145 research outputs found
Parallel block preconditioners for three-dimensional virtual element discretizations of saddle-point problems
Get PDFSeveral physical phenomena are described by systems of partial differential equations (PDEs) that, after space discretization, yield the solution of saddle point algebraic linear systems. In realistic three-dimensional numerical simulations, these linear systems are large scale and ill-conditioned, thus they require the development of effective solvers. The aim of this work is the construction and numerical validation of parallel block preconditioners for a set of three-dimensional saddle point problems discretized by the low order virtual element method (VEM). VEM is a recent numerical technology for the approximation of PDEs on polygonal and polyhedral meshes. We focus on the following systems of PDEs: stationary Maxwell equations in the mixed Kikuchi formulation; elliptic equations in mixed form; Stokes system; linear elasticity in the mixed Hellinger–Reissner formulation. We provide two parallel block preconditioners: one based on the approximate Schur complement and the other on a regularization technique. Several numerical experiments are run in parallel on a Linux cluster. We analyze the performance of the iterative solvers in terms of GMRES iterations and computational time. We verify the robustness of the solvers with respect to different polyhedral meshes and the scalability of both the assembling and solution time by varying the number of processors. The performance of the two iterative solvers is also compared with state-of-the-art parallel direct linear solvers
Parallel solvers for virtual element discretizations of elliptic equations in mixed form
Get PDFThe aim of this paper is twofold. On the one hand, we numerically test the performance of mixed virtual elements in three dimensions to solve the mixed formulation of three-dimensional elliptic equations on polyhedral meshes. On the other hand, we focus on the parallel solution of the linear system arising from such discretization, considering both direct and iterative parallel solvers. In the latter case, we develop two block preconditioners, one based on the approximate Schur complement and one on a regularization technique. Both these topics are numerically validated by several parallel tests performed on a Linux cluster. More specifically, we show that the proposed virtual element discretization recovers the expected theoretical convergence rates and we analyze the performance of the direct and iterative parallel solvers taken into account
Parallel block preconditioners for virtual element discretizations of the time-dependent Maxwell equations
No full textThe focus of this study is the construction and numerical validation of parallel block preconditioners for low order virtual element discretizations of the three-dimensional Maxwell equations. The virtual element method (VEM) is a recent technology for the numerical approximation of partial differential equations (PDEs), that generalizes finite elements to polytopal computational grids. So far, VEM has been extended to several problems described by PDEs, and recently also to the time-dependent Maxwell equations. When the time discretization of PDEs is performed implicitly, at each time-step a large-scale and ill-conditioned linear system must be solved, that, in case of Maxwell equations, is particularly challenging, because of the presence of both H(div) and H(curl) discretization spaces. We propose here a parallel preconditioner, that exploits the Schur complement block factorization of the linear system matrix and consists of a Jacobi preconditioner for the H(div) block and an auxiliary space preconditioner for the H(curl) block. Several parallel numerical tests have been performed to study the robustness of the solver with respect to mesh refinement, shape of polyhedral elements, time step size and the VEM stabilization parameter
BDDC Preconditioners for Virtual Element Approximations of the Three-Dimensional Stokes Equations
Get PDFThe virtual element method (VEM) is a novel family of numerical methods for approximating partial differential equations on very general polygonal or polyhedral computational grids. This work aims to propose a balancing domain decomposition by constraints (BDDC) preconditioner that allows using the conjugate gradient method to compute the solution of the saddle-point linear systems arising from the VEM discretization of the three-dimensional Stokes equations. We prove the scalability and quasi-optimality of the algorithm and confirm the theoretical findings with parallel computations. Numerical results with adaptively generated coarse spaces confirm the method's robustness in the presence of large jumps in the viscosity and with high-order VEM discretizations
A denoising tool for the reconstruction of cortical geometries from MRI
No full textThe reconstruction of individual geometries from medical imaging is quite a standard in the framework of patient-specific medicine. A major drawback in such a context is represented by noise inherent to the data acquisition. Low signal-to-noise ratios can negatively impact extraction algorithms, and result in artefacts or poor quality of the reconstructed meshes. Direct application of numerical methods on such meshes can yield misleading results. Indeed, artefacts and badly shaped elements may corrupt numerical simulations or induce relevant errors in the computation of meaningful geometrical quantities, such as the curvature or the geodesic surface distance. In this paper, we propose a denoising procedure to remove artefacts from a triangular mesh of a three-dimensional closed surface which represents a brain cortex. For this purpose, we combine a smoothing technique (i.e., the Taubin or the HC-Laplacian smoothing) with an edge-flipping algorithm. To control the denoising procedure, we introduce a stopping criterion that takes into account both the improvement of the mesh quality and the loss of volume enclosed by the surface. On a brain cortical surface reconstructed from Magnetic Resonance Imaging (MRI) data, we first perform a tuning analysis of the parameters involved in the smoothing algorithm, then we investigate the effectiveness of the denoising procedure. Finally, as an example of relevant geometrical feature, we study the improvement generated by the proposed algorithm on the computation of the cortical curvature
