Time Reversed Absorbing Condition (trac): Recreate the past & Applications to Inverse Problems
نویسندگان
چکیده
We introduce time reversed absorbing conditions (TRAC) in time reversal methods. They enable one to “recreate the past” without knowing the source which has emitted the signals that are back-propagated. Two applications in inverse problems are presented. The method does not rely on any a priori knowledge of the physical properties of the inclusion. Numerical tests with the wave equation illustrate the efficiency of the method. This technique is fairly insensitive with respect to noise in the data.
منابع مشابه
Time Reversed Absorbing Condition: Application to inverse problems
The aim of this paper is to introduce the time-reversed absorbing conditions (TRAC) in time-reversal methods. They enable one to “recreate the past” without knowing the source which has emitted the signals that are back-propagated. We present two applications in inverse problems: the reduction of the size of the computational domain and the determination, from boundary measurements, of the loca...
متن کاملA new approach to solve the inverse scattering problem for waves: combining the TRAC and the adaptive inversion methods
The aim of this paper is to propose a new method to solve the inverse scattering problem. This method works directly in the time-dependent domain, using the wave equation and proceeds in two steps. The first step is the Time-Reversed Absorbing Condition (TRAC) method to reconstruct and regularize the signal and to reduce the computational domain. The second step is the Adaptive Inversion method...
متن کاملTime Reversed Absorbing Conditions
The aim of this paper is to introduce the time reversed absorbing conditions (TRAC) in time reversal methods. These new boundary conditions enable one to “recreate the past” without knowing the source which has emitted the signals that are back-propagated. This new method does not rely on any a priori knowledge of the physical properties of the inclusion. We prove an energy estimate for the res...
متن کاملApplications of He’s Variational Principle method and the Kudryashov method to nonlinear time-fractional differential equations
In this paper, we establish exact solutions for the time-fractional Klein-Gordon equation, and the time-fractional Hirota-Satsuma coupled KdV system. The He’s semi-inverse and the Kudryashov methods are used to construct exact solutions of these equations. We apply He’s semi-inverse method to establish a variational theory for the time-fractional Klein-Gordon equation, and the time-fractiona...
متن کاملImplementation of Sinc-Galerkin on Parabolic Inverse problem with unknown boundary condition
The determination of an unknown boundary condition, in a nonlinaer inverse diffusion problem is considered. For solving these ill-posed inverse problems, Galerkin method based on Sinc basis functions for space and time will be used. To solve the system of linear equation, a noise is imposed and Tikhonove regularization is applied. By using a sensor located at a point in the domain of $x$, say $...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2011