Model functions in the modified L-curve method—case study: the heat flux reconstruction in pool boiling

The L-curve method is known as one of the most popular heuristic regularization parameter choice rules in solving discrete ill-posed problems: Ax = yδ. A modification of the L-curve method proposed by Regińska (1996 SIAM J. Sci. Comput. 17 740–9) consists in finding the minimizer of the functional Ψμ = ∥Ax(α)-yδ∥2∥x(α)∥2μ, where −1/μ is the slope at the corner of the L-curve. In this paper we propose a model function approach in the modified L-curve method for the choice of the regularization parameter. The idea is to replace the residual norm and the regularized solution norm with appropriate model functions. With such an approach, the computational cost of the minimization procedure can be essentially reduced. This approach is applied to pool boiling data to reconstruct unknown heat fluxes at the boiling surface