Gyroid Lattice Heat Exchangers: Comparative Analysis on Thermo-Fluid Dynamic Performances
Get PDFIn recent years, additive manufacturing has reached the required reliability to effectively compete with standard production techniques of mechanical components. In particular, the geometrical freedom enabled by innovative manufacturing techniques has revolutionized the design trends for compact heat exchangers. Bioinspired structures, such as the gyroid lattice, have relevant mechanical and heat exchange properties for their light weight and increased heat exchange area, which also promotes the turbulent regime of the coolant. This work focuses its attention on the effect of the relevant design parameters of the gyroid lattice on heat exchange performances. A numerical comparative analysis is carried out from the thermal and fluid dynamic points of view to give design guidelines. The results of numerical analyses, performed on cylindrical samples, are compared to the experimental results on the pressure drop. Lattices samples were successfully printed with material extrusion, which is a low-cost and easy-to-use metal AM technology. For each lattice sample, counter pressure, heat exchange, and turbulence intensity ratio are calculated from the numerical point of view and discussed. At the end, the gyroid lattice is proven to be very effective at enhancing the heat exchange in cylindrical pipes. Guidelines are given about the choice of the best lattice, depending on the considered applications
The mixed virtual element method for grids with curved interfaces in single-phase flow problems
No full textIn many applications the accurate representation of the computational domain is a key factor to obtain reliable and effective numerical solutions. Curved interfaces, which might be internal, related to physical data, or portions of the physical boundary, are often met in real applications. However, they are often approximated leading to a geometrical error that might become dominant and deteriorate the quality of the results. Underground problems often involve the motion of fluids where the fundamental governing equation is the Darcy law. High quality velocity fields are of paramount importance for the successful subsequent coupling with other physical phenomena such as transport. The virtual element method, as solution scheme, is known to be applicable in problems whose discretizations requires cells of general shape, and the mixed formulation is here preferred to obtain accurate velocity fields. To overcome the issues associated to the complex geometries and, at the same time, retaining the quality of the solutions, we present here the virtual element method to solve the Darcy problem, in mixed form, in presence of curved interfaces in two and three dimensions. The numerical scheme is presented in detail explaining the discrete setting with a focus on the treatment of curved interfaces. Examples, inspired from industrial applications, are presented showing the validity of the proposed approach
Giorgio Raimondo Cardona : La lingua e la cultura
No full textGiorgio Raimondo Cardona (1943 – 1988). After his university degree in 1965 with Walter Belardi, he became, in 1968, first assistant and then professor of glottology at the University of Rome; Then, from 1968 to 1980, he taught Armenian language and literature at the Oriental University Institute in Naples, and in 1980 he was appointed full professor of glottology at the University of Rome ‘La Sapienza’, where he directed, from 1985 to 1988, the department of glottoanthropological studies, that he strongly desired and that marked a very fruitful and innovative research season, both for linguistics and anthropology, in the sign of the inter- weaving of the two disciplines. Also indicative of this turmoil is the fact that when he passed away in August 1988, Cardona’s bibliography counted more than two hundred titles: monographs, essays, articles, dictionaries, edited works and translations. The core intuition of Giorgio Cardona, that provided him with the opportunity to open up a research path challenging not only in itself, but especially because of the resistance and friction he encountered, both on the linguistic and on the anthropological side, concerns the knot “thought” (perception, recognition, conceptualization, association, memory, ...) / “language” (words, syntagmas, grammatical categories, writing, actions...): although it is evident that «many traces of what we think and commonly know filter into what we say... » (1965a: 2), that knot is not is not a tight one (in deterministic sense). Indeed, «We shall not find in language an exact replica of any- thing the community thinks ... » (1985a: 1). In other words, «... between the purely noetic and linguistic levels there is not necessarily isomorphism» (1985b: 37). This insight, which emerges in all its potentiality in the memorable works I sei lati del mondo e La foresta di piume, unlocks the vital space of elasticity, approximation, indeterminacy, the ‘blurred boundaries’ between the flow of thought and the systems we have to en- code it, and expresses the essential nature of the human condition.
