Performance Analysis of FEM Solvers on Practical Electromagnetic Problems

The paper presents a comparative analysis of different commercial and academic software. The comparison aims to examine how the integrated adaptive grid refinement methodologies can deal with challenging, electromagnetic-field related problems. For this comparison, two bench-mark problems were examined in the paper. The first example is a solution of an L-shape domain like test problem, which has a singularity at a certain point in the geometry. The second problem is an induction heated aluminum rod, which accurate solution needs to solve non-linear, coupled physical fields. The accurate solution of this problem requires applying adaptive mesh generation strategies or applying a very fine mesh in the electromagnetic domain, which can significantly increase the computational complexity. The results show that the fully-hp adaptive meshing strategies, which are integrated into Agros Suite, can significantly reduce the task's computational complexity compared to the automatic h-adaptivity, which is part of the examined, popular commercial solvers.

Adaptive Algorithm for Three-Dimensional Mesh Generation Based on Constrained Delaunay

Mesh generation is a key step for many areas. Here, an adaptive mesh generation algorithm for piecewise linear domains based on constrained Delaunay is proposed. We focus on improving the quality of the meshes generated and make them conforming to an isotropic size function which is specified by the user. The preliminary mesh with boundaries conforming is generated first. We try to add points to split the mesh either bad shape or not conforming to the size function. The new point can be added to the domain only if it is not close to the existing point in the domain. Finally, local meshes are reconstructed to make all meshes comply with the constrained Delaunay. Experimental comparisons show that the new algorithm is advantageous in generating adaptive mesh. The presented method can be used in a wide range of areas such as computer vision, finite element method and many other areas.