Eddy-current inverse technique is a very important method to reconstruct the shape of flaws or cracks. Using the domain derivative of the far-field pattern for eddy- current inverse problem with Dirichlet boundary con...Eddy-current inverse technique is a very important method to reconstruct the shape of flaws or cracks. Using the domain derivative of the far-field pattern for eddy- current inverse problem with Dirichlet boundary condition, a new algorithm to recover the shape of cracks was constructed and some numerical examples were given. The algorithm demonstrates that the algorithm is feasible and correct for obtaining a reasonable reconstruction of a shape of flaws or cracks from the far-field measurements even though using less data of directions of incidence and observations for fewer wave numbers are gived.展开更多
We introduce the equivalent sources for the Helmholtz equation and estab-lish their connections to the naturally induced sources for the sound-soft,sound-hard,and impedance obstacles for the inverse scattering problem...We introduce the equivalent sources for the Helmholtz equation and estab-lish their connections to the naturally induced sources for the sound-soft,sound-hard,and impedance obstacles for the inverse scattering problems of the Helmholtz equation.As two applications,we employ the naturally induced sources to improve the bound-ary integral equation formulations for the obstacle scattering problems,and develop a unified,straightforward approach to establishing boundary conditions governing the domain derivatives of scattered waves for the soft,hard,and impedance obstacles.展开更多
文摘Eddy-current inverse technique is a very important method to reconstruct the shape of flaws or cracks. Using the domain derivative of the far-field pattern for eddy- current inverse problem with Dirichlet boundary condition, a new algorithm to recover the shape of cracks was constructed and some numerical examples were given. The algorithm demonstrates that the algorithm is feasible and correct for obtaining a reasonable reconstruction of a shape of flaws or cracks from the far-field measurements even though using less data of directions of incidence and observations for fewer wave numbers are gived.
文摘We introduce the equivalent sources for the Helmholtz equation and estab-lish their connections to the naturally induced sources for the sound-soft,sound-hard,and impedance obstacles for the inverse scattering problems of the Helmholtz equation.As two applications,we employ the naturally induced sources to improve the bound-ary integral equation formulations for the obstacle scattering problems,and develop a unified,straightforward approach to establishing boundary conditions governing the domain derivatives of scattered waves for the soft,hard,and impedance obstacles.
