This paper presents a novel and useful 3D nonlinear magnetostatic integral formulation for volume integral method. Like every other integral formulation, its main advantage is that it does not require air region mesh, only ferromagnetic regions being discretized. The formulation is based on magnetic flux density interpolation on facet elements. Special care is taken in order to accurately compute the singularity of Green's kernel. The application of an equivalent circuit approach allows preserving the solenoidality of magnetic induction. It is shown that the formulation is very accurate even if it is associated with coarse meshes. Thus, computation time can be very competitive. Computed results for the TEAM Workshop problem 13 and for a multiply-connected regions case-test are reported.
Volume integral equation methods are particularly well suited to solve electromagnetic problems, where the air domain is predominant. However, their use leads to the heavy resolution of a dense matrix system. The Adaptive Cross Approximation (ACA) combined with hierarchical matrices (H-matrices) decomposition is an algebraic method allowing the compression of fully populated matrices. This paper presents the ACA technique applied to a volume integral equation to solve nonlinear magnetostatic problems.
Volume integral method (VIM) has been known as an interesting alternative to the finite-element method for electromagnetic field computation. Since only the active regions have to be meshed, VIM is very efficient for modeling of electromagnetic devices containing a predominated air volume. It is also adapted for multistatic studies with motion or optimization strategies. The aim of this paper is to propose a magnetic vector potential volume integral formulation in order to deal with the 3-D nonlinear magnetostatic problems. The main advantage of this formulation is that the convergence of nonlinear material solution can be easily reached after a few iterations without any relaxation. Moreover, the use of coarse meshes can lead to accurate results. Computed results for the TEAM Workshop problem 13 and for an actuator are reported.
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