This article compares the isotropic and anisotropic TV regularizations used in inverse acoustic scattering. It is observed that compared with the traditional Tikhonov regularization, isotropic and anisotropic TV regul...This article compares the isotropic and anisotropic TV regularizations used in inverse acoustic scattering. It is observed that compared with the traditional Tikhonov regularization, isotropic and anisotropic TV regularizations perform better in the sense of edge preserving. While anisotropic TV regularization will cause distortions along axes. To minimize the energy function with isotropic and anisotropic regularization terms, we use split Bregman scheme. We do several 2D numerical experiments to validate the above arguments.展开更多
The paper concerns the numerical solution for the acoustic scattering problems in a two-layer medium.The perfectly matched layer(PML)technique is adopted to truncate the unbounded physical domain into a bounded comput...The paper concerns the numerical solution for the acoustic scattering problems in a two-layer medium.The perfectly matched layer(PML)technique is adopted to truncate the unbounded physical domain into a bounded computational domain.An a posteriori error estimate based adaptive finite element method is developed to solve the scattering problem.Numerical experiments are included to demonstrate the efficiency of the proposed method.展开更多
A numerical method of solving acoustic wave scattering pnblem in fluids is described. Radiation boundary condition (RBC) obtained by factorization method of Helmholtz equation is applied to transforming the exterior b...A numerical method of solving acoustic wave scattering pnblem in fluids is described. Radiation boundary condition (RBC) obtained by factorization method of Helmholtz equation is applied to transforming the exterior boundary value problem in unbounded region into one in a finite region. Combined with RBC and scatterer surface boundary condition, Helmholtz equation is solved numerically by the finite difference method. Computational results for sphere and prolate spheroidal scatterers are in excellent agreement with eigenfunction solutions and much better than the results of OSRC method.展开更多
We propose a numerical procedure to extend to full aperture the acoustic farfield pattern(FFP)when measured in only few observation angles.The reconstruction procedure is a multi-step technique that combines a total v...We propose a numerical procedure to extend to full aperture the acoustic farfield pattern(FFP)when measured in only few observation angles.The reconstruction procedure is a multi-step technique that combines a total variation regularized iterative method with the standard Tikhonov regularized pseudo-inversion.The proposed approach distinguishes itself from existing solution methodologies by using an exact representation of the total variation which is crucial for the stability and robustness of Newton algorithms.We present numerical results in the case of two-dimensional acoustic scattering problems to illustrate the potential of the proposed procedure for reconstructing the full aperture of the FFP from very few noisy data such as backscattering synthetic measurements.展开更多
文摘This article compares the isotropic and anisotropic TV regularizations used in inverse acoustic scattering. It is observed that compared with the traditional Tikhonov regularization, isotropic and anisotropic TV regularizations perform better in the sense of edge preserving. While anisotropic TV regularization will cause distortions along axes. To minimize the energy function with isotropic and anisotropic regularization terms, we use split Bregman scheme. We do several 2D numerical experiments to validate the above arguments.
基金supported by China NSF grants 11771057,11401040,11671052supported by China NSF grants 1167105。
文摘The paper concerns the numerical solution for the acoustic scattering problems in a two-layer medium.The perfectly matched layer(PML)technique is adopted to truncate the unbounded physical domain into a bounded computational domain.An a posteriori error estimate based adaptive finite element method is developed to solve the scattering problem.Numerical experiments are included to demonstrate the efficiency of the proposed method.
基金The Project is supported by the National Natural Science Foundation of China.
文摘A numerical method of solving acoustic wave scattering pnblem in fluids is described. Radiation boundary condition (RBC) obtained by factorization method of Helmholtz equation is applied to transforming the exterior boundary value problem in unbounded region into one in a finite region. Combined with RBC and scatterer surface boundary condition, Helmholtz equation is solved numerically by the finite difference method. Computational results for sphere and prolate spheroidal scatterers are in excellent agreement with eigenfunction solutions and much better than the results of OSRC method.
文摘We propose a numerical procedure to extend to full aperture the acoustic farfield pattern(FFP)when measured in only few observation angles.The reconstruction procedure is a multi-step technique that combines a total variation regularized iterative method with the standard Tikhonov regularized pseudo-inversion.The proposed approach distinguishes itself from existing solution methodologies by using an exact representation of the total variation which is crucial for the stability and robustness of Newton algorithms.We present numerical results in the case of two-dimensional acoustic scattering problems to illustrate the potential of the proposed procedure for reconstructing the full aperture of the FFP from very few noisy data such as backscattering synthetic measurements.
