Application of MPRGP algorithm for ice sheet melting problems

Abstract

Melting of glaciers and ice sheets poses several ecosystem threats, making the accurate modelling of their thermodynamic behaviour crucial. When simulating these dynamics, boundary conditions often involve inequality constraints that can be formulated as quadratic programming (QP) problems. The Modified Proportioning with Reduced Gradient Projections algorithm (MPRGP) is highly effective for solving QP problems.

The thesis focuses on applying MPRGP to problems arising in glaciology, specifically on solving the heat equation with a simple temperature upper bound inequality constraint. The main goal is to develop an interface between the PERMON toolbox, utilising its QP solver methods, and the Elmer/Ice software used for glacier modelling. The proposed solution is then benchmarked on a thermo-mechanically coupled steady state simulation for the Midtre Lovénbreen glacier in Svalbard.