Solving the inverse conductivity problems of nonlinear elliptic equations by the superposition of homogenization functions method

摘要

The inverse conductivity problem of a nonlinear elliptic equation is solved by using two sets of single-parameter homogenization functions as the bases for solution and conductivity function. When the solution is obtained by solving a linear system to satisfy the over-specified Neumann boundary condition on a partial boundary, the unknown conductivity function can be recovered by solving another linear system generated from the governing equation by collocation technique. The maximum absolute error of the recovered conductivity is smaller than the noise being imposed on the Neumann data. The superposition of homogenization functions method (SHFM) is quite accurate to find the whole solution and the conductivity function, and the required extra data are parsimonious. (C) 2019 Elsevier Ltd. All rights reserved.