Determination Of The Heat Source And The Initial Temperature By A Method Of Fundamental Solutions

The problem of recovering a heat source and the initial temperature is investi-gated in this paper. Because the heat source is space-dependent only, we transform the original problem into a homogenous backward heat conduction problem and a Dirichlet boundary value problem for Poisson’s equation. A theorem given in this paper shows that the heat source and the initial temperature can be unique-ly determined from the specified condition. We apply a method of fundamental solutions to the homogenous backward heat conduction problem, and finite el-ement method to the Dirichlet boundary value problem for Poisson’s equation. Ⅲ-posedness of backward heat conduction problem leads to the ill-conditioned linear system from discretization by the method of fundamental solutions. We use a discrete Tikhonov regularization to obtain a stable regularization solution of the ill-conditioned linear system, and the generalized cross validation(GCV) to selec-t an appropriate regularization parameter. Finally, four numerical experiments show that our proposed method is stable and effective.