Starting a cooperation with Biophysics at the Medical University of Graz
on cardivascular simulations 13 years ago lead to various interesting
mathematically research topics, especially in modelling and solving the underlying PDEs (partial differential equations).
We will present some ideas from our Algebraic Multigrid solver approach, incorporated in the cardiac modeling framework CARP
(Cardiac Arrhythmia Research Package),
that solves discretized PDEs on clusters of CPUs/GPUs with up to 8192 CPU cores.
This solver is applied to the bidomain equations (electrical potential) as well as
to the non-linear elasticity. Some implementational details reagarding performance will be discussed.
Recent CFD simulations of hemodynamics in the aorta take into account moving valves.
Avoiding a full fluid-structure-interaction (FSI), a re-modelling of Navier-Stokes-Brinkman equation
with changing permeability in the region of the valve achieves excellent results in
representing the blood flow when the valve opens/closes.
When only specific details as the electrical excitation of the heart are of interest then
much simpler models as the Eikonal equation (arrivel times of a wave) can be considered.
We will present our Eikonal solver for tetrahedral meshes and discuss implementational details
on CPUs and GPUs. This fast simulation is used in a parameter estimation approach.
Very briefly, a recent project on reinforcement learning with the local automotive industry is presented.