The mollification method and the numerical solution of the inverse heat conduction problem by finite differences

Abstract The inverse heat conduction problem involves the calculation of surface heat flux and/or temperature histories from transient, measured temperatures inside solids. We consider the one dimensional semi-infinite linear case and present a new solution algorithm based on a data filtering interpretation of the mollification method that automatically determines the radius of mollification depending on the amount of noise in the data and finite differences. A fully explicit and stable space marching scheme is developed. We describe several numerical experiments of interest showing that the new procedure is accurate and stable with respect to perturbations in the data even for small dimensionless time steps.

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