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Article type: Research Article
Authors: Kumbhakar, Dharmadas
Affiliations: Department of Physics, B. B. College, Asansol 713303, West Bengal, India. E-mail: [email protected]
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
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