Solving Random Differential Equations with HPC and UQ techniques

In the field of scientific computing, random effects become increasingly important to allow for an accurate modelling of realistic effects. Random Differential Equations (RODEs) have proven to be one useful mathematical approach for applications with such effects. In this talk, we will introduce the foundations of RODEs, their relation to stochastic differential equations, and methods to solve them numerically. The Kanai-Tajimi earthquake model is used as an example application. An approach to tackle RODEs with typical techniques of Uncertainty Quantification (UQ) and Sparse Grids is discussed.

In addition, we briefly present a parallel approach to solve RODEs efficiently on modern high-performance computing (HPC) architectures, i.e. in our case clusters accelerated by general purpose graphics processing units (GPGPUs) which represent a way to boost computational performance.