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Overlapping domain decomposition methods for linear inverse problems
1. | School of Mathematics and Statistics, Central China Normal University, Wuhan 430079, China |
2. | School of Mathematics and Statistics, Wuhan University, Wuhan 430072, China |
3. | Department of Mathematics, The Chinese University of Hong Kong, Shatin, N.T., Hong Kong |
References:
[1] |
R. C. Aster, B. Borchers and C. H. Thurber, Parameter Estimation and Inverse Problems, Elsevier Academic Press, New York, 2005. |
[2] |
H. T. Banks and K. Kunisch, Estimation Techniques for Distributed Parameter Systems, Birkhauser, Boston, 1989. |
[3] |
X. Cai, S. Liu and J. Zou, Parallel overlapping domain decomposition methods for coupled inverse elliptic problems, Comm. Appl. Math. Comput. Sci., 4 (2009), 1-26.
doi: 10.2140/camcos.2009.4.1. |
[4] |
T. Chan and T. Mathew, Domain decomposition algorithms, Acta Numerica, (1994), 61-143. |
[5] |
T. Chan and X. Tai, Identification of discontinuous coefficients from elliptic problems using total variation regularization, SIAM J. Sci. Comput., 25 (2003), 881-904.
doi: 10.1137/S1064827599326020. |
[6] |
H. Chang and D. Yang, A Schwarz domain decomposition method with gradient projection for optimal control governed by elliptic partial differential equations, J. Comput. Appl. Math., 235 (2011), 5078-5094.
doi: 10.1016/j.cam.2011.04.037. |
[7] |
I. Daubechies, M. Defrise and C. Demol, An iterative thresholding algorithm for linear inverse problems, Comm. Pure Appl. Math., 57 (2004), 1413-1457.
doi: 10.1002/cpa.20042. |
[8] |
H. Engl, M. Hanke and A. Neubauer, Regularization of Inverse Problems, Kluwer Academic Publishers, The Netherlands, 2000. |
[9] |
M. Heinkenschloss and M. Herty, A spatial domain decomposition method for parabolic optimal control problems, J. Comput. Appl. Math., 201 (2007), 88-111.
doi: 10.1016/j.cam.2006.02.002. |
[10] |
M. Heinkenschloss and H. Nguyen, Neumann-Neumann domain decomposition preconditioners for linear-quadratic elliptic optimal control problems, SIAM Journal on Scientific Computing, 28 (2006), 1001-1028.
doi: 10.1137/040612774. |
[11] |
K. Ito and J. Zou, Identification of some source densities of the distribution type, J. Comput. Appl. Math., 132 (2001), 295-308.
doi: 10.1016/S0377-0427(00)00332-0. |
[12] |
J. Li and J. Zou, A multilevel model correction method for parameter identification, Inverse Problems, 23 (2007), 1759-1786.
doi: 10.1088/0266-5611/23/5/001. |
[13] |
X. Tai, J. Froyen, M. Espedal and T. Chan, Overlapping domain decomposition and multigrid methods for inverse problems, Contemporary Mathematics, 218 (1998), 523-529. |
[14] |
A. Toselli and O. Widlund, Domain Decomposition Methods-Algorithms and Theory, Springer-Verlag, New York, 2004. |
[15] |
L. Wang and J. Zou, Error estimates of finite element methods for parameter identifications in elliptic and parabolic systems, Disc. Cont. Dynam. Sys., Series B, 14 (2010), 1641-1670.
