Parallel solvers for virtual element discretizations of elliptic equations in mixed form

The 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

Lowest order Virtual Element approximation of magnetostatic problems

We give here a simplified presentation of the lowest order Serendipity Virtual Element method, and show its use for the numerical solution of linear magneto-static problems in three dimensions. The method can be applied to very general decompositions of the computational domain (as is natural for Virtual Element Methods) and uses as unknowns the (constant) tangential component of the magnetic field $\mathbf{H}$ on each edge, and the vertex values of the Lagrange multiplier $p$ (used to enforce the solenoidality of the magnetic induction $\mathbf{B}=\mu\mathbf{H}$). In this respect the method can be seen as the natural generalization of the lowest order Edge Finite Element Method (the so-called "first kind N\'ed\'elec" elements) to polyhedra of almost arbitrary shape, and as we show on some numerical examples it exhibits very good accuracy (for being a lowest order element) and excellent robustness with respect to distortions

A three-dimensional Hellinger-Reissner Virtual Element Method for linear elasticity problems

We present a Virtual Element Method for the 3D linear elasticity problems, based on Hellinger-Reissner variational principle. In the framework of the small strain theory, we propose a low-order scheme with a-priori symmetric stresses and continuous tractions across element interfaces. A convergence and stability analysis is developed and we confirm the theoretical predictions via some numerical tests.Comment: submitted to CMAM

SUPG-stabilized Virtual Elements for diffusion-convection problems: a robustness analysis

The objective of this contribution is to develop a convergence analysis for SUPG-stabilized Virtual Element Methods in diffusion-convection problems that is robust also in the convection dominated regime. For the original method introduced in [Benedetto et al, CMAME 2016] we are able to show an "almost uniform" error bound (in the sense that the unique term that depends in an unfavorable way on the parameters is damped by a higher order mesh-size multiplicative factor). We also introduce a novel discretization of the convection term that allows us to develop error estimates that are fully robust in the convection dominated cases. We finally present some numerical result

A family of three-dimensional virtual elements with applications to magnetostatic

We consider, as a simple model problem, the application of Virtual Element Methods (VEM) to the linear Magnetostatic three-dimensional problem in the formulation of F. Kikuchi. In doing so, we also introduce new serendipity VEM spaces, where the serendipity reduction is made only on the faces of a general polyhedral decomposition (assuming that internal degrees of freedom could be more easily eliminated by static condensation). These new spaces are meant, more generally, for the combined approximation of $H^1$-conforming ($0$-forms), $H({\rm {\bf curl}})$-conforming ($1$-forms), and $H({\rm div})$-conforming ($2$-forms) functional spaces in three dimensions, and they would surely be useful for other problems and in more general contexts.Comment: Submitted to SINU

Coeficiente de metabolizabilidade aparente de diferentes fontes lipídicas com ou sem emulsificante para frangos de corte de 1 a 8 dias.

Óleos e gorduras são utilizados nas rações de aves devido às suas altas concentrações calóricas. Entretanto, a escolha da fonte lipídica a ser utilizada na formulação dependerá de seu custo e da qualidade. O uso de emulsificantes em aves jovens tem o objetivo de auxiliar na digestão e absorção da gordura da dieta devido à imaturidade da circulação entero-hepática nesses animais (5). O objetivo do estudo foi avaliar o coeficiente de metabolizabilidade aparente da matéria seca (CMAMS) e extrato etéreo (CMAEE) e energia metabolizável (EM) em frangos de corte de 1 a 8 dias de idade alimentados com diferentes fontes lipídicas com ou sem a adição de emulsificantes

Human dyskerin binds to cytoplasmic H/ACA-box-containing transcripts affecting nuclear hormone receptor dependence

Background Dyskerin is a nuclear protein involved in H/ACA box snoRNA-guided uridine modification of RNA. In humans, its defective function is associated with cancer development and induces specific post-transcriptional alterations of gene expression. In this study, we seek to unbiasedly identify mRNAs regulated by dyskerin in human breast cancer-derived cells. Results We find that dyskerin depletion affects the expression and the association with polysomes of selected mRNA isoforms characterized by the retention of H/ACA box snoRNA-containing introns. These snoRNA retaining transcripts (snoRTs) are bound by dyskerin in the cytoplasm in the form of shorter 3 ' snoRT fragments. We then characterize the whole cytoplasmic dyskerin RNA interactome and find both H/ACA box snoRTs and protein-coding transcripts which may be targeted by the snoRTs' guide properties. Since a fraction of these protein-coding transcripts is involved in the nuclear hormone receptor binding, we test to see if this specific activity is affected by dyskerin. Obtained results indicate that dyskerin dysregulation may alter the dependence on nuclear hormone receptor ligands in breast cancer cells. These results are paralleled by consistent observations on the outcome of primary breast cancer patients stratified according to their tumor hormonal status. Accordingly, experiments in nude mice show that the reduction of dyskerin levels in estrogen-dependent cells favors xenograft development in the absence of estrogen supplementation. Conclusions Our work suggests a cytoplasmic function for dyskerin which could affect mRNA post-transcriptional networks relevant for nuclear hormone receptor functions