Computed Basis Functions for 2-D Edge Elements

Abstract

The nonconforming voxel finite-element method (NVFEM) models material boundaries in a staircase fashion. Recently, a technique called the computed basis function (CBF) method was introduced to reduce the errors arising from this, but it was applied only to scalar fields. Here, the CBF method is developed for vector fields that are represented with 2-D edge elements. The method is tested by solving the vector wave equation for problems involving perfectly conducting or dielectric obstacles. Results show that NVFEM enhanced with CBF can achieve the same accuracy as NVFEM with between 6 and 10 times fewer unknowns, with no reduction in the sparsity of the global FE matrix.