Theory and implementation of H\mathcal{H}-matrix based iterative and direct solvers for Helmholtz and elastodynamic oscillatory kernels

In this work, we study the accuracy and efficiency of hierarchical matrix ($\mathcal{H}$-matrix) based fast methods for solving dense linear systems arising from the discretization of the 3D elastodynamic Green's tensors. It is well known in the literature that standard $\mathcal{H}$-matrix based methods, although very efficient tools for asymptotically smooth kernels, are not optimal for oscillatory kernels. $\mathcal{H}^2$-matrix and directional approaches have been proposed to overcome this problem. However the implementation of such methods is much more involved than the standard $\mathcal{H}$-matrix representation. The central questions we address are twofold. (i) What is the frequency-range in which the $\mathcal{H}$-matrix format is an efficient representation for 3D elastodynamic problems? (ii) What can be expected of such an approach to model problems in mechanical engineering? We show that even though the method is not optimal (in the sense that more involved representations can lead to faster algorithms) an efficient solver can be easily developed. The capabilities of the method are illustrated on numerical examples using the Boundary Element Method

Efficient solution of two-dimensional wave propagation problems by Cq-Wavelet BEM: Algorithm and applications

In this paper we consider wave propagation problems in two-dimensional unbounded domains, including dissipative effects, reformulated in terms of space-time boundary integral equa- tions. For their solution, we employ a convolution quadrature (CQ) for the temporal and a Galerkin boundary element method (BEM) for the spatial discretization. It is known that one of the main advantages of the CQ-BEMs is the use of the FFT algorithm to retrieve the discrete time integral operators with an optimal linear complexity in time, up to a logarithmic term. It is also known that a key ingredient for the success of such methods is the efficient and accurate evaluation of all the integrals that define the matrix entries associated to the full space-time discretization. This topic has been successfully addressed when standard Lagrangian basis functions are considered for the space discretization. However, it results that, for such a choice of the basis, the BEM matrices are in general fully populated, a drawback that prevents the application of CQ-BEMs to large-scale problems. In this paper, as a possible remedy to reduce the global complexity of the method, we consider approximant functions of wavelet type. In particular, we propose a numerical procedure that, by taking advantage of the fast wavelet transform, allows us on the one hand to compute the matrix entries associated to the choice of wavelet basis functions by maintaining the accuracy of those associated to the Lagrangian basis ones and, on the other hand, to generate sparse matrices without the need of storing a priori the fully populated ones. Such an approach allows in principle the use of wavelet basis of any type and order, combined with CQ based on any stable ordinary differential equations solver. Several numerical results, showing the accuracy of the solution and the gain in terms of computer memory saving, are presented and discussed

Efficient Solution of Two-Dimensional Wave Propagation Problems by CQ-Wavelet BEM: Algorithm and Applications

In this paper we consider wave propagation problems in two-dimensional unbounded domains, including dissipative effects, reformulated in terms of space-time boundary integral equations. For their solution, we employ a convolution quadrature (CQ) for the temporal and a Galerkin boundary element method (BEM) for the spatial discretization. It is known that one of the main advantages of the CQ-BEMs is the use of the FFT algorithm to retrieve the discrete time integraloperators with an optimal linear complexity in time, up to a logarithmic term. It is also known that a key ingredient for the success of such methods is the efficient and accurate evaluation of all the integrals that define the matrix entries associated to the full space-time discretization. This topic has been successfully addressed when standard Lagrangian basis functions are considered for the space discretization. However, it results that, for such a choice of the basis, the BEM matrices are in general fully populated, a drawback that prevents the application of CQ-BEMs to large-scale problems. In this paper, as a possible remedy to reduce the global complexity of the method, we consider approximant functions of wavelet type. In particular, we propose a numerical procedure that, by taking advantage of the fast wavelet transform, allows us on the one hand to compute the matrix entries associated to the choice of wavelet basis functions by maintaining the accuracy of those associated to the Lagrangian basis ones and, on the other hand, to generate sparse matrices without the need of storing a priori the fully populated ones. Such an approach allows in principle the use of wavelet basis of any type and order, combined with CQ based on any stable ordinary differential equations solver. Several numerical results, showing the accuracy of the solution and the gain in terms of computer memory saving, are presented and discusse