doi: 10.3934/dcdsb.2010.14.1641. |
[16] |
J. Xie and J. Zou, Numerical reconstruction of heat fluxes, SIAM J. Numer. Anal., 43 (2005), 1504-1535.
doi: 10.1137/030602551. |
[17] |
J. Xu, Iterative methods by space decomposition and subspace correction, SIAM Review, 34 (1992), 581-613.
doi: 10.1137/1034116. |
[18] |
J. Xu and J. Zou, Some nonoverlapping domain decomposition methods, SIAM Review, 40 (1998), 857-914.
doi: 10.1137/S0036144596306800. |
show all references
References:
[1] |
R. C. Aster, B. Borchers and C. H. Thurber, Parameter Estimation and Inverse Problems, Elsevier Academic Press, New York, 2005. |
[2] |
H. T. Banks and K. Kunisch, Estimation Techniques for Distributed Parameter Systems, Birkhauser, Boston, 1989. |
[3] |
X. Cai, S. Liu and J. Zou, Parallel overlapping domain decomposition methods for coupled inverse elliptic problems, Comm. Appl. Math. Comput. Sci., 4 (2009), 1-26.
doi: 10.2140/camcos.2009.4.1. |
[4] |
T. Chan and T. Mathew, Domain decomposition algorithms, Acta Numerica, (1994), 61-143. |
[5] |
T. Chan and X. Tai, Identification of discontinuous coefficients from elliptic problems using total variation regularization, SIAM J. Sci. Comput., 25 (2003), 881-904.
doi: 10.1137/S1064827599326020. |
[6] |
H. Chang and D. Yang, A Schwarz domain decomposition method with gradient projection for optimal control governed by elliptic partial differential equations, J. Comput. Appl. Math., 235 (2011), 5078-5094.
doi: 10.1016/j.cam.2011.04.037. |
[7] |
I. Daubechies, M. Defrise and C. Demol, An iterative thresholding algorithm for linear inverse problems, Comm. Pure Appl. Math., 57 (2004), 1413-1457.
doi: 10.1002/cpa.20042. |
[8] |
H. Engl, M. Hanke and A. Neubauer, Regularization of Inverse Problems, Kluwer Academic Publishers, The Netherlands, 2000. |
[9] |
M. Heinkenschloss and M. Herty, A spatial domain decomposition method for parabolic optimal control problems, J. Comput. Appl. Math., 201 (2007), 88-111.
doi: 10.1016/j.cam.2006.02.002. |
[10] |
M. Heinkenschloss and H. Nguyen, Neumann-Neumann domain decomposition preconditioners for linear-quadratic elliptic optimal control problems, SIAM Journal on Scientific Computing, 28 (2006), 1001-1028.
doi: 10.1137/040612774. |
[11] |
K. Ito and J. Zou, Identification of some source densities of the distribution type, J. Comput. Appl. Math., 132 (2001), 295-308.
doi: 10.1016/S0377-0427(00)00332-0. |
[12] |
J. Li and J. Zou, A multilevel model correction method for parameter identification, Inverse Problems, 23 (2007), 1759-1786.
doi: 10.1088/0266-5611/23/5/001. |
[13] |
X. Tai, J. Froyen, M. Espedal and T. Chan, Overlapping domain decomposition and multigrid methods for inverse problems, Contemporary Mathematics, 218 (1998), 523-529. |
[14] |
A. Toselli and O. Widlund, Domain Decomposition Methods-Algorithms and Theory, Springer-Verlag, New York, 2004. |
[15] |
L. Wang and J. Zou, Error estimates of finite element methods for parameter identifications in elliptic and parabolic systems, Disc. Cont. Dynam. Sys., Series B, 14 (2010), 1641-1670.
doi: 10.3934/dcdsb.2010.14.1641. |
[16] |
J. Xie and J. Zou, Numerical reconstruction of heat fluxes, SIAM J. Numer. Anal., 43 (2005), 1504-1535.
doi: 10.1137/030602551. |
[17] |
J. Xu, Iterative methods by space decomposition and subspace correction, SIAM Review, 34 (1992), 581-613.
doi: 10.1137/1034116. |
[18] |
J. Xu and J. Zou, Some nonoverlapping domain decomposition methods, SIAM Review, 40 (1998), 857-914.
doi: 10.1137/S0036144596306800. |
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