| Summary: | Modeling glacier and ice sheet flow is a computationally challenging problem. The most challenging part in simulating ice sheet flow is modeling the fastest moving part of ice sheets, ice streams. In the first part of the thesis, we have constructed two numerical models of isothermal ice stream flow, a three-dimensional full-Stokes ice-sheet/ice-stream/ice-shelf model and a modified MacAyeal-Morland ice-stream/ice-shelf model. In the second part of the thesis, we studied the possibility of using SuperLU-DIST multiprocessor software package for solving the systems of linear equations generated by the model. The uniqueness of the modified MacAyeal-Morland model is in its inclusion of the basal shear friction in the derivation of the equations. In the original MacAyeal-Morland equations, the shear friction is not included in the fundamental formulation but instead is added as a small correction to the final equations. Inclusion of the basal friction in the derivation generates equations that contain a term that depends on the bed gradients; that is, it generates equations that show how the ice stream flow may depend on the bed topography. To validate the model, the European Ice Sheet Modeling Initiative 1 intercomparison test is conducted and the results are compared with the results generated by MacAyeal (1994). The three-dimensional full-Stokes model includes all higher-order stress gradients in the force-balance equation. To validate the full-Stokes model, experiments demonstrating the importance of the inclusion of all higher order stresses in the model, such as simulation of the evolution of an ice stream within the ice sheet and simulation of iceberg profiles, are conducted. The computational demands of the full-Stokes model do not allow us using it in large problem domains. To solve this problem, application of SuperLU-DIST multiprocessor software package has been examined. The software's performance characteristics have been explored and benchmarked on the matrices generated by the three-dimensional full-Stokes model. The performed tests indicate that for the big-size matrices computations may not be stable. However, we have shown that it is possible to improve stability of the algorithm by using a priori knowledge of the matrix and permuting rows prior to applying the algorithm.
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