Date on Master's Thesis/Doctoral Dissertation


Document Type

Master's Thesis

Degree Name

M. Eng.



Committee Chair

Frieboes, Hermann B.

Committee Co-Chair (if applicable)

Steinbach-Rankins, Jill

Committee Member

Steinbach-Rankins, Jill

Committee Member

Rouchka, Eric

Author's Keywords

Parallel Processing; Mathematical Modeling; Distributed Computing; Cancer Modeling


Mathematical modeling aims to provide a theoretical framework for understanding tissue dynamics and for establishing treatment response for diseased tissues, such as tumors. Previously published continuum models have successfully represented idealized two-dimensional and three-dimensional tissue for short periods of time. A recently published continuum model of cancer increases model complexity and describes three-dimensional tissue that, due to the required complexity of the geometric multigrid solver, can only be feasibly applied to millimeter-scale simulations. Furthermore, the computational cost for such models has hindered their application in the laboratory and in the clinic. With computational demands greatly outpacing current openMP-based approaches on single-CPU-socket machines, higher performance solvers for large-scale tissue models remain a critical need. In this thesis, preliminary results of a CUDA and CUDA-MPI based parallelization applied to a tissue model are presented, with significant speedups seen in solution calculation for an initial time step. With further access to larger distributed computing, these parallel frameworks could potentially scale to simulate large-scale tissues.