Talk by Benjamin Unger on "Decoupling time-discretization schemes for poroelasticity"

Biot’s consolidation model for poroelasticity is used as a mathematical model to simulate the deformation of a porous material saturated by a fluid and has diverse applications ranging from geophysical understanding to tumor modeling. From a mathematical point of view, the system consists of an elliptic PDE that is coupled with a parabolic equation. Due to the (operator) differential-algebraic character of the coupled system, explicit time-discretization schemes cannot be used, rendering this a computationally challenging problem. In this talk, we propose a novel semi-explicit time-discretization scheme that decouples the porous media flow and the mechanical problem with guaranteed convergence order if a weak coupling condition is satisfied. The convergence analysis is based on an interpretation of the semi-explicit scheme as an implicit scheme for a related time-delay equation. Using the theory of delay differential equations, we are able to explicitly quantify the weak coupling condition and illustrate that such a condition is, in fact, necessary for convergence. We close this talk by explaining how this idea can be extended to schemes with higher convergence order.

The lecture will take place in presence in the faculty room 8.122 and will be broadcast online via Webex.

We would like to inform you that wearing a mask is mandatory in the faculty room 8.122. We ask online participants to turn off your camera and microphone before joining so as not to disrupt the lecture.