A Structured Grid Finite-Element Method Using Computed Basis Functions

Structured (e.g., rectangular) meshes in finite-element (FE) analysis offer several advantages, but are not often used because of the error introduced in fitting material interfaces. The nonconforming voxel FE method (NVFEM) is a hierarchical structured method that systematically reduces the geometric error in an adaptive way, but it requires large numbers of elements and therefore is expensive. By computing basis functions that take into account the interface cutting through an element, the number of elements needed is greatly reduced. The resulting method, CBF-NVFEM, is applied to the computation of the radar cross section of free-space scatterers. Results indicate that CBF-NVFEM is much more efficient than NVFEM and is competitive with FEM using unstructured meshes of tetrahedra.