Abstract
Abstract. A hybrid higher-order finite element boundary integral (FE-BI) technique is discussed where the higher-order FE matrix elements are computed by a fully analytical procedure and where the gobal matrix assembly is organized by a self-identifying procedure of the local to global transformation. This assembly procedure applys to both, the FE part as well as the BI part of the algorithm. The geometry is meshed into three-dimensional tetrahedra as finite elements and nearly orthogonal hierarchical basis functions are employed. The boundary conditions are implemented in a strong sense such that the boundary values of the volume basis functions are directly utilized within the BI, either for the tangential electric and magnetic fields or for the asssociated equivalent surface current densities by applying a cross product with the unit surface normals. The self-identified method for the global matrix assembly automatically discerns the global order of the basis functions for generating the matrix elements. Higher order basis functions do need more unknowns for each single FE, however, fewer FEs are needed to achieve the same satisfiable accuracy. This improvement provides a lot more flexibility for meshing and allows the mesh size to raise up to λ/3. The performance of the implemented system is evaluated in terms of computation time, accuracy and memory occupation, where excellent results with respect to precision and computation times of large scale simulations are found.
Highlights
The Finite Element Boundary Integral (FE-boundary integral (BI)) method (Jin, 2002; Tzoulis and Eibert, 2005; Eibert and Hansen, 1997) is an efficient numerical technique for solving electromagnetic field problems
All arbitrarily shaped components are meshed into tetrahedra (Volakis et al, 1998) apart from perfect electric conductors (PEC) or perfect magnetic conductors (PMC) where E and H are forced to vanish inside the volume
Self-identified hierarchical 3-D vector basis functions were generated for the hybrid finite element (FE) – boundary integal (BI) technique, where analytical solutions for the FE matrix elements have been presented up to 2nd order
Summary
The Finite Element Boundary Integral (FE-BI) method (Jin, 2002; Tzoulis and Eibert, 2005; Eibert and Hansen, 1997) is an efficient numerical technique for solving electromagnetic field problems. Facing low order (LO) basis functions, the local-global transformation is easy as edge related elements only follow the edge directions. Without fixing the node order or the sequence order of the basis functions for the local FEs, the self-identified hierarchical basis function organization allows a simple assembly of the global equation system. This method guarantees the compatibility between FE and BI (Ismatullah and Eibert, 2009) fluently. The accuracy of HO testing cases is good, and the simulation results based on HO basis functions are compared with LO situations
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