Fast Green Function Evaluation for Method of Moment
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In this letter, an approach to accelerate the matrix filling in method of moment (MOM) is proposed. Based on the fact that the Green function is dependent on the Euclidean distance between the source and the observation points, we constructed an efficient adaptive one-dimensional interpolation approach to fast calculate the Green function and Exp function values. In the proposed method, several adaptive interpolation tables are constructed based on the maximum and minimum distance between any two integration points with local refinement near zero function values to obtain relatively uniform error rate in the overall computational domain. An efficient approach to obtain the sampling points used in the interpolation phase is carefully designed. Then, any function values could be efficiently calculated through a linear interpolation method for Exp and a Lagrange polynomial interpolation method for the Green function. In addition, the error bound of the proposed method is rigorously investigated. The proposed method could be quite easily integrated into the available MOM codes for different integration equation (IE) formulations, like the electrical field integral equation (EFIE), magnetic field integral equation (MFIE), the combined field integral equation (CFIE), the Poggio-Miller-Chan-Harrington-Wu-Tsai(PMCHWT), with few efforts. Comprehensive numerical experiments validate its accuracy and efficiency through several IE formulations. Results show that over 20 achieved without sacrificing the accuracy.
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