A Multiresolution Approach to the Electric Field Integral Equation in Antenna Problems

Abstract. This paper deals with a multiresolution approach to the finite-element solution of the Electric Field Integral Equation (EFIE) formulation of the boundary value problem for Maxwell equations. After defining a multiresolution set of discretized spaces, each of them is first separated into solenoidal and non-solenoidal complementary spaces. The possibility of obtaining these two spaces with a scalar-to-vector space mappings is used to consider first two separate scalar wavelet decompositions, and then to transform them properly into the two desired vector finite element sets, finally joined to obtain the complete multiresolution basis. Numerical results, obtained for real life antennas, are presented to verify the actual sparsity of the system matrix and to show the fast convergence behaviour of iterative solvers.