ローラン係数を介した2次元ポアソン方程式ソース項同定逆問題の解法

抄録

Solution for an inverse source problem of the two-dimensional Poisson equation via Laurent coefficients is proposed. Positions of N dipoles on the complex plane are represented as the N solutions of the equation of N-th degree whose coefficients are expressed by the Laurent coefficients. The dipole moments are also obtained by the positions and the Laurent coefficients. The algorithm is robust against noise because the Laurent coefficients are obtained by phase-sensitive detection. Our analysis shows that measuring the Laurent coefficients of the potential on the boundary is important for the inverse source problem.