A Generalized Cross Validation Method for the Inverse Problem of 3-D Maxwell's Equation

Mathematical and Computational Applications

Ding, Liang¹ 

关键词: Maxwell’s Equation;    Nonlinear;    Ill-posed;    Inversion;    Damped Gauss-Newton;    GCV;   

DOI  :  10.3390/mca15050784

学科分类：计算数学

来源: mdpi

【 摘 要 】

The inverse problem of estimation of the electrical conductivity in the Maxwell’s equation is considered, which is reformulated as a nonlinear equation. The Generalized Cross Validation is used to estimate the global regularization parameter and the damped Gauss-Newton is applied to impose local regularization. The damped Gauss-Newton method requires no calculation of the Hessian matrix which is expensive for traditional Newton method. GCV method decreases the computational expense and overcomes the influence of nonlinearity and ill-posedness. The results of numerical simulation testify that this method is efficient.

【 授权许可】

CC BY