Reconstruction algorithms of an inverse source problem for the Helmholtz equation

Numerical Algorithms - Tập 84 Số 3 - Trang 909-933 - 2020
Ji-Chuan Liu1, Xiaochen Li2
1School of Mathematics, China University of Mining and Technology, Xuzhou, People’s Republic of China
2Teaching Section of Mathematic, Department of Basic, Army Logistics University of PLA, Chongqing, People’s Republic of China

Tóm tắt

Từ khóa


Tài liệu tham khảo

Acosta, S., Chow, S., Taylor, J., Villamizar, V.: On the multi-frequency inverse source problem in heterogeneous media. Inverse Probl. 28(7), 075013 (2012)

Alves, C., Kress, R., Serranho, P.: Iterative and range test methods for an inverse source problem for acoustic waves. Inverse Probl. 25(5), 055005 (2009)

Alves, C., Mamud, R., Martins, N., Roberty, N.: On inverse problems for characteristic sources in Helmholtz equations. Math. Probl. Eng. 2017, 1–16 (2017)

Alves, C., Martins, N., Roberty, N.: Full identification of acoustic sources with multiple frequencies and boundary measurements. Inverse Probl. Imag. 3(2), 275–294 (2009)

Badia, A., Nara, T.: An inverse source problem for Helmholtz’s equation from the cauchy data with a single wave number. Inverse Probl. 27(10), 105001 (2011)

Coleman, T., Li, Y.: On the convergence of interior-reflective newton methods for nonlinear minimization subject to bounds. Math. Program. 67(1), 189–224 (1994)

Coleman, T., Li, Y.: An interior, trust region approach for nonlinear minimization subject to bounds. SIAM J. Optim. 6, 418–445 (1996)

Colton, D., Kress, R.: Inverse Acoustic and Electromagnetic Scattering Theory. Applied Mathematical Sciences, 2nd edn., p 93. Springer, New-York (1998)

Hamad, A., Tadi, M.: A numerical method for inverse source problems for poisson and Helmholtz equations. Phys. Lett. A 380(44), 3707–3716 (2016)

Hämäläinen, M., Hari, R., Ilmoniemi, R., Knuutila, J., Lounasmaa, O.: Magnetoencephalography-theory, instrumentation, and applications to noninvasive studies of the working human brain. Rev. Modern Phys. 65, 413–497 (1993)

Hanke, M., Rundell, W.: On rational approximation methods for inverse source problems. Inverse Probl. Imag. 5(1), 185–202 (2011)

He, S., Romanov, V.: Identification of dipole sources in a bounded domain for Maxwell’s equations. Wave Motion 28(1), 25–40 (1998)

Ikehata, M.: Reconstruction of a source domain from the cauchy data. Inverse Probl. 15(2), 637 (1999)

Isakov, V.: Inverse Source Problems. Mathematical Surveys and Monographs. American Mathematical Society (1990)

Kress, R., Rundell, W.: Reconstruction of extended sources for the Helmholtz equation. Inverse Probl. 29(3), 035005 (2013)

Levenberg, K.: A method for the solution of certain problems in least-squares. Q. Appl. Math. 2, 164–168 (1944)

Marquardt, D.: An algorithm for least-squares estimation of nonlinear parameters. J. Soc. Ind. Appl. Math. 11(2), 431–441 (1963)

Meyer, R., Roth, P.: Modified damped least squares: an algorithm for non-linear estimation. IMA J. Appl. Math. 9(2), 218–233 (1972)

Moré, J.: The Levenberg-Marquardt algorithm: implementation and theory. Lect. Notes Math. 630, 105–116 (1978)

Novikov, P.: Sur le probléme inverse du potentiel. Dokl.akad.nauk Sssr 18, 165–168 (1938)

Rainha, M., Roberty, N.: Integral and variational formulations for the Helmholtz equation inverse source problem. Math. Probl. Eng. 2012(1), 95–100 (2012)

Roberty, N., Alves, C.: On the identification of star-shape sources from boundary measurements using a reciprocity functional. Inverse Probl. Sci. Eng. 17 (2), 187–202 (2009)

Sakai, M.: A moment problem on Jordan domains. Proc. Am. Math. Soc. 70 (1), 35–38 (1978)

Schuhmacher, A., Hald, J., Rasmussen, K., Hansen, P.: Sound source reconstruction using inverse boundary element calculations. J. Acous. Soc. America 113(1), 114 (2003)

Proskurowski, W.: On the numerical solution of the eigenvalue problem of the laplace operator by a capacitance matrix method. Computing 20(2), 139–151 (1978)