NCSU Differential Equations/Nonlinear Analysis Seminars

Location and Time: SAS 4201, Wednesday 15:00 -16:00

Organizers: Lorena Bociu, Patrick Combettes, Ryan Murray, and Khai T. Nguyen

NEXT TALK

Wednesday, Mar 26, 15:00-16:00, Room: SAS 4201

Speaker: Wonjun Lee, University of Minnesota
Title:  An efficient numerical scheme for tumor growth models
Abstract: Cancer is a leading cause of mortality, and despite extensive research, a cure remains elusive. This paper focuses on the mathematical modeling of tumor growth using a continuum PDE approach. Specifically, we investigate models where tumor growth is driven by competition for space, treating cells as a viscous incompressible fluid, with pressure influencing cell dynamics. The model is governed by a reaction-diffusion equation that describes the evolution of cell density, incorporating complex interactions such as nutrient availability and heterogeneous growth rates across multiple cell populations.

We introduce a novel numerical method for solving multi-species tumor growth models based on the dual problem in a JKO-type scheme by Jacobs, Kim, and Tong (2021) for approximating Darcy’s law with a source term. This method provides a significant improvement over existing approaches, offering more accurate and efficient simulations. We apply this method to solve the coupled system in both compressible and incompressible regimes, as well as under nutrient-abundant and nutrient-deficient conditions, in high-resolution grid settings (1024×1024 or 2048×2048 grid pixels). The results demonstrate the method’s effectiveness in producing high-quality numerical solutions.

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