Sinc-Galerkin Estimation of Diffusivity in Parabolic Problems
INSTITUTE FOR COMPUTER APPLICATIONS IN SCIENCE AND ENGINEERING HAMPTON VA
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A fully Sinc Galerkin method for the numerical recovery of spatially varying diffusion coefficients in linear partial differential equations is presented. Because the parameter recovery problems are inherently ill-posed, an output error criterion in conjunction with Tikhonov regularization is used to formulate them as infinite-dimensional minimization problems. The forward problems are discretized with a sinc basis in both the spatial and temporal domains thus yielding an approximate solution which displays an exponential convergence rate and is valid on the infinite time interval. The minimization problems are then solved via a quasi-Newtontrust region algorithm. The L-curve technique for determining an appropriate value of the regularization parameter is briefly discussed, and numerical examples are given which demonstrate the applicability of the method both for problems with noise-free data as well as for those whose data contains white noise.
- Numerical Mathematics