In my text, I partially represent the intellectual climate in which the figure of Cardona is placed – as I grasped and remember it today – from my point of view as a student who asked him for and then wrote his degree thesis
Continuous 24-hour assessment of the neural regulation of systemic arterial pressure and RR variabilities in ambulant subjects
No full textIn this study, we tested the hypothesis that the neural control of circulation in humans undergoes continuous but in part predictable changes throughout the day and night. Dynamic 24-hour recordings were obtained in two groups of ambulant subjects. In 18 hospitalized patients free to move, direct high-fidelity arterial pressures and electrocardiograms were recorded, and in an additional 28 nonhospitalized subjects, only electrocardiograms were obtained. Spectral analysis of systolic arterial pressure and of RR interval variabilities provided quantitative markers of sympathetic and vagal control of the sinus node and of sympathetic modulation of vasomotor tone. With this approach, the low-frequency (approximately 0.1 Hz) component of RR interval and systolic arterial pressure variabilities is considered a marker primarily of sympathetic activity, whereas the high-frequency (approximately 0.25 Hz) component of RR interval variability, related to respiration, seems to be a marker primarily of vagal activity. We observed a pronounced and consistent reduction in the markers of sympathetic activity and an increase in those of vagal activity during the night. In the invasive studies, while the subjects were still lying in bed after waking up, the markers of sympathetic activity rose rapidly and concomitantly with a simultaneous vagal withdrawal. Noninvasive studies confirmed the early morning rise of the markers of sympathetic activity and the circadian pattern of sympathovagal balance. These data indicate that the ominously increased rate of cardiovascular events in the morning hours may reflect the sudden rise of sympathetic activity and the reduction of vagal tone
Anisotropic finite element mesh adaptation via higher dimensional embedding
Get PDFAbstractIn this paper we provide a novel anisotropic mesh adaptation technique for adaptive finite element analysis. It is based on the concept of higher dimensional embedding, which was exploited in [1–4] to obtain an anisotropic curvature adapted mesh that fits a complex surface in R3. In the context of adaptive finite element simulation, the solution (which is an unknown function f : Ω ⊂ d → ) is sought by iteratively modifying a finite element mesh according to a mesh sizing field described via a (discrete) metric tensor field that is typically obtained through an error estimator. We proposed to use a higher dimensional embedding, Φf (x):= (x1, …, xd, s f (x1, …, xd), s ▿ f (x1, …, xd))t, instead of the mesh sizing field for the mesh adaption. This embedding contains both informations of the function f itself and its gradient. An isotropic mesh in this embedded space will correspond to an anisotropic mesh in the actual space, where the mesh elements are stretched and aligned according to the features of the function f. To better capture the anisotropy and gradation of the mesh, it is necessary to balance the contribution of the components in this embedding. We have properly adjusted Φf (x) for adaptive finite element analysis. To better understand and validate the proposed mesh adaptation strategy, we first provide a series of experimental tests for piecewise linear interpolation of known functions. We then applied this approach in an adaptive finite element solution of partial differential equations. Both tests are performed on two-dimensional domains in which adaptive triangular meshes are generated. We compared these results with the ones obtained by the software BAMG – a metric-based adaptive mesh generator. The errors measured in the L2 norm are comparable. Moreover, our meshes captured the anisotropy more accurately than the meshes of BAMG
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