in this paper, we demonstrate the existence and uniqueness a semianalytical solution of an inverse heat conduction problem (ihcp) in the form: ut = uxx in the domain d = {(x, t)| 0 < x < 1, 0 < t t}, u(x, t) = f(x), u(0, t) = g(t), and ux(0, t) = p(t), for any 0 t t. some numerical experiments are given in the final section.

Electrical impedance tomography (EIT) uses surface electrodes to make measurements from which an image of the conductivity distribution within some medium is calculated. Calculation of conductivity solutions requires inverting large linear systems that have to date restricted reconstructions to 2D or coarse 3D domains. This paper presents a Nodal Jacobian Inverse Solver that scales with the num...

It is well known that the parabolic partial differential equations in two or more space dimensions with overspecified boundary data, feature in the mathematical modeling of many phenomena. In this article, an inverse problem of determining an unknown time-dependent source term of a parabolic equation in general dimensions is considered. Employing some transformations, we change the inverse prob...

in this paper, two inverse problems of stephen kind with local (dirichlet) boundary conditions are investigated. in the first problem only a part of boundary is unknown and in the second problem, the whole of boundary is unknown. for the both of problems, at first, analytic expressions for unknown boundary are presented, then by using these analytic expressions for unknown boundaries and bounda...

2 Hierarchical Preconditioner for Scalar Bases 3 2.1 General Hierarchical Preconditioner Formula . . . . . . . . . . . 3 2.2 Hierarchical Splitting in Case of Nodal Basis Functions . . . . . 4 2.3 Hierarchical Preconditioner Formula for Bases of Nodal Basis Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2.4 Implementation . . . . . . . . . . . . . . . . . . . . . . . . ...

Parallel to the signless Laplacian spectral theory, we introduce and develop the nonlinear spectral theory of signless 1-Laplacian on graphs. Again, the first eigenvalue μ1 of the signless 1-Laplacian precisely characterizes the bipartiteness of a graph and naturally connects to the maxcut problem. However, the dual Cheeger constant h+, which has only some upper and lower bounds in the Laplacia...