Numerical solution of an inverse initial boundary-value problem for the full time-dependent Maxwell's equations in the presence of imperfections of small volume

References

• Ammari , H . 2003 . An inverse initial boundary value problem for the wave equation in the presence of imperfections of small volume . SIAM J. Control Optim. , 41 : 1194 – 1211 .
   Web of Science ®Google Scholar
• Ammari , H , Kang , H , Kim , E and Lim , M . 2005 . Reconstruction of closely spaced small inclusions . SIAM J. Numer. Anal. , 42 ( 6 ) : 2408 – 2428 .
   Web of Science ®Google Scholar
• Ammari , H , Moskow , S and Vogelius , M . 2003 . Boundary integral formulas for the reconstruction of electromagnetic imperfections of small diameter . ESAIM: COCV , 9 : 49 – 66 .
   Web of Science ®Google Scholar
• Ammari , H , Vogelius , M and Volkov , D . 2001 . Asymptotic formulas for perturbations in the electromagnetic fields due to the presence of inhomogeneities of small diameter: II The full Maxwell equations . J. Math. Pures Appl. , 80 : 769 – 814 .
   Web of Science ®Google Scholar
• Volkov , D . 2001 . “ An inverse problem for the time harmonic Maxwell equations ” . In Ph.D. thesis , New Brunswick , , NJ : Rutgers University .
   Google Scholar
• Sylvester , J and Uhlmann , G . 1987 . A global uniqueness theorem for an inverse boundary-value problem . Ann. Math. , 125 : 153 – 169 .
   Web of Science ®Google Scholar
• Vogelius , M and Volkov , D . 2000 . Asymptotic formulas for perturbations in the electromagnetic fields due to the presence of inhomogeneities . Math. Model. Numer. Anal. , 34 : 723 – 748 .
   Web of Science ®Google Scholar
• Cedio-Fengya , DJ , Moskow , S and Vogelius , M . 1998 . Identification of conductivity imperfections of small diameter by boundary measurements. Continuous dependence and computional reconstruction . Inverse Probl. , 14 : 553 – 595 .
   Web of Science ®Google Scholar
• Friedman , A and Vogelius , M . 1989 . Identification of small inhomogeneities of extreme conductivity by boundary measurements: A theorem on continuous dependence . Arch. Rat. Mech. Anal. , 105 : 299 – 326 .
   Web of Science ®Google Scholar
• Ammari , H . 2008 . “ An Introduction to Mathematics of Emerging Biomedical Imaging ” . In Mathematics and Applications , Vol. 62 , Berlin : Springer-Verlag .
   Google Scholar
• Ammari , H , Asch , M , Jugnon , V , Guadarrama Bustos , L and Khang , H . Transient wave imaging with limited-view data . SIAM J. Imaging Sci. , (to appear)
   Web of Science ®Google Scholar
• Asch , M , Darbas , M and Duval , J-B . 2010 . Numerical solution of an inverse initial boundary-value problem for the wave equation in the presence of imperfections of small volume , ESAIM-COCV . (to appear)
   Google Scholar
• Daveau , C , Khelifi , A and Sushchenko , A . 2009 . Reconstruction of closely spaced small inhomogeneities via boundary measurements for the full time-dependent Maxwell's equations . Math. Appl. Model. , 9 : 1719 – 1728 .
   Google Scholar
• Shushenko , A . 2010 . “ Résolution numérique d'un problème tridimentionnel en présence d'imperfections de petit volume ” . In Ph.D. thesis , Cergy-Pontoise University .
   Google Scholar
• Nicaise , S . 2000 . Exact boundary controllability of Maxwell's equations in heterogeneous media and an application to an inverse source problem . SIAM J. Control Optim. , 38 : 1145 – 1170 .
   Web of Science ®Google Scholar
• Ammari , H , Garapon , P , Guadarrama Bustos , L and Khang , H . 2010 . Transcient anormaly imaging by the acoustic radiation force . J. Differ. Eqns , 249 : 1579 – 1595 .
   Google Scholar
• Daveau , C , Khelifi , A and Shuschenko , A . 2009 . Reconstruction of small inhomogeneities for the full time-dependent Maxwell's equations . Aplimat , 2 02
   Google Scholar
• Lions , JL and Magenes , E . 1972 . Nonhomogeneous Boundary Value Problems and Applications , Vol. 1 , New York : Springer .
   Google Scholar
• Lions , JL . 1988 . Contrôlabilité Exacte, Perturbations et Stabilisation de Systèmes Distribués, Tome 1, Contrôlabilité Exacte , Paris : Masson .
   Google Scholar
• Evans , LC . 1998 . Partial Differential Equations , Providence, RI : Graduate Studies in Mathematics, AMS .
   Google Scholar
• Daveau , C and Zaghdani , A . 2009 . A hp-discontinuous Galerkin method for the time-dependent Maxwell's equations: A priori error estimate . J. Appl. Math. Comput. ,
   Google Scholar
• Zaghdani , A . 2007 . “ Formulations discontinues pour les équations de Maxwell ” . In Ph.D. thesis , Orsay University .
   Google Scholar
• Raviart , PA and Thomas , JM . 1983 . Introduction à l'analyse Numérique des Équations aux Dérivées Partielles , Paris : Masson .
   Google Scholar
• Asch , M and Lebeau , G . 1998 . Geometrical aspects of exact boundary controllability for the wave equation – A numerical study . ESAIM: Control, Optim. Calculus Var. , 3 : 163 – 212 .
   Google Scholar
• Bardos , C , Lebeau , G and Rauch , J . 1992 . Sharp sufficient conditions for the observation, control, and stabilization of waves from the boundary . SIAM J. Control Optim. , 30 : 1024 – 1065 .
   Web of Science ®Google Scholar
• Glowinski , R , Li , C-H and Lions , J-L . 1990 . A numerical approach to the exact boundary controllability of the wave equation . Japan J. Appl. Math. , 7 : 1 – 76 .
   Google Scholar