Optimal control of wave energy systems considering nonlinear Froude–Krylov effects: control-oriented modelling and moment-based control

Motivated by the relevance of so-called nonlinear Froude–Krylov (FK) hydrodynamic effects in the accurate dynamical description of wave energy converters (WECs) under controlled conditions, and the apparent lack of a suitable control framework effectively capable of optimally harvesting ocean wave energy in such circumstances, we present, in this paper, an integrated framework to achieve such a control objective, by means of two main contributions. We first propose a data-based, control-oriented, modelling procedure, able to compute a suitable mathematical representation for nonlinear FK effects, fully compatible with state-of-the-art control procedures. Secondly, we propose a moment-based optimal control solution, capable of transcribing the energy-maximising optimal control problem for WECs subject to nonlinear FK effects, by incorporating the corresponding data-based FK model via moment-based theory, with real-time capabilities. We illustrate the application of the proposed framework, including energy absorption performance, by means of a comprehensive case study, comprising both the data-based modelling, and the optimal moment-based control of a heaving point absorber WEC subject to nonlinear FK force

Transverse electric scattering on inhomogeneous objects: spectrum of integral operator and preconditioning

The domain integral equation method with its FFT-based matrix-vector products is a viable alternative to local methods in free-space scattering problems. However, it often suffers from the extremely slow convergence of iterative methods, especially in the transverse electric (TE) case with large or negative permittivity. We identify the nontrivial essential spectrum of the pertaining integral operator as partly responsible for this behavior, and the main reason why a normally efficient deflating preconditioner does not work. We solve this problem by applying an explicit multiplicative regularizing operator, which transforms the system to the form `identity plus compact', yet allows the resulting matrix-vector products to be carried out at the FFT speed. Such a regularized system is then further preconditioned by deflating an apparently stable set of eigenvalues with largest magnitudes, which results in a robust acceleration of the restarted GMRES under constraint memory conditions.Comment: 20 pages, 8 figure

MADNESS: A Multiresolution, Adaptive Numerical Environment for Scientific Simulation

MADNESS (multiresolution adaptive numerical environment for scientific simulation) is a high-level software environment for solving integral and differential equations in many dimensions that uses adaptive and fast harmonic analysis methods with guaranteed precision based on multiresolution analysis and separated representations. Underpinning the numerical capabilities is a powerful petascale parallel programming environment that aims to increase both programmer productivity and code scalability. This paper describes the features and capabilities of MADNESS and briefly discusses some current applications in chemistry and several areas of physics