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The purpose of this paper is to develop a solving method based on the parallelization of the calculus of the finite integration technique on many processors and discuss its efficiency following the number of processors.

The finite integration technique is used in different engineering domains as well as to compute the electromagnetic phenomena. This technique is efficient and generates a linear system with regular structure, this system can be implemented and solved in parallel with a direct solver. In fact, in reordering the unknowns by the nested dissection method, the lower triangular matrix of the Cholesky factorization can be constructed with many processors without assembling the matrix system.

This paper deals with the parallelization of the finite integration technique which is performed by data partitioning and leads to a high‐performance.

The paper presents a parallel implementation of the finite integration technique associated to a direct solver which is practical and efficient.

To compare the numerical solutions in primal and dual meshes of magnetostatic problems solved with the finite integration technique.

The development of the whole set of magnetostatic discrete formulations is proposed. Four formulations are computed: two in terms of fields and two in terms of potentials. Moreover, each computation is carried out on the primal and dual mesh. Two applications are presented and the results are analysed and discussed.

The whole set of magnetostatic formulations gives only two solutions. The solutions do not depend of the formulation, but they depend of the choice of the field discretisation in primal or dual mesh.

The computation is carried out on the dual mesh.