Accuracy and Convergence Rate Comparative Investigation on ‎Polytope Smoothed and Scaled Boundary Finite Element

Abstract

Continuity and discontinuity of two-dimensional domains are thoroughly investigated for accuracy and convergence rate using two prominent discretization methods, namely smoothed and scaled boundary finite element. Because of their capability and versatility when compared to primitive elements, N-sided polygonal elements discretized from modified DistMesh and PolyMesher schemes are used. In terms of accuracy and convergence rate, NSFEM and SBFEM are found to be superior to CSFEM and ESFEM regardless of meshing alternative. The best accuracy occurs at NSFEM and SBFEM, and the obtained convergence rates are optimal. Particularly, in the smoothing domain, it is believed that DistMesh has more promising potential than PolyMesher does; yet, in the discontinuity domain, PolyMesher has been discovered to be more powerful while maintaining its efficiency.

Keywords

• polytope
• smoothed finite element
• scaled boundary finite element
• mesh schemes