The article “Consistency of the Douglas–Rachford splitting algorithm for the sum of three nonlinear operators: application to the Stefan problem in permafrost” was published in the peer-reviewed journal Applied and Computational Mathematics Vol. 2, No. 4, August 2013.

Abstract: Consistency of the Douglas–Rachford dimensional splitting scheme is proved for the sum of three nonlinear operators constituting an evolution equation. It is shown that the operators must be densely defined, maximal monotone and single valued on a real Hilbert space in order to satisfy conditions, under which the splitting algorithm can be applied. Numerical experiment conducted for a three-dimensional Stefan problem in permafrost suggests that the Douglas–Rachford scheme produces reasonable results, although the convergence rate remains unestablished.

Numerical experiment, conducted for 3D Stefan problem in permafrost indicates that Douglas-Rachford algorithm gives reliable results, although the convergence rate remains unknown.

Read the original article (PDF) on the publisher website.

The algorithm, given in this article, is used in the numerical solver of the Frost 3D software, designed for simulating artificial freezing and thermal stabilization of the foundations of soils.