A regularized integral equation method for the inverse geometry heat conduction problem

An adaptive greedy technique for inverse boundary determination problem

“…satisfies the Eq. (1) and the following initial-boundary conditions uðx; yÞ ¼ 100; ðx; yÞ 2 c; @uð0; yÞ @x ¼ 0; 0 6 y 6 sð0Þ; @uð10; yÞ @x ¼ 0; 0 6 y 6 sð10Þ; @uðx; 0Þ @y ¼ À20; 0 6 x 6 10; & The value of u(x, 0) = f(x) is obtained from solving the direct problem corresponding to (1)-(3) using the collocation method given in [10]. In Fig.…”

“…The numerical scheme based on the BEM in conjunction with the Tikhonov first-order regularization procedure has been studied by Lesnic et al [9]. Recently, Liu et al [10] have proposed the Fourier expansion technique with the Lavrentiev regularization to solve the inverse geometry heat conduction problem in a two-dimensional rectangle.…”

Fuzzy estimation for unknown boundary shape of fluid-solid conjugate heat transfer problem

“…The inverse heat transfer problems (IHTPs) is to use the temperature information inside or on the surface of the heat transfer system to estimate the unknown characteristic parameters, such as thermal physical parameters [1], geometry configurations [2], boundary conditions [3], the source term [4], etc.…”

An Analytical Method for the Inverse Cauchy Problem of Laplace Equation in a Rectangular Plate

“…By utilizing the separating characteristic of kernel function and eigenfunctions expansion technique we can derive a closed-form regularization solution of the second-kind Fredholm integral equation. Liu et al [31] have used this technique to solve the inverse geometric problem, and Liu [32] has solved the backward heat conduction problem. This method was first used by Liu [33] to solve a direct problem of elastic torsion of a bar with arbitrary cross-section, where it was called a meshless regularized integral equation method.…”