Synthesis of global convergence and adaptivity for a hyperbolic coefficient inverse problem in 3D
نویسندگان
چکیده
norwegian university of science and technology trondheim, norway A globally convergent numerical method for a multidimensional Coefficient Inverse Problem for a hyperbolic equation is presented. The global convergence is analytically established. It is shown that this technique provides a good first guess for the adaptivity method, which entails to a synthesis of both approaches. Numerical results for the 3-D case are presented. keywords: two-stage numerical procedure, globally convergent numerical method, adap-tive finite element method
منابع مشابه
A posteriori error estimates for the adaptivity technique for the Tikhonov functional and global convergence for a coefficient inverse problem
A synthesis of a globally convergent numerical method for a coefficient inverse problem and the adaptivity technique is presented. First, the globally convergent method provides a good approximation for the unknown coefficient. Next, this approximation is refined via the adaptivity technique. The analytical effort is focused on a posteriori error estimates for the adaptivity. A numerical test i...
متن کاملA globally convergent numerical method and adaptivity for a hyperbolic coefficient inverse problem
norwegian university of science and technology trondheim, norway A globally convergent numerical method for a multidimensional Coefficient Inverse Problem for a hyperbolic equation is presented. It is shown that this technique provides a good starting point for the so-called finite element adaptive method (adaptivity). This leads to a natural two-stage numerical procedure, which synthesizes bot...
متن کاملAdaptivity with Relaxation for Ill-posed Problems and Global Convergence for a Coefficient Inverse Problem
GLOBAL CONVERGENCE FOR A COEFFICIENT INVERSE PROBLEM ∗ LARISA BEILINA† , MICHAEL V. KLIBANOV ‡ , AND MIKHAIL YU. KOKURIN § Abstra t. A new framework of the Fun tional Analysis is developed for the adaptive FEM (adaptivity) for the Tikhonov regularization fun tional for ill-posed problems. As a result, the relaxation property for adaptive mesh re nements is established. An appli ation to a multi...
متن کاملApproximate global convergence and quasi-reversibility for a coefficient inverse problem with backscattering data
A numerical method with the approximate global convergence property is developed for a 3-D Coefficient Inverse Problem for a hyperbolic PDE with the backscattering data. An important part of this technique is the quasi-reversibility method. Approximate global convergence theorem is proven. Results of two numerical experiments are presented.
متن کاملGlobal convergence and quasi-reversibility for a coefficient inverse problem with backscattering data
A globally convergent numerical method is developed for a 2-d Coefficient Inverse Problem for a hyperbolic PDE with the backscattering data. An important part of this technique is the quasi-reversibility method. A global convergence theorem is proven via a Carleman estimate. Results of numerical experiments for the problem modeling imaging of plastic land mines are presented.
متن کامل