Efficient hyperbolic-parabolic models on multi-dimensional unbounded domains using an extended DG approach

We introduce an extended discontinuous Galerkin discretization of hyperbolic-parabolic problems on multidimensional semi-infinite domains. Building on previous work on the one-dimensional case, we split the strip-shaped computational domain into a bounded region, discretized by means of discontinuous finite elements using Legendre basis functions, and an unbounded subdomain, where scaled Laguerre functions are used as a basis. Numerical fluxes at the interface allow for a seamless coupling of the two regions. The resulting coupling strategy is shown to produce accurate numerical solutions in tests on both linear and non-linear scalar and vectorial model problems. In addition, an efficient absorbing layer can be simulated in the semi-infinite part of the domain in order to damp outgoing signals with negligible spurious reflections at the interface. By tuning the scaling parameter of the Laguerre basis functions, the extended DG scheme simulates transient dynamics over large spatial scales with a substantial reduction in computational cost at a given accuracy level compared to standard single-domain discontinuous finite element techniques.Comment: 28 pages, 13 figure

Gradient-preserving hyper-reduction of nonlinear dynamical systems via discrete empirical interpolation

This work proposes a hyper-reduction method for nonlinear parametric dynamical systems characterized by gradient fields such as Hamiltonian systems and gradient flows. The gradient structure is associated with conservation of invariants or with dissipation and hence plays a crucial role in the description of the physical properties of the system. Traditional hyper-reduction of nonlinear gradient fields yields efficient approximations that, however, lack the gradient structure. We focus on Hamiltonian gradients and we propose to first decompose the nonlinear part of the Hamiltonian, mapped into a suitable reduced space, into the sum of d terms, each characterized by a sparse dependence on the system state. Then, the hyper-reduced approximation is obtained via discrete empirical interpolation (DEIM) of the Jacobian of the derived d-valued nonlinear function. The resulting hyper-reduced model retains the gradient structure and its computationally complexity is independent of the size of the full model. Moreover, a priori error estimates show that the hyper-reduced model converges to the reduced model and the Hamiltonian is asymptotically preserved. Whenever the nonlinear Hamiltonian gradient is not globally reducible, i.e. its evolution requires high-dimensional DEIM approximation spaces, an adaptive strategy is performed. This consists in updating the hyper-reduced Hamiltonian via a low-rank correction of the DEIM basis. Numerical tests demonstrate the applicability of the proposed approach to general nonlinear operators and runtime speedups compared to the full and the reduced models

Fully adaptive structure-preserving hyper-reduction of parametric Hamiltonian systems

Model order reduction provides low-complexity high-fidelity surrogate models that allow rapid and accurate solutions of parametric differential equations. The development of reduced order models for parametric nonlinear Hamiltonian systems is still challenged by several factors: (i) the geometric structure encoding the physical properties of the dynamics; (ii) the slowly decaying Kolmogorov $n$-width of conservative dynamics; (iii) the gradient structure of the nonlinear flow velocity; (iv) high variations in the numerical rank of the state as a function of time and parameters. We propose to address these aspects via a structure-preserving adaptive approach that combines symplectic dynamical low-rank approximation with adaptive gradient-preserving hyper-reduction and parameters sampling. Additionally, we propose to vary in time the dimensions of both the reduced basis space and the hyper-reduction space by monitoring the quality of the reduced solution via an error indicator related to the projection error of the Hamiltonian vector field. The resulting adaptive hyper-reduced models preserve the geometric structure of the Hamiltonian flow, do not rely on prior information on the dynamics, and can be solved at a cost that is linear in the dimension of the full order model and linear in the number of test parameters. Numerical experiments demonstrate the improved performances of the resulting fully adaptive models compared to the original and reduced order models

A seamless, extended DG approach for advection-diffusion problems on unbounded domains

We propose and analyze a seamless extended Discontinuous Galerkin (DG) discretization of advection-diffusion equations on semi-infinite domains. The semi-infinite half line is split into a finite subdomain where the model uses a standard polynomial basis, and a semi-unbounded subdomain where scaled Laguerre functions are employed as basis and test functions. Numerical fluxes enable the coupling at the interface between the two subdomains in the same way as standard single domain DG interelement fluxes. A novel linear analysis on the extended DG model yields unconditional stability with respect to the P\'eclet number. Errors due to the use of different sets of basis functions on different portions of the domain are negligible, as highlighted in numerical experiments with the linear advection-diffusion and viscous Burgers' equations. With an added damping term on the semi-infinite subdomain, the extended framework is able to efficiently simulate absorbing boundary conditions without additional conditions at the interface. A few modes in the semi-infinite subdomain are found to suffice to deal with outgoing single wave and wave train signals more accurately than standard approaches at a given computational cost, thus providing an appealing model for fluid flow simulations in unbounded regions.Comment: 27 pages, 8 figure

Prolongation of incubation time improves clinical diagnosis of Mycobacterium xenopi infection and allows susceptibility testing of mycobacterial strains against multiple antibiotics.

