Wide Angle One-way Helmholtz equation. Preprint SC 99-45, ZIB, 1999. Note: Submitted to J. Comp. Phys.


  9. F. Schmidt, T. Friese, and D. Yevick. Transparent Boundary Conditions for Split-Step Padé Approximations of the One-Way Helmholtz equation. Submitted to J. Comp. Phys., Preprint SC 99-46, ZIB, 1999. [WWW ] [PS ]


  10. Frank Schmidt. An Alternative Derivation of the Exact DtN-Map on a Circle. Preprint SC 98-32, Konrad-Zuse-Zentrum Berlin, December 1998. [WWW ] [PS ]


  11. P. Deuflhard, T. Friese, and F. Schmidt. A Nonlinear Multigrid Eigenproblem Solver for the Complex Helmholtz Equation. Preprint SC 97-55, Konrad-Zuse-Zentrum Berlin, 1997. [WWW ] [PS ]


  12. F. Schmidt. Construction of Discrete Transparent Boundary Conditions for Schrödinger-Type equations. Technical report SC 97-60, ZIB, December 1997. Note: Appears in Surv. Math. Ind. [WWW ] [PS ]


  13. F. Schmidt. Simultaneous Computation of the Lowest Eigenvectors and Eigenvalues for the Helmholtz-Equation. Technical report, Konrad-Zuse-Zentrum, Berlin, 1995.






Last modified: Tue Dec 14 18:52:38 2004
Author: F. Schmidt.

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