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
A new solution methodology is proposed for solving efficiently Helmholtz problems.The proposed method falls in the category of the discontinuous Galerkin methods.However,unlike the existing solution methodologies,this...A new solution methodology is proposed for solving efficiently Helmholtz problems.The proposed method falls in the category of the discontinuous Galerkin methods.However,unlike the existing solution methodologies,this method requires solving(a)well-posed local problems to determine the primal variable,and(b)a global positive semi-definite Hermitian system to evaluate the Lagrange multiplier needed to restore the continuity across the element edges.Illustrative numerical results obtained for two-dimensional interior Helmholtz problems are presented to assess the accuracy and the stability of the proposed solution methodology.展开更多
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.
基金support by TOTAL and INRIA/CSUN Associate Team Magic,INRIA Bordeaux Sud-Ouest Center.Any opinions,findings,and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of TOTAL,INRIA or CSUN.
文摘A new solution methodology is proposed for solving efficiently Helmholtz problems.The proposed method falls in the category of the discontinuous Galerkin methods.However,unlike the existing solution methodologies,this method requires solving(a)well-posed local problems to determine the primal variable,and(b)a global positive semi-definite Hermitian system to evaluate the Lagrange multiplier needed to restore the continuity across the element edges.Illustrative numerical results obtained for two-dimensional interior Helmholtz problems are presented to assess the accuracy and the stability of the proposed solution methodology.
