Abdullah Mujahid

Decoupling integration schemes of higher order for poroelastic networks
The study of multiphysics phenomena in geomechanics and design of biomedicine in the case of human brain tumours leads to coupled Partial Differential Equation (PDE) systems. These are coupled systems of elliptic and parabolic type which are computationally challenging, especially in the 3-dimensional cases. We develop semi-explicit time integration schemes that decouple into the elliptic and the parabolic subsystems, thus enabling the use of modular single-physics solvers for the subsystems with highly optimized preconditioners. The error analysis of the proposed higher-order semi-explicit time integration methods is based on the novel idea of employing the asymptotic stability theory of delay differential-algebraic equations.