scholarly journals Linear Lavrent'ev Integral Equation for the Numerical Solution of a Nonlinear Coefficient Inverse Problem

2021 ◽  
Vol 81 (5) ◽  
pp. 1954-1978
Author(s):  
Michael V. Klibanov ◽  
Jingzhi Li ◽  
Wenlong Zhang
Keyword(s):  
Inverse Problem ◽  
Integral Equation ◽  
Numerical Solution ◽  
Nonlinear Coefficient ◽  
Coefficient Inverse Problem

scholarly journals Numerical solution of a coefficient inverse problem with multi-frequency experimental raw data by a globally convergent algorithm

2017 ◽  
Vol 345 ◽  
pp. 17-32 ◽  
Author(s):  
Dinh-Liem Nguyen ◽  
Michael V. Klibanov ◽  
Loc H. Nguyen ◽  
Aleksandr E. Kolesov ◽  
Michael A. Fiddy ◽  
...  
Keyword(s):  
Inverse Problem ◽  
Numerical Solution ◽  
Coefficient Inverse Problem ◽  
Raw Data ◽  
Globally Convergent ◽  
Convergent Algorithm

On One Approach to the Numerical Solution of a Coefficient Inverse Problem

2021 ◽  
Vol 104 (1) ◽  
pp. 208-211
Author(s):  
A. F. Albu ◽  
Yu. G. Evtushenko ◽  
V. I. Zubov
Keyword(s):  
Inverse Problem ◽  
Numerical Solution ◽  
Coefficient Inverse Problem

scholarly journals A numerical method for an inverse source problem for parabolic equations and its application to a coefficient inverse problem

2020 ◽  
Vol 28 (3) ◽  
pp. 323-339 ◽  
Author(s):  
Phuong Mai Nguyen ◽  
Loc Hoang Nguyen
Keyword(s):  
Inverse Problem ◽  
Numerical Method ◽  
Parabolic Equations ◽  
Source Term ◽  
Nonlinear Coefficient ◽  
Time Variable ◽  
Inverse Source Problem ◽  
Coefficient Inverse Problem ◽  
Second Stage ◽  
Two Stages

AbstractTwo main aims of this paper are to develop a numerical method to solve an inverse source problem for parabolic equations and apply it to solve a nonlinear coefficient inverse problem. The inverse source problem in this paper is the problem to reconstruct a source term from external observations. Our method to solve this inverse source problem consists of two stages. We first establish an equation of the derivative of the solution to the parabolic equation with respect to the time variable. Then, in the second stage, we solve this equation by the quasi-reversibility method. The inverse source problem considered in this paper is the linearization of a nonlinear coefficient inverse problem. Hence, iteratively solving the inverse source problem provides the numerical solution to that coefficient inverse problem. Numerical results for the inverse source problem under consideration and the corresponding nonlinear coefficient inverse problem are presented.

On the construction of orthogonal curvilinear grids for regional oceanic modeling: algorithm and user guide

2020 ◽  
Vol 48 (4) ◽  
pp. 45-111
Author(s):  
A. F. Shepetkin
Keyword(s):  
Inverse Problem ◽  
Numerical Solution ◽  
Elliptic Problem ◽  
Software Package ◽  
Conformal Transformation ◽  
Iterative Procedure ◽  
Geometric Shape ◽  
Curvilinear Grids ◽  
Grid Points ◽  
Grid Nodes

A new algorithm for constructing orthogonal curvilinear grids on a sphere for a fairly general geometric shape of the modeling region is implemented as a “compile-once - use forever” software package. It is based on the numerical solution of the inverse problem by an iterative procedure -- finding such distribution of grid points along its perimeter, so that the conformal transformation of the perimeter into a rectangle turns this distribution into uniform one. The iterative procedure itself turns out to be multilevel - i.e. an iterative loop built around another, internal iterative procedure. Thereafter, knowing this distribution, the grid nodes inside the region are obtained solving an elliptic problem. It is shown that it was possible to obtain the exact orthogonality of the perimeter at the corners of the grid, to achieve very small, previously unattainable level of orthogonality errors, as well as make it isotropic -- local distances between grid nodes about both directions are equal to each other.

Sign in / Sign up

Export Citation Format

Share Document