Condensed matrix method for implicit type scheme in imaginary distance beam propagation method

Article type: Research Article

Authors: Kumbhakar, Dharmadas

Affiliations: Department of Physics, B. B. College, Asansol 713303, West Bengal, India. E-mail: dksk2006@gmail.com

Abstract: The modes of a waveguide structure can be accurately determined using finite difference imaginary distance beam propagation method. In implicit type formulation of the problem, a matrix equation has to be solved. The matrix is sparse and large. The sparsity of the matrix can be used to form a condensed matrix of much lower dimension leaving aside the zero element blocks; this condensed matrix takes much smaller storage space and consequently saves a great deal of run-time. The algorithm for the solution of the matrix equation from such a condensed matrix is developed here. This method is comparable with other sparse matrix methods in terms of CPU usage.

Keywords: Finite difference, finite element, beam propagation method, implicit type scheme, sparse matrix, LU decomposition, conjugate gradient method, fill-ins

DOI: 10.3233/JCM-2008-81-206

Journal: Journal of Computational Methods in Sciences and Engineering, vol. 8, no. 1-2, pp. 139-146, 2008