Many complicated engineering problems are governed by mathematical models that can be traced back to well-established theory and experimentation in the natural sciences, e.g. on fluid dynamics, electrodynamics, tomography, and stability analysis for structures such as wind turbines. More generally, these types of problems fall into the following categories, which are the focus areas of this work package:

• Direct problems on simulating physical phenomena.
• Inverse problems on reversing a physical phenomenon to determine its cause.
• Uncertainty quantification on understanding uncertainties between different mathematical models.

While the mathematical models may hint at certain properties, typically numerical approximations are required for a more explicit understanding of the engineering problems. A key part of Scientific Computing is on realizing such models via state-of-the-art computer simulation, in both an efficient and reliable way. This involves certain guarantees on the simulations such as error estimates, convergence rates, and obeying physical laws.

The computer simulations comprise several techniques from numerical analysis, including finite difference/element/volume methods for solving partial differential equations, and optimization methods used to match parameters of a model to experimental data. The actual computations rely on efficient computer implementations, using parallel computing on large clusters and exploiting structures in the models to solve large systems of equations.