FETI-DP algorithms for 2D Biot model with discontinuous Galerkin discretization

TL;DR

This paper develops and tests FETI-DP algorithms for a 2D Biot model discretized with mixed finite elements, demonstrating scalability and effectiveness in modeling coupled elasticity and Darcy flow.

Contribution

It introduces FETI-DP algorithms tailored for a 2D Biot model with mixed finite element discretization, including stability and parallel scalability analysis.

Findings

FETI-DP algorithms effectively solve the 2D Biot model.

Numerical experiments show scalability in elasticity and Darcy flow.

Algorithms perform well with Dirichlet preconditioners.

Abstract

Dual-Primal Finite Element Tearing and Interconnecting (FETI-DP) algorithms are developed for a 2D Biot model. The model is formulated with mixed-finite elements as a saddle-point problem. The displacement $\mathbf{u}$ and the Darcy flux flow $\mathbf{z}$ are represented with $P_1$ piecewise continuous elements and pore-pressure $p$ with $P_0$ piecewise constant elements, {\it i.e.}, overall three fields with a stabilizing term. We have tested the functionality of FETI-DP with Dirichlet preconditioners. Numerical experiments show a signature of scalability of the resulting parallel algorithm in the compressible elasticity with permeable Darcy flow as well as almost incompressible elasticity.