Samplet basis pursuit

We consider kernel-based learning in samplet coordinates with l1-regularization. The application of an l1-regularization term enforces sparsity of the coefficients with respect to the samplet basis. Therefore, we call this approach samplet basis pursuit. Samplets are wavelet-type signed measures, which are tailored to scattered data. They provide similar properties as wavelets in terms of localization, multiresolution analysis, and data compression. The class of signals that can sparsely be represented in a samplet basis is considerably larger than the class of signals which exhibit a sparse representation in the single-scale basis. In particular, every signal that can be represented by the superposition of only a few features of the canonical feature map is also sparse in samplet coordinates. We propose the efficient solution of the problem under consideration by combining soft-shrinkage with the semi-smooth Newton method and compare the approach to the fast iterative shrinkage thresholding algorithm. We present numerical benchmarks as well as applications to surface reconstruction from noisy data and to the reconstruction of temperature data using a dictionary of multiple kernels

Modelling and analysis of flow-driven energy harvesting devices and associated reduced order models

A specific class of energy harvester devices for renewable energy resources allows conversion of ambient fluid flow energy to electrical energy via flow-induced vibrations of a piezo-ceramic composite structure positioned in the flow field. This energy converter technology simultaneously involves the interaction of a composite structure and a surrounding fluid, the electric charge accumulated in the piezo-ceramic material and a controlling electrical circuit. In order to predict the efficiency and operational properties of such future devices and to increase their robustness and performance, a mathematical and numerical model of the complex physical system is required to allow systematic computational investigation of the involved phenomena and coupling characteristics. The presentation will discuss a monolithic modelling approach that allows simultaneous analysis of the harvester, which involves surface-coupled fluid-structure interaction, volume-coupled electro-mechanics and a controlling energy harvesting circuit. Based on a finite element discretisation of the weighted residual form of the governing equations, time- and frequency-domain analysis enables investigation of different types of structures (plate, shells) subject to exterior/interior flow with varying parameters, and attached electrical circuits with respect to the electrical power output generated. Consequently, options for parametric reduced-order modelling of flow-driven energy harvesters will be discussed

Comparison of Several RANS Modelling for the Pavia TRIGA Mark II Research Reactor

In this study, a detailed analysis of the turbulent regime within the core of the Pavia TRIGA Mark II reactor is perfomed by means of an in-depth comparison of the RAS (Reynolds-Averaged Simulation) turbulence models implemented in OpenFOAM. Aim of this analysis is to give some important information with respect to the flow regime within the core. The performance of the various models is tested against a LES (Large Eddy Simulation) of the innermost channel

Convergence of a stabilized discontinuous Galerkin method for incompressible nonlinear elasticity

In this paper we present a discontinuous Galerkin method applied to incompressible nonlinear elastostatics in a total Lagrangian deformation-pressure formulation, for which a suitable interior penalty stabilization is applied. We prove that the proposed discrete formulation for the linearized problem is well-posed, asymptotically consistent and that it converges to the corresponding weak solution. The derived convergence rates are optimal and further confirmed by a set of numerical examples in two and three spatial dimension

Convergence of a stabilized discontinuous Galerkin method for incompressible nonlinear elasticity

In this paper we present a discontinuous Galerkin method applied to incompressible nonlinear elastostatics in a total Lagrangian deformation-pressure formulation, for which a suitable interior penalty stabilization is applied. We prove that the proposed discrete formulation for the linearized problem is well-posed, asymptotically consistent and that it converges to the corresponding weak solution. The derived convergence rates are optimal and further confirmed by a set of numerical examples in two and three spatial dimensions

Reduced basis Nitsche-based domain decomposition: a biomedical application

Nowadays, the personalized biomedical simulations demand real-time efficient and reliable method to alleviate the computational complexity of high-fidelity simulation. In such applications, the necessity of solving different substructure, e.g. tissues or organs, with different numbers of the degrees of freedom and of coupling the reduced order spaces for each substructure poses a challenge in the on-fly simulation. In this talk, this challenge is taken into account employing the Nitsche-based domain decomposition technique inside the reduced order model [1]. This technique with respect to other domain decomposition approach allows obtaining a solution with the same accuracy of underlying finite element formulation and to flexibly treat interface with non-matching mesh. The robustness of the coupling is determined by the penalty coefficients that is chosen using ghost penalty technique [2]. Furthermore, to reduce the computational complexity of the on-fly assembling it is employed the empirical interpolation approach proposed in [3]. The numerical tests, performed using FEniCS[4], petsc4py and slepc4py [5], shows the good performance of the method and the reduction of computation cost. [1] Baroli, D., Beex L. and Bordas, S. Reduced basis Nitsche-based domain decomposition. In preparation. [2] Burman, E., Claus, S., Hansbo, P., Larson, M. G., & Massing, A. (2015). CutFEM: Discretizing geometry and partial differential equations. International Journal for Numerical Methods in Engineering, 104(7), 472-501. [3] E. Schenone, E., Beex,L., Hale, J.S., Bordas S. Proper Orthogonal Decomposition with reduced integration method. Application to nonlinear problems. In preparation. [4] A. Logg, K.-A. Mardal, G. N. Wells et al. Automated Solution of Differential Equations by the Finite Element Method, Springer 2012. [5] L. Dalcin, P. Kler, R. Paz, and A. Cosimo, Parallel Distributed Computing using Python, Advances in Water Resources, 34(9):1124-1139, 2011. http://dx.doi.org/10.1016/j.advwatres.2011.04.01

A Reduced Order Kalman Filter for Computational Fluid-Dynamics Applications

In the last decade, the importance of numerical simulations for the analysis of complex engineering systems, such as thermo-fluid dynamics in nuclear reactors, has grown exponentially. In spite of the large experimental databases available for validation of mathematical models, in order to identify the most suitable one for the system under investigation, the inverse integration of such data into the CFD model is nowadays an ongoing challenge. In addition, such integration could tackle the problem of propagation of epistemic uncertainties, both in the numerical model and in the experimental data. In this framework, the data-assimilation method allows for the dynamic incorporation of observations within the computational model. Perhaps the most famous among these methods, due to its simple implementation and yet robust nature, is the Kalman filter. Although this approach has found success in fields such as weather forecast and geoscience, its application in Computational Fluid-Dynamics (CFD) is still in its first stages. In this setting, a new algorithm based on the integration between the segregated approach, which is the most common method adopted by CFD applications for the solution of the incompressible Navier-Stokes equations, and a Kalman filter modified for fluid-dynamics problems, while preserving mass conservation of the solution, has already been developed and tested in a previous work. Whereas such method is able to robustly integrate experimental data within the numerical model, its computational cost increases with model complexity. In particular, in high-fidelity realistic scenarios the error covariance matrix for the model, which represents the uncertainties associated with it, becomes dense, thus affecting the efficiency and computational cost of the method. For this reason, due to the promised reduction of computational requirements recently investigated, which combines model reduction and data-assimilation, in this work a combination of reduced order model and mass-conservative Kalman filter within a segregated approach for CFD analysis is proposed. The novelty lies in the peculiar formulation of the Kalman filter and how to construct a low-dimensional manifold to approximate, with sufficient accuracy, the high fidelity model. With respect to literature, in which the full-order Kalman filter is applied to a reduced model, the reduction is performed directly on the integrated model in order to obtain a reduced-order Kalman filter already optimised for fluid-dynamics applications. In order to verify the capabilities of this approach, this reduced-order algorithm has been tested against the lid-driven cavity test case.</jats:p