Year of Award


Document Type


Degree Type

Master of Science (MS)

Degree Name

Computer Science

Department or School/College

Department of Computer Science

Committee Chair

Jesse Johnson

Commitee Members

Alden Wright, Marco Maneta


approximation, discretization, finite elements, first variation, fortran, fortran 90, galerkin, ice sheet, incompressible, l1l2, model, momentum balance, non-newtonian, partial differential equations, rheology, sea-level rise, shallow ice, shallow shelf


University of Montana


A new high-fidelity ice sheet momentum balance model meant for inclusion in the Glimmer community ice-sheet model is presented. As a component of the Community Earth Systems Model the newly developed momentum balance will directly benefit from ice/ocean and ice/atmosphere coupling efforts occurring elsewhere. The objectives of this thesis are to develop a model which converges quickly (quadratic convergence rates) for non-Newtonian Stokes flow approximations, and to provide a clear and low-level discussion of its derivation, variation and discretization. The model utilizes the Finite Element Method to discretize variational forms of the first variation arising from the Galerkin method and for vertically-integrated Stokes flow. The model employs a hybridization of two commonly used approximations to Stokes flow. It couples the Shallow Shelf Approximation (SSA) and Shallow Ice Approximation (SIA). This approximation is then differentiated symbolically. Efficient sparse matrix formats are manipulated directly to avoid invoking costly sorting routines in the underlying linear solvers. The code was not only developed for standards-compliant FORTRAN 90 compilers but also for automatic differentiation tools. The model is verified against published model intercomparison projects.



© Copyright 2013 Joshua Charles Campbell