Parallel fast isogeometric L2 projection solver with GALOIS system for 3D tumor growth simulations

Abstract

We present a parallel solver for isogeometric L2 projections implemented in GALOIS system. We use the solver for isogeometric finite element method simulations of tumor growth. First, we describe the dependencies between the quantities describing the melanoma tumor growth in three-dimensions. Later, we derive the system of partial differential equations modeling the tumor dynamics, including tumor cell density, tumor angiogenic factor, flux, pressure, extracellular and degraded extracellular matrices. The continuous model is coupled every ten-time steps with graph grammar model describing the vasculature network. The resulting system of PDEs is solved with our parallel solver over the shared memory Linux cluster node. We show high computational efficiency and accuracy of our model and we demonstrate its perfect parallel scalability with the number of CPU cores. We discuss the application of our solver in predictive oncology.