关键词: 反源问题； 柯西积分公式； 极点； 支点, 单极子源； 偶极子源

Abstract:

This paper deals with an inverse source problem of the Poisson equation in a disc domain. Based on the complex expression of the solution to the boundary problem, an algebraic relation between the parameters of the point sources and the boundary conditions was deduced by means of the Cauchy integral formula. Then an algebraic numerical algorithm was proposed to reconstruct the dipoles or monopoles. Since the algorithm does not need solving the forward problem or any iterative procedure,  it is direct and reduces the calculation amount. For the purpose of verifying the validity of the algorithm, numerical examples were provided.

Key words: inverse source problem； Cauchy integral formula； pole； branch point, monopole source, dipole source