(A) study on numerically efficient finite element-boundary element hybrid method for open-boundary electromagnetic field problems

Abstract

To overcome excessive storage requirement of hybrid finite element-boundary element method for open-boundary electromagnetic field problems, two schemes are devised to choose proper boundary meshes. The first scheme utilize symmetry of regular polyhedra. In the case of dodecahedral boundary mesh the full boundary element matrix can be expressed by only four sub-matrices, and the storage requirement is reduced up to factor of 1/90. The second scheme utilize axi-symmetry to form block circulant boundary element matrices, and results in up to 64-fold reduction in matrix storage. Also the block circulant nature of the boundary element matrices provides a numerically efficient algorithm for solution of the coupled matrix equations. Impedance/admittance matrices also have same storage reduction, and may be pre-calculated to form a database for later use. To demonstrate its efficiency both schemes are applied to three-dimensional magneto-static field problem. The second scheme is also applied to time-harmonic electromagnetic scattering from a double-layer dielectric sphere. To satisfy vector boundary conditions edge elements and incorporated for both finite element and boundary element equations. With this efficiency these schemes become more advantageous than pure finite element method with approximate boundary conditions in both static and time-harmonic electromagnetic field problems, and allow us to solve large 3-dimensional open boundary field problems with small workstations.