Multigrid waveform relaxation for the time-fractional heat equation

In this work, we propose an efficient and robust multigrid method for solving the time-fractional heat equation. Due to the nonlocal property of fractional differential operators, numerical methods usually generate systems of equations for which the coefficient matrix is dense. Therefore, the design of efficient solvers for the numerical simulation of these problems is a difficult task. We develop a parallel-in-time multigrid algorithm based on the waveform relaxation approach, whose application to time-fractional problems seems very natural due to the fact that the fractional derivative at each spatial point depends on the values of the function at this point at all earlier times. Exploiting the Toeplitz-like structure of the coefficient matrix, the proposed multigrid waveform relaxation method has a computational cost of $O(N M \log(M))$ operations, where $M$ is the number of time steps and $N$ is the number of spatial grid points. A semi-algebraic mode analysis is also developed to theoretically confirm the good results obtained. Several numerical experiments, including examples with non-smooth solutions and a nonlinear problem with applications in porous media, are presented

Vinylic Addition Polynorbornene in Catalysis

Vinylic addition polynorbornenes (VA-PNB) result from the insertion polymerization of norbornene or specific norbornene derivatives catalyzed by transition metal com- plexes. The VA-PNB skeleton is completely aliphatic and keeps the bicyclic structure of norbornene. This saturated polymer is thermally and chemically very stable and it is a very robust scaffold to support catalysts or reagents for catalytic applications. Several VA-PNBs are now available with suitable functional groups (halogen, alkenyl, carbonates) that can be used as starting materials to introduce the functionalization of choice by post-polymerization reactions. This has been applied to anchor organocatalysts on VA-PNB as well as ligands that can be used to synthesize supported metal catalysts. The reported examples of the use of VA-PNB-linked catalysts and their recyclability will be presented. VA-PNBs have also proved useful in the context of organotin chemistry to solve the problem of tin contamination by an efficient separation and the reuse of tin byproducts. Its uses in the Stille cross-coupling reaction and tin-hydride radical proc- esses will be discussed.MINECO (SGPI, grant CTQ2016-80913-P)Junta de Castilla y León (grants VA062G18 and VA051P17 and a fellowship to RGL

Stability and Monotonicity for Some Discretizations of the Biot's Model

We consider finite element discretizations of the Biot's consolidation model in poroelasticity with MINI and stabilized P1-P1 elements. We analyze the convergence of the fully discrete model based on spatial discretization with these types of finite elements and implicit Euler method in time. We also address the issue related to the presence of non-physical oscillations in the pressure approximation for low permeabilities and/or small time steps. We show that even in 1D a Stokes-stable finite element pair fails to provide a monotone discretization for the pressure in such regimes. We then introduce a stabilization term which removes the oscillations. We present numerical results confirming the monotone behavior of the stabilized schemes

La situación de las mujeres españolas en el mercado de trabajo, ¿diferencia o discriminación?

En el presente artículo se analizan las causas no jurídicas que inciden en la desigualdad entre hombres y mujeres. Se parte de datos estadísticos: la tasa de actividad femenina es muy baja y el paro femenino es muy alto; los contratos laborales realizados por mujeres suelen ser temporales o a tiempo parcial; rara vez promocionan a puestos de dirección y ocupan los puestos de trabajo poco cualificados y suelen ser una extensión de las funciones reproductivas (cuidado de los demás, higiene y limpieza, educación, etc.). Por otra parte , el salario femenino es inferior en un 29% respecto del masculino. Precisamente, uno de los temas que se abordan en el presente artículo son los cambios que se están produciendo en materia de igualdad retributiva tanto en Europa como en España. El análisis se lleva a cabo tanto desde un punto de vista jurídico como desde el estudio de las denominadas políticas flojas o de buenas prácticas para empresas y agentes sociales.________________________________The present paper analyzes the not juridical reasons that affect in the inequality between men and women workers. The contribution starts with statistical information: the rate of feminine activity is very low and the feminine unemployment is very high; the femenine labour contracts are normaly, temporary or parttime: rarely they promote to the places of direction; they occupy a low qualified jobs and their jobs are ordinarily, an extension of the reproductive functions (care of the others, hygiene and cleanliness, education. etc.). On the other hand, the feminine salary is lower --29 %-- than the masculine. Precisely, one of the approaches in the present contribution are the changes that are taking place in Europe and in Spain for remunerative equality. The analysis is from a juridical point of view and from the study of the weak politicy, called good practices of the companies and social agents

Poroelasticity problem: numerical difficulties and efficient multigrid solution

This work contains some of the more relevant results obtained by the author regarding the numerical solution of the Biot’s consolidation problem. The emphasis here is on the stable discretization and the highly efficient solution of the resulting algebraic system of equations, which is of saddle point type. On the one hand, a stabilized linear finite element scheme providing oscillation-free solutions for this model is proposed and theoretically analyzed. On the other hand, a monolithic multigrid method is considered for the solution of the resulting system of equations after discretization by using the stabilized scheme. Since this system is of saddle point type, special smoothers of “Vanka”-type have to be considered. This multigrid method is designed with the help of an special local Fourier analysis that takes into account the specific characteristics of the considered block-relaxations. Results from this analysis are presented and compared with those experimentally computed