Searching for a Longevity Food, We Bump into Hericium erinaceus Primordium Rich in Ergothioneine: The “Longevity Vitamin” Improves Locomotor Performances during Aging

Phenotypic frailty is characterized by a progressive decline in physical functioning. During ageing, morphological and functional alterations involve the brain, and chief theories involve ox-idative stress, free radical accumulation, and reduced antioxidant defenses as the most implicated mechanisms. From boosting the immune system to fighting senescence, medicinal mushrooms have been found to have a number of health and longevity benefits. Among them, Hericium erinaceus (He) has been demonstrated to display a variety of physiological effects, including anti-aging properties. Thus, He represents an attractive natural source for developing novel medicines and functional foods, based on the identification of its active ingredients and metabolites. Particularly, H. erinaceus primordium (He2) extract contains a high amount of Ergothioneine (ERGO), the longevity vitamin. Herein, we revealed the preventive effect of ERGO-rich He2 extract in a preclinical model, focusing on locomotor decline during ageing monitored through spontaneous behavioral test. This effect was accompanied by a significant decrease in some oxidative stress markers (NOS2, COX2) paralleled by an increase in P53, showed in cerebellar cortex cells and fibres by immunohistochemistry. In summary, we demonstrated the neuro-protective and preventive effects of He2 extract during aging, probably due to its peculiarly high ERGO content

Pharmacological targeting of the ephrin receptor kinase signalling by GLPG1790 in vitro and in vivo reverts oncophenotype, induces myogenic differentiation and radiosensitizes embryonal rhabdomyosarcoma cells

EPH (erythropoietin-producing hepatocellular) receptors are clinically relevant targets in several malignancies. This report describes the effects of GLPG1790, a new potent pan-EPH inhibitor, in human embryonal rhabdomyosarcoma (ERMS) cell lines

Different spectroscopic behavior of coupled and freestanding monolayer graphene deposited by CVD on Cu foil

The growth of graphene on copper foil has been performed, following the well-known low-pressure chemical vapor (LP-CVD) procedure. The as-deposited monolayer graphene clearly exhibits two different coupling behaviors with the metal substrate, as demonstrated by visual microscopic investigation and by other experimental techniques, like Scanning Electron Microscopy (SEM) and micro-Raman spectroscopy. The single graphene sheet shows both large areas where it is coupled to the metal substrate and others where it exhibits freestanding-like characteristics. This phenomenology appears to be related to oxidation of the copper surface. In addition, we demonstrate the possibility to induce a variation of the coupling state by visible-light irradiation above a proper power threshold. The resulting change of the coupling with the metal substrate is associated to a local variation of the work function. Applications in high-performance electronic devices can be suitably tailored by optical methods and, in principle, by any local probe producing "hot spots" such as Scanning Tunneling Microscopy (STM) tips and electron beams.</p

Evaluation of appendicitis risk prediction models in adults with suspected appendicitis

Background Appendicitis is the most common general surgical emergency worldwide, but its diagnosis remains challenging. The aim of this study was to determine whether existing risk prediction models can reliably identify patients presenting to hospital in the UK with acute right iliac fossa (RIF) pain who are at low risk of appendicitis. Methods A systematic search was completed to identify all existing appendicitis risk prediction models. Models were validated using UK data from an international prospective cohort study that captured consecutive patients aged 16–45 years presenting to hospital with acute RIF in March to June 2017. The main outcome was best achievable model specificity (proportion of patients who did not have appendicitis correctly classified as low risk) whilst maintaining a failure rate below 5 per cent (proportion of patients identified as low risk who actually had appendicitis). Results Some 5345 patients across 154 UK hospitals were identified, of which two‐thirds (3613 of 5345, 67·6 per cent) were women. Women were more than twice as likely to undergo surgery with removal of a histologically normal appendix (272 of 964, 28·2 per cent) than men (120 of 993, 12·1 per cent) (relative risk 2·33, 95 per cent c.i. 1·92 to 2·84; P < 0·001). Of 15 validated risk prediction models, the Adult Appendicitis Score performed best (cut‐off score 8 or less, specificity 63·1 per cent, failure rate 3·7 per cent). The Appendicitis Inflammatory Response Score performed best for men (cut‐off score 2 or less, specificity 24·7 per cent, failure rate 2·4 per cent). Conclusion Women in the UK had a disproportionate risk of admission without surgical intervention and had high rates of normal appendicectomy. Risk prediction models to support shared decision‐making by identifying adults in the UK at low risk of appendicitis were identified

