Hybridized Discontinuous Galerkin Methods for a Multiple Network Poroelasticity Model with Medical Applications

TL;DR

This paper introduces a new hybridized discontinuous Galerkin method for the MPET model, enabling stable, efficient, and parameter-robust simulations of multi-network poroelasticity with medical applications, demonstrated through brain modeling.

Contribution

A novel hybridized discontinuous Galerkin method for MPET that ensures stability, fluid mass conservation, and robustness across varying parameters, with efficient preconditioners developed.

Findings

Method is stable and parameter-robust.

Numerical results demonstrate effectiveness in brain modeling.

Preconditioners improve computational efficiency.

Abstract

The quasi-static multiple network poroelastic theory (MPET) model, first introduced in the context of geomechanics, has recently found new applications in medicine. In practice, the parameters in the MPET equations can vary over several orders of magnitude which makes their stable discretization and fast solution a challenging task. Here, a new efficient parameter-robust hybridized discontinuous Galerkin method, which also features fluid mass conservation, is proposed for the MPET model. Its stability analysis which is crucial for the well-posedness of the discrete problem is performed and cost-efficient fast parameter-robust preconditioners are derived. We present a series of numerical computations for a 4-network MPET model of a human brain which support the performance of the new algorithms.