Adaptive wavelet methods and sparsity reconstruction for inverse heat conduction problems

Authors:
Thomas Bonesky;Stephan Dahlke;Peter Maass;Thorsten Raasch
Affiliations:
Center for Industrial Mathematics/Fachbereich 3, University of Bremen, Bremen, Germany 28334;Philipps-Universität Marburg, Marburg, Germany 35032;Center for Industrial Mathematics/Fachbereich 3, University of Bremen, Bremen, Germany 28334;Institut für Mathematik, Johannes Gutenberg-Universität Mainz, Mainz, Germany 55099
Venue:
Advances in Computational Mathematics
Year:
2010

Citing 7
Cited 0

Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems

Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems
Stable multiscale bases and local error estimation for elliptic problems

Applied Numerical Mathematics - Special issue on multilevel methods
Composite wavelet bases for operator equations

Mathematics of Computation
Adaptive wavelet methods for elliptic operator equations: convergence rates

Mathematics of Computation
Adaptive Solution of Operator Equations Using Wavelet Frames

SIAM Journal on Numerical Analysis
Iterated Hard Shrinkage for Minimization Problems with Sparsity Constraints

SIAM Journal on Scientific Computing
A generalized conditional gradient method and its connection to an iterative shrinkage method

Computational Optimization and Applications

Quantified Score

Hi-index	0.00

Visualization

Abstract

This paper is concerned with the numerical treatment of inverse heat conduction problems. In particular, we combine recent results on the regularization of ill-posed problems by iterated soft shrinkage with adaptive wavelet algorithms for the forward problem. The analysis is applied to an inverse parabolic problem that stems from the industrial process of melting iron ore in a steel furnace. Some numerical experiments that confirm the applicability of our approach are presented.