论文标题
电阻断层扫描中电导率恢复的高阶不连续的盖尔金方法
A high order discontinuous Galerkin method for the recovery of the conductivity in Electrical Impedance Tomography
论文作者
论文摘要
在这项工作中，我们开发了一种有效的高阶不连续盖尔金（DG）方法来解决电阻抗断层扫描（EIT）。 EIT是一个高度非线性的逆问题，从电压和电流通量的表面测量值中回收物体的内部电导率。我们首先提出了一个新的优化问题，基于从Dirichlet到Neumann地图的电导率恢复，以最大程度地减少预测电流与边界上测得的电流之间的不匹配。我们进一步证明了最小化器的存在。从数值上讲，优化问题通过使用二次多项式的三阶DG方法解决。证明了单个和多个夹杂物的几个二维问题的数值结果，以显示拟议的高阶DG方法的高{精度和效率}。这项工作还研究了不连续电导率的分析和计算。
In this work, we develop an efficient high order discontinuous Galerkin (DG) method for solving the Electrical Impedance Tomography (EIT). EIT is a highly nonlinear ill-posed inverse problem where the interior conductivity of an object is recovered from the surface measurements of voltage and current flux. We first propose a new optimization problem based on the recovery of the conductivity from the Dirichlet-to-Neumann map to minimize the mismatch between the predicted current and the measured current on the boundary. And we further prove the existence of the minimizer. Numerically the optimization problem is solved by a third order DG method with quadratic polynomials. Numerical results for several two-dimensional problems with both single and multiple inclusions are demonstrated to show the high {accuracy and efficiency} of the proposed high order DG method. Analysis and computation for discontinuous conductivities are also studied in this work.