Objectives: Mycobacterium xenopi is a nontuberculous mycobacterium (NTM) whose clinical diagnosis and drug susceptibility studies are frequently hampered by poor in vitro growth. Extending the culture incubation time from 42 days (common-standard) to 56 days could improve the likelihood of diagnosis and provide strains for phenotypic drug susceptibility profiling of this poorly studied but clinically relevant mycobacterium. Methods: Time-to-positivity of mycobacterial cultures incubated for 56 days were analysed and compared. Clinical mycobacteriosis was defined by ATS/IDSA criteria. In vitro susceptibility of M. xenopi isolates was tested by broth microdilution. Results: Of 3852 mycobacteria-positive cultures (26 different mycobacterial species),M. xenopi required by far the longest growth time in culture, exceeding the 42 days commonly used in routine diagnostics in 41.2% of cases versus 4.7% for other NTM and 2.0% for Mycobacterium tuberculosis complex (P < 0.001). Prolonging the incubation time to 56 days had a great impact on M. xenopi diagnosis, as 56.3% (27/48) of patients would have not fulfilled the ATS/IDSA criteria at an incubation limited to 42 days. All 40 M. xenopi isolates from patients with clinical mycobacteriosis were fully susceptibility to macrolides and rifamycins in vitro and to moxifloxacin, amikacin and linezolid. Conclusion: These results indicate that a significant percentage (56.3%) of positive culture forM. xenopi would have incorrectly been reported as negative to clinicians without prolonging the incubation time to 56 days. Moreover, 56.3% of patients with M. xenopi disease would have missed the diagnosis along with an appropriate germ-based antimycobacterial treatment, otherwise fully effective

Treatment of Tricuspid Regurgitation at Subvalvular Level: Hemodynamic and Morphological Assessment in Ex-Vivo Beating Heart Model

ABSTRACTBackground: Functional tricuspid regurgitation (FTR) treatment is challenging and most therapies targeting tricuspid valve (TV) annulus have shown limited durability with high rate of resid..

Transcatheter Edge-to-Edge Treatment of Functional Tricuspid Regurgitation in an Ex Vivo Pulsatile Heart Model

Although associated with left heart pathologies, functional tricuspid regurgitation (FTR) is often left untreated during left heart surgery. Hence, owing to its degenerative character, reoperation is often needed, encompassing an impressive (25% to 35%) mortality rate. Thus transcatheter approaches to FTR are raising great interest

Business performance and angels presence: A fresh look from France 2008–2011

Business angels enjoy a strong reputation for being more efficient than other investors among policy makers, practitioners, and scholars. However, due to the limited availability of specific financial data, previous research has barely assessed the impact of angels on companies’ performance. This paper seeks to bridge this gap by providing evidence from a unique dataset made up of 432 angel-backed French companies which are compared to two control groups, one randomly selected and another one consisting of similar enterprises. This double comparison process enables us to purge our analysis of structural effect and to demonstrate the importance of the methodology in generating the sample. Indeed, the results we obtain significantly differ depending on the control group. Our results show that the positive influence of angels depends on the condition of the comparison. The set of BA-backed companies is more likely to exhibit superior performance when it is compared to a random sample whereas the companies’ performance is either identical or worse when it is compared to a sample composed of k-nearest neighbors. In addition, using a quantile regression technique makes it possible to differentiate the effect of business angels based on the distribution of the value of the growth rate. © 2017, Springer Science+Business Media New York

Sporadic Model Predictive Control

We present a control scheme combining a Model Predictive Control (MPC) layer and a hierarchically inferior one, in general not of the MPC type. The purpose is to avoid solving the MPC optimisation problem at each control step, thereby lightening the computational burden. The MPC controller can be designed within the classical receding horizon framework, and independently of the lower layer. This makes it easy to apply the scheme to existing systems, where the lower layer may just be the pre-existing control, in a view to enhancing industrial applicability. We name the approach grounding the scheme “sporadic” MPC, owing to the characteristic just evidenced, and in particular to the particular interplay with the existing control layer. We show some simulation examples to demonstrate the achievable advantages

Leaflet kinematics after the Yacoub and Florida-sleeve operations: results of an in vitro study

The Florida-sleeve is a valve-sparing technique that causes minimal interference to leaflet kinematics and aortic root dynamism. The aim of this in vitro study was to evaluate the effects of the Florida-sleeve and Yacoub techniques on aortic leaflet kinematics