Istituto di Matematica Applicata e Tecnologie Informatiche     
El Boukili A., Arioli M., Pietra P. The multifrontal solution of sparse unsymmetric matrices arising from bidimensional semiconductor equations. Technical report ercim.cnr.ian//1997-1067, 1997.
The problem addressed in this paper is an attractive application of the multifrontal approach for the sparse unsymmetric LU factorization. A degenerate drift-diffusion model for a realistic double heterojunction bipolar transistor is considered. The stationary problem is solved using an artificial transient approach based on the nonlinear implicit scheme, coupled with a block nonlinear Gauss-Seidel method. For each implicit step, we apply the exact Newton-Raphson method to solve the nonlinear systems. The obtained linear systems involve two large unsymmetric ill conditioned matrices with symmetric pattern. The Harwell Subroutine Library routine based on the LU multifrontal algorithms for sparse unsymmetric matrices with symmetric pattern ( developped by Amestoy and Duff) is used. The robustness and the high efficiency of this approach was born out by our numerical experiences. The performances are compared with the classical LU factorization for skyline matrices.
Subject LU factorization, Large sparse unsymmetric matrices, Multifrontal method, Degenerate drift-diffusion model, Realistic device

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