A reliable estimation method of a dipole for three-dimensional Poisson equation
A reliable estimation method of a dipole for three-dimensional Poisson equation
复制标题
三维泊松方程偶极子的可靠估计方法
DOI：
10.1016/s0377-0427(98)00082-x
复制
发表时间：
1998
影响因子：
2.4
通讯作者：
K. Ohnaka
中科院分区：
文献类型：
--
作者：
K. Yamatani;K. Ohnaka
我们讨论三维泊松方程的逆源问题。源项表示为由两个连续点源组成的偶极子。我们的问题是在边界上可以观察到电势和通量的情况下估计偶极矩及其位置。我们提出了一种基于加权残差方法的数值方法，该方法不需要对控制方程进行直接分析。该方法应该是可靠的，因为数值积分和观测噪声引起的误差可以在理论上进行评估。通过数值算例证明了该方法的有效性。
We discuss an inverse source problem for three-dimensional Poisson equation. The source term is expressed as a dipole that consists of two contiguous point sources. Our problem is estimating the dipole moment and its location under the condition that the potential and flux can be observed on the boundary. We propose a numerical method based on a weighted residual approach, which need not use direct analysis for the governing equation. The method should be reliable since the error caused by the numerical integration and observation noise can be evaluated theoretically. The effectiveness of the method is shown by numerical examples.