论文标题
椭圆方程的分段常数领导系数的数值恢复
Numerical recovery of the piecewise constant leading coefficient of an elliptic equation
论文作者
论文摘要
我们提出了一种数值算法，用于重建椭圆问题的分段常数前导系数。逆问题减少为形状重建问题。所提出的算法基于成本函数的最小化，其中控制函数是辅助椭圆方程的右侧，用于未知形状的水平集表示。数值实现基于有限元方法和开源计算平台Fenics。该算法的性能在计算模拟数据上证明。
We propose a numerical algorithm for the reconstruction of a piecewise constant leading coefficient of an elliptic problem. The inverse problem is reduced to a shape reconstruction problem. The proposed algorithm is based on the minimization of a cost functional where a control function is the right-hand side of an auxiliary elliptic equation for a level set representation of unknown shape. The numerical implementation is based on the finite element method and the open-source computing platform FEniCS. The performance of the algorithm is demonstrated on computationally simulated data.
