Title :
Parallel Direct Solver for the Finite Integration Technique in Electrokinetic Problems
Author :
Tinzefte, Abdellatif ; Le Menach, Yvonnick ; Korecki, Julien ; Guyomarch, Frederic ; Piriou, Francis
Author_Institution :
L2EP-LAMEL, Univ. de Lille, Villeneuve-d´´Ascq, France
Abstract :
The finite integration technique allows the simulation of real-world electromagnetic field problems with complex geometries. It provides a discrete reformulation of Maxwell´s equations in their integral form suitable for numerical computing. The resulting matrix equations of the discretized fields can be used for efficient numerical simulations on modern computers and can be exploited to use a parallel computing. In fact, by reordering the unknowns by the nested dissection method, it is possible to directly construct the lower triangular matrix of the Cholesky factorization with many processors without assembling the matrix system. In this paper, a parallel algorithm is proposed for the direct solution of large sparse linear systems with the finite integration technique. This direct solver has the advantage of handling singularities in the matrix of linear systems. The computational effort for these linear systems, often encountered in numerical simulation of electromagnetic phenomena by finite integration technique, is very significant in terms of run-time and memory requirements. Many numerical tests have been carried out to evaluate the performance of the parallel direct solver.
Keywords :
Maxwell equations; electromagnetic field theory; matrix algebra; numerical analysis; Cholesky factorization; Maxwell´s equations; electrokinetic problems; electromagnetic field; electromagnetic phenomena; finite integration technique; matrix equations; numerical simulations; parallel direct solver; sparse linear systems; Computational modeling; Electrokinetics; Electromagnetic fields; Geometry; Integral equations; Linear systems; Maxwell equations; Numerical simulation; Solid modeling; Sparse matrices; Finite element methods; finite integration technique; linear systems; numerical analysis; parallel algorithms;
Journal_Title :
Magnetics, IEEE Transactions on
DOI :
10.1109/TMAG.2010.2045886