Title :
Wide-Angle Alternating-Direction Implicit Finite-Difference BPM
Author :
Bekker, Ella V. ; Sewell, Phillip ; Benson, Trevor M. ; Vukovic, Ana
Author_Institution :
Univ. of Nottingham, Nottingham
Abstract :
We introduce an improved Alternating Direction Implicit (ADI) scheme for each of the wide-angle (WA) Pade approximant multi-steps, and moreover, employ an iterative approach to correct for the splitting error. The resulting finite-difference scheme is conditionally stable and can be straightforwardly solved using the efficient Thomas algorithm for tri-diagonal band matrices. Valuable reductions in both the memory and calculation time are obtained, especially for complex geometries.
Keywords :
approximation theory; finite difference methods; matrix algebra; optical waveguide theory; Pade approximantion; beam propagation method; finite-difference BPM; iterative method; optical waveguide; splitting error; tri-diagonal band matrices; wide-angle alternating-direction implicit scheme; Dispersion; Electromagnetic waveguides; Error correction; Finite difference methods; Geometrical optics; Optical propagation; Optical waveguides; Partial differential equations; Polynomials; Refractive index;
Conference_Titel :
Transparent Optical Networks, 2007. ICTON '07. 9th International Conference on
Conference_Location :
Rome
Print_ISBN :
1-4244-1249-8
Electronic_ISBN :
1-4244-1249-8
DOI :
10.1109/ICTON.2007.4296081
