Vector algorithms for solving 3D~nonlinear magnetostatic problems

E. P. Zhidkov ; M. B. Yuldasheva ; O. I. Yuldashev

Matematičeskoe modelirovanie, Tome 6 (1994) no. 9, pp. 99-116.

Résumé

The differential formulation of the magnetostatic problem using two scalar potentials is considered. The discretization by finite element method reduces the problem to system of the nonlinear equations with sparse matrix. To solve the system some iteration process is used and on each iteration step the solving linearized system is required. For this purpose the vector algorithms are elaborated based on the incomplete Choleski factorization with conjugate gradient method. The use of combination of natural and suggested multicolor ordering of unknowns in the nodes of regular grid allowed one to keep the good qualities of the preconditioner and essentially to increase the degree of vectorization of matrix-vector multiplication and of solving the system with preconditioner. The advantages of the suggested approach are demonstrated on the example of three-dimensional spectrometrical magnet field simulation on vector computer CONVEX С120. The comparison of the computed results for grid consisting 42120 nodes, when the suggested vector algorithms and the compiled with vector option standard algorithms are used, showed that the processor time of the solving nonlinear system in the first case is in 2.3 times less than in second case.