Sparse Reconstructions for Inverse PDE Problems

Structured Decompositions and Efficient Algorithms

计算机科学;物理学

Thorsten Raasch1

PID  :  82178

学科分类：计算机科学（综合）

来源: CEUR

【 摘 要 】

We are concerned with the numerical solution of linear parameter identification problems for parabolic PDE, written as an oper ator equation Ku = f . The target object u is assumed to have a sparse expansion with respect to a wavelet system= {} in spacetime. For the recovery of the unknown coefficient array, we use Tikhonov regular ization with `p coefficient penalties and the associated iterative shrinkage algorithms. Since any application of K and K involves the numerical solution of a PDE, perturbed versions of the iteration have to be stud ied. In particular, for reasons of efficiency, adaptive operator applications are indispensable. By a suitable choice of the respective tolerances and stopping criteria, also the adaptive iteration converges and it has regular izing properties. We illustrate the performance of the resulting method by numerical computations for one and twodimensional inverse heat conduction problems.