Physics-oriented solvers for multicompartmental poromechanics

• Applicant: Professor Dr. Johannes Kraus
• Subject Area: Mathematics
• Term: since 2021
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 456235063

Classical Biot theory provides the foundation for a fully dynamic poroelasticity model describing the propagation of elastic waves in fluid-saturated media. Multiple network poroelastic theory (MPET) takes into account that the elastic matrix (solid) can be permeated by one or several superimposed interacting single fluid networks of possibly highly diverse characteristics. Biological multicompartmental poroelasticity models can be used to embed more specific medical models, e.g., to describe water transport in the cerebral environment.This project focuses on physics-oriented solvers for the quasi-static and dynamic MPET models. Solvers are understood here to be combined discretization and iterative solution methods. By physics-oriented, we mean that formulations are used which adequately describe the physics of the studied problem, discretizations are chosen that preserve its differential algebraic structure and correctly reflect physical properties such as energy dissipation, conservation of mass and momentum, and, finally, iterative solution methods are carefully adjusted to harmonize with the discretization process--resulting in high-performance solvers. Their design and numerical analysis are the ultimate goals of this project.

• DFG Programme: Research Grants