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| PDE-constrained Optimization |
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Engineering technologies are often governed by complex non-linear partial differential equations (PDEs). In recent reports, the US Department of Energy and NASA explored the potential of future-generation exa-scale high-performance computing systems (1018 operations per second) for energy research [3], and future-generation aircrafts [1]. They identified the use of optimization in large-parameter spaces, covering multi-scale optimization over multiple time stages, as a key element for future technology innovations. A recent Science Perspectives publication [4] focused on optimization and control of transport phenomena in flows as an important research direction for achieving new leaps in energy technology, aerospace, and chemical engineering. These examples all rely on optimization models constrained by complex nonlinear PDEs, requiring advanced optimization algorithms, which incorporate the handling of large multiscale simulations into massively parallel computer platforms.
It aims at the elaboration and application of efficient multi-scale multi-physics optimization algorithms. Emphasis is on the development of efficient and generic algorithms for PDE-constrained optimization, and on the use of these solvers in a selected number of application fields.
The PDE Optimization research at OPTEC is focus around:
- Efficient algorithms for robust optimization of large-scale PDE-constrained systems. The discretization of PDE-constrained optimization problems leads to numerical models with possibly millions of optimization variables. To solve such models, we will focus on extending multilevel one-shot methods, and optimized transmission condition domain decomposition methods. The effectiveness of these approaches is well-known for simple problems, yet many open questions remain for the case of systems of PDEs, irregular domains models, and nonlinear equations. Additional computational and memory complexity issues arise in the simulation and optimization of models with time-periodic boundary conditions. Recently, for certain model problems, novel parallel multiple shooting variants have been developed based on a double time-integration: an accurate (but complex) and inaccurate (but highly efficient) formula. The possibilities of these approaches towards engineering optimization problems and large PDE systems will be elaborated.
- Large-scale computationally intensive optimization of multi-disciplinary applications governed by multi-scale PDE systems. Technologies are envisaged where the use of advanced optimization promises to have a large impact, and which are situated in the expertise area of the work group members. We will focuss on two application areas in particular, i.e. wind energy and large-scale wind farms and (bio-)chemical reactor technology. The call for increased wind-energy capacity (e.g. the EU aims at 11% of its gross electricity by wind power in 2020 [5]), will require the building of large wind farms both on- and off-shore. Optimization of wind-turbine placement for optimal turbineturbine interaction and turbine-atmospheric-boundary-layer interaction is still uncharted territory, and requires the aggressive use of computational power with new multi-level optimization algorithms, and robust methods which can incorporate uncertainty. In the field of chemical reactors, replacing standard steady-state operation modes, by a transient cyclic operation in time, allows the integration of reaction and separations steps, and enhances process performance [2]. The optimization of such processes requires efficient algorithms for time-periodic problems Moreover, conflicting objectives and model uncertainties, require robust optimization methods.
