Analytical finite element matrix elements and global matrix assembly forhierarchical 3-D vector basis functions within the hybrid finite elementboundary integral method

[摘要] A hybrid higher-order finite element boundary integral (FE-BI) technique isdiscussed where the higher-order FE matrix elements are computed by a fullyanalytical procedure and where the gobal matrix assembly is organized by aself-identifying procedure of the local to global transformation. Thisassembly procedure applys to both, the FE part as well as the BI part of thealgorithm. The geometry is meshed into three-dimensional tetrahedra as finiteelements and nearly orthogonal hierarchical basis functions are employed. Theboundary conditions are implemented in a strong sense such that the boundaryvalues of the volume basis functions are directly utilized within the BI,either for the tangential electric and magnetic fields or for the asssociatedequivalent surface current densities by applying a cross product with theunit surface normals. The self-identified method for the global matrixassembly automatically discerns the global order of the basis functions forgenerating the matrix elements. Higher order basis functions do need moreunknowns for each single FE, however, fewer FEs are needed to achieve thesame satisfiable accuracy. This improvement provides a lot more flexibilityfor meshing and allows the mesh size to raise up to λ/3. Theperformance of the implemented system is evaluated in terms of computationtime, accuracy and memory occupation, where excellent results with respect toprecision and computation times of large scale simulations are found.

[学科分类] 电子、光学、磁材料