A Hybrid Finite Element-Boundary Integral Method For Electromagnetic Scattering Problems

The finite element method (FEM) suits specially to solve the electromagnetic problems of the structures consisting of an inhomogeneous dielectric body of arbitrary shape. In the electromagnetic domain, the finite element method has widely used in solving problems such as radiation, scattering, wave guide transmission and resonant cavity problem. Since the electromagnetic radiation and scattering analysis of many problems is in open space, the absorbing boundary elements at the outer surface of the meshed region must be employed when the finite element method is used, thus the computation burden is increased out of question. Although the boundary integral method based on the integral equation is very efficient at solving the open radiation problems, the matrix gained by this method is full and requires too much memory. So the boundary integral method is only suitable to solve the problem of the electrically small object. To take advantage the strengths of the both methods and avoid their disadvantages, a hybrid method is presented, viz. the hybrid finite element-boundary integral method. The principle of this hybrid method is that the FEM is employed to handle the interior domain of bodies and the boundary integrate is used to develop surface integrals that relate the field quantities on boundary surfaces with the equivalent surface currents. These integral equations are then coupled to the finite element equations through the continuity of the tangential magnetic fields across the hybrid boundaries.Based on the edge-based vector basis functions defined within tetrahedrons, the finite element formulae are deduced and the program is written to compute the fields within the wave-guide and transmission line. The computed results are in excellent agreement with the exact solutions. Then, based on the principle of the hybrid finite element-boundary integral method, the formulae of this hybrid method are deduced. In the interior region the edge-based vector finite elements are used and on the surface the RWG basis functions are used. Based on these formulae, another program is also written. The electromagnetic scattering programs of the three-dimensional objects are computed using our hybrid method program and the computed results agree well with the results computed by the moment method and the finite element method.