A Domain Map Finite Element Method for Solving Open Boundary Electromagnetic Field Problem and its Application

A domain map finite element method was applied to the three dimensional (3-D) numerical mode-matching (NMM) method to solve the 3-D electric logging problem. This method divides the infinite field domain of every layer into inner and outer field domains, in inner domain the matrices are formed by standard FEM and in outer domain, the Kelvin transformation is applied and the matrices are formed by a new infinite element format. Matrices of two different parts are coupled in the domains' common interface to form the final matrices of the original problem. This method generates smaller size of generalized matrices than original 3-D NMM method. In addition, this method changes the distribution of eigenvalues which needs less eigenvalues under the same error. Results show that the new method spends only 1/7 CPU time and uses only 1/3 memory of the original method.