Infinite element method for solving open boundary field problem and its application in resitivity well-logging

An infinite element method (IEM) is introduced in this paper to solve open boundary field problems. The method converts the original infinite field domain into bounded field domain, which can save the memory and CPU time greatly. This algorithm is successfully applied to the 3-D numerical mode matching method (NMM) for resistivity well-logging. Comparing with the original finite element method used in 3-D NMM for solving the well-logging problem, this new approach decreases the total number of nodal points to form the 2-D Finite Element Method (FEM) matrices, which are the matrices of generalized matrix eigenvalue equation used in 3-D NMM. Results show that the new method is almost 7 times faster than the original one.