Toward Optimal Mesh Quality Improvements for Adaptive Finite Element Electromagnetics With Tetrahedra

Impact of mesh quality improvement systems on the accuracy of adaptive finite-element electromagnetics with tetrahedra

“…These elements can significantly degrade the accuracy of the solution. For this reason, the development of an efficient mesh improvement stage is considered a priority for -adaptive FE electromagnetic analysis [5]- [7]. Prior to selecting a mesh improvement algorithm, a theoretical basis must be established for detecting poor quality elements and making fine distinctions between mesh improvement systems.…”

“…Therefore, considerable attention has been given to mesh quality improvement over the past several years. Among the most promising mesh quality improvement methods for 3-D meshes are smoothing-based techniques [5]- [7], [10].…”

“…Typically, several iterations of smoothing are performed to improve the overall quality of the mesh. Smart-Laplacian smoothing and optimization-based smoothing are two variants that have received much attention [5], [6], [10]. Smart-Laplacian smoothing repositions a vertex to the average location of the vertices connected to it by edges only if the quality of the local submesh is improved according to a specific quality measure.…”

“…In certain cases, a single bad element can cause a high-discretization error throughout the entire problem domain. When employing -adaptive FEMs for electromagnetics, a mesh improvement stage is required in order to ensure high-quality tetrahedra [5]- [7]. However, mesh improvement techniques and quality indicators are often subjective or based on purely geometrical considerations [4].…”

“…Novel mesh improvement techniques D1-D4 were shown to outperform previous combined mesh smoothing techniques in geometric mesh quality [5]. This work focuses on evaluating the performance of the new family of mesh smoothing systems using the proposed theoretical mesh quality indicators.…”