An ℋ-matrix based direct solver for the boundary element method in 3D elastodynamics

In this work we present a fast direct solver for 3D elastodynamic problems in frequency-domain. We use the Boundary Element Method as discretization technique, in association with the hierarchical matrix technique for the fast solution of the resulting linear system. The accuracy and the efficiency of the solver is demonstrated through numerical examples, showing a significant reduction of memory requirement and CPU time with respect to the standard Boundary Element Method. The proposed solver therefore offers perspectives to study large-scale 3D transient elastodynamic problems, with possible applications in seismology

Solveurs fondés sur la méthode des H-matrices pour les équations intégrales en élastodynamique 3D

This thesis focuses on the theoretical and numerical study of fast methods to solve the equations of 3D elastodynamics in frequency-domain. We use the Boundary Element Method (BEM) as discretization technique, in association with the hierarchical matrices (H-matrices) technique for the fast solution of the resulting linear system. The BEM is based on a boundary integral formulation which requires the discretization of the only domain boundaries. Thus, this method is well suited to treat seismic wave propagation problems. A major drawback of classical BEM is that it results in dense matrices, which leads to high memory requirement (O (N 2 ), if N is the number of degrees of freedom) and computational costs.Therefore, the simulation of realistic problems is limited by the number of degrees of freedom. Several fast BEMs have been developed to improve the computational efficiency. We propose a fast H-matrix based direct BEM solver.Cette thèse porte sur l'étude théorique et numérique des méthodes rapides pour résoudre les équations de l'élastodynamique 3D en domaine fréquentiel, et se place dans le cadre d'une collaboration avec la société Shell en vue d'optimiser la convergence des problèmes d'inversion sismique. La méthode repose sur l'utilisation des éléments finis de frontière (BEM) pour la discrétisation et sur les techniques de matrices hiérarchiques (H-matrices) pour l'accélération de la résolution du système linéaire. Dans le cadre de cette thèse on a développé un solveur direct pour les BEMs en utilisant une factorisation LU et un stockage hiérarchique. Si le concept des H-matrices est simple à comprendre, sa mise en oeuvre requiert des développements algorithmiques importants tels que la gestion de la multiplication de matrices représentées par des structures différentes (compressées ou non) qui ne comprend pas mois de 27 sous-cas. Un autre point délicat est l'utilisation des méthodes d'approximations par matrices compressées (de rang faible) dans le cadre des problèmes vectoriels. Une étude algorithmique a donc été faite pour mettre en oeuvre la méthode des H-matrices. Nous avons par ailleurs estimé théoriquement le rang faible attendu pour les noyaux oscillants, ce qui constitue une nouveauté, et montré que la méthode est utilisable en élastodynamique. En outre on a étudié l'influence des divers paramètres de la méthode en acoustique et en élastodynamique 3D, à fin de calibrer leur valeurs numériques optimales. Dans le cadre de la collaboration avec Shell, un cas test spécifique a été étudié. Il s'agit d'un problème de propagation d'une onde sismique dans un demi-espace élastique soumis à une force ponctuelle en surface. Enfin le solveur direct développé a été intégré au code COFFEE développé a POEMS (environ 25000 lignes en Fortran 90