多重極展開に基づく3次元ポアソン方程式ソース推定逆問題の代数解法

概要

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In this paper, a non-iterative, algebraic method for an inverse source problem of the three-dimensional Poisson equation is proposed. The method is based on the multipole expansion of potential by N point sources. We show an relation between the source strength, the source positions projected onto the complex plane and the expansion coefficients of the potential. This relation can be transformed into the algebraic equation of N-th degree for the projected positions of the N sources with the coefficients expressed by the expansion coefficients. Thus, by projecting the three-dimensional sources onto two orthogonal planes, the strength and the positions in the three-dimensional space can be estimated. The number of the sources is also obtained by the property of the minor determinants of the matrix composed of the expansion coefficients.
一般社団法人日本機械学会の論文
2002-03-25