Lorena Bociu, NC State University
2023 AWM Research Symposium
Recent Developments in Control, Optimization, and the Analysis of Partial Differential Equations [Organized by Lorena Bociu and Pelin Guven Geredeli]

Complex problems in biomedicine often need to be modeled by multiscale couplings between partial differential equations (PDEs) and ordinary differential equations (ODEs), in order to combine the accurate three-dimensional (3D) description of a local region of interest with the global features of the problem represented by reduced lumped models. We focus on a PDE/ODE system stemming from the multiscale interface coupling between a local description of tissue perfusion via a 3D deformable porous medium and a 0D lumped hydraulic circuit accounting for the blood circulation to and from the tissue. We present solution methods of the multiscale problem described above, focusing on a detailed comparison between functional iterations and an energy-based operator splitting method and how they handle the nonlocal interface conditions.

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