An estimation method for point sources of multidimensional diffusion equation
An estimation method for point sources of multidimensional diffusion equation
复制标题
多维扩散方程点源估计方法
DOI：
10.1016/s0307-904x(96)00148-5
复制
发表时间：
1997
影响因子：
5
通讯作者：
K. Ohnaka
中科院分区：
文献类型：
--
作者：
K. Yamatani;K. Ohnaka
考虑了多维扩散方程的源反问题。源项由未知点源之和表示，这些点源的数量也是未知的。我们的问题是在边界上观测到势和通量的条件下估计未知源项。我们提出了一种数值方法，不需要使用直接分析的控制方程。我们的方法是基于一个加权残差的方法与适当的加权函数类比的基本解决方案的一维情况下。数值算例表明了该方法的有效性。
An inverse source problem is considered for the multidimensional diffusion equation. The source term is expressed by a sum of unknown point sources, and the number of these point sources is also unknown. Our problem is to estimate the unknown source term under the condition that the potential and flux are observed on the boundary. We propose a numerical method that need not use a direct analysis for the governing equation. Our method is based on a weighted residual approach with suitable weighting functions analogized from the fundamental solution of the one-dimensional case. The effectiveness of the method is shown by numerical examples.