We develope the space and time adaptive algorithms for the solution of Fresnel's equation based on Rothe's method.

• F. Schmidt
  Solution of Interior-Exterior Helmholtz-Type Problems Based on the Pole Condition Concept: Theory and Algorithms
  Free University Berlin, Fachbereich Mathematik und Informatik  Habilitation thesis (2002)
  PS   URL  
• F. Schmidt, T. Friese, D. Yevick
  Transparent Boundary Conditions for Split-Step Padé Approximations of the One-Way Helmholtz equation
  J. Comp. Phys,  Vol. 170,   696-719 (2001)
• T.  Friese, F.  Schmidt, D.  Yevick
  Transparent boundary conditions for a wide-angle approximation of the one-way Helmholtz equation
  J. Comput. Phys.,  Vol. 165  (2) ,   645-659 (2000)
  Preprint  
• T. Friese, F. Schmidt, D. Yevick
  Transparent Boundary Conditions for Wide Angle One-way Helmholtz equation
   (SC 99-45) ZIB  Preprint  -Appeared in J. Comp. Phys. 165 (2000) 645-659 (1999)
  PS  
• F. Schmidt, D. Yevick
  Discrete Transparent Boundary Conditions for the Fresnel Equation
  In: Proceedings of the 8th European Conference on Integrated Optics,   222-225,  Royal Institute of Technology, Stockholm, Sweden (1997)
• F. Schmidt, R. März
  On the Reference Wave Vector of Paraxial Helmholtz Equations
  IEEE Journal of Lightwave Technology,  Vol. 14,   2395-2400 (1996)
• F.  Schmidt, P.  Deuflhard
  Discrete Transparent Boundary Conditions for the Numerical Solution of Fresnel's Equation.
  Comput. Math. Appl.,  Vol. 29,   53-76 (1995)
• F. Schmidt, P. Deuflhard
  Discrete Transparent Boundary Conditions for Fresnel's Equation
  In: Integrated Photonics Research,   45-47,  San Francisco, California, USA (1994)
• F. Schmidt
  Phase-adaptive basis functions for a multilevel finite element solution of the paraxial wave equation
  In: Euro-Opto Series: Linear and Nonlinear Integrated Optics.,  G. C. Righini, D. Yevick  (ed) ,   57-61,  Lindau, Germany (1994)
• F. Schmidt
  An Adaptive Approach to the Numerical Solution of Fresnel's Wave Equation.
  IEEE Journal of Lightwave Technology,  Vol. 11  (9) ,   1425-1435 (1993)