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A parallel computational algorithm for an inverse problem of low frequency. (English) Zbl 0900.65383


MSC:

65R20 Numerical methods for integral equations
65R30 Numerical methods for ill-posed problems for integral equations
45E10 Integral equations of the convolution type (Abel, Picard, Toeplitz and Wiener-Hopf type)
Full Text: DOI

References:

[1] Ramm, A. G., Scattering by Obstacles (1986), Reidel: Reidel Dordrecht · Zbl 0607.35006
[2] Ramm, A. G., Uniqueness theorems for 3D inverse problems with incomplete data, Appl. Math. Lett., 3, 41 (1990) · Zbl 0721.35087
[3] Li, P.; Ramm, A. G., Numerical recovery of the layered medium, J. Comput. Appl. Math., 25, 267 (1989) · Zbl 0673.65091
[4] Zou, Q.; Ramm, A. G., Numerical solution of some inverse problems of geophysics, Comput. Math. Appl., 21, 75 (1991) · Zbl 0718.65092
[5] Zou, Q.; Xie, G.-q., A numerical approach for solving Ramm’s integral equation, (Gustafson, K.; Wyss, W., Proc. IMACS 1st Int. Conf. Computational Physics (1990), Univ. of Colorado: Univ. of Colorado Boulder, CO), 332
[6] Xie, G.-q.; Li, J., Nonlinear integral equation of inverse scattering problems of wave equation and iteration, J. Comput. Math., 8, 321 (1990) · Zbl 0724.65112
[7] Xie, G.-q.; Zou, Q., A parallel numerical method for solving 3D inverse scattering problem, Comput. Phys. Commun., 65, 320 (1991), this volume · Zbl 0900.65348
[8] Douglas, C. C.; Smith, B. F., Using symmetry and antisymmetry to analyze a parallel multigrid algorithm: the elliptic boundary value problem case, SIAM J. Num. Anal., 26, 1439 (1989) · Zbl 0688.65060
[9] Weglein, A., (Development in Geophysical Exploration Methods, 6 (1985), Elsevier: Elsevier Essex)
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