The increasing demand on the quality and reliability of scientific computing makes the quantification of uncertainties in mathematical models and imput data a crucial task. Including Uncertainty Quantification to scientific computing leads to a shift of paradigm from purely deterministic problems to the stochastic models. In addition, the development of new hardware technologies enables us to tackle the challenges arising from Uncertainty Quantification associated to the growth in complexity and quantity of numerical computation, it requires therefore the adaption and new development of exascale computing methods.
The overall scientific goal of building a bridge between Uncertainty Quantification and High Performance Computing is therefore addressed on several interacting research tasks at EMCL:
- non-intrusive and intrusive methods in Uncertainty Quantification for systems of partial differential equations (PDEs) and ordinary differential equations (ODEs) with uncertain parameters;
- model reduction techniques in order to deal with the curse of dimensionality and for enhancing parallelism;
- efficient accelerator and preconditioning technologies to be used on large-scale super-computing clusters;
- open-source software-development for making the implementations accessible for the worldwide research community;
- real-word application, with strong emphasis on complex geometries and coupling systems.
Application example :
Blood pump scenario, the inflow boundary condition, viscosity and the rotation speed are modeled as uncertain parameter.