Multiscale stabilization for convection-dominated diffusion in heterogeneous media

We develop a Petrov-Galerkin stabilization method for multiscale convection-diffusion transport systems. Existing stabilization techniques add a limited number of degrees of freedom in the form of bubble functions or a modified diffusion, which may not be sufficient to stabilize multiscale systems. We seek a local reduced-order model for this kind of multiscale transport problems and thus, develop a systematic approach for finding reduced-order approximations of the solution. We start from a Petrov-Galerkin framework using optimal weighting functions. We introduce an auxiliary variable to a mixed formulation of the problem. The auxiliary variable stands for the optimal weighting function. The problem reduces to finding a test space (a dimensionally reduced space for this auxiliary variable), which guarantees that the error in the primal variable (representing the solution) is close to the projection error of the full solution on the dimensionally reduced space that approximates the solution. To find the test space, we reformulate some recent mixed Generalized Multiscale Finite Element Methods. We introduce snapshots and local spectral problems that appropriately define local weight and trial spaces. In particular, we use energy minimizing snapshots and local spectral decompositions in the natural norm associated with the auxiliary variable. The resulting spectral decomposition adaptively identifies and builds the optimal multiscale space to stabilize the system. We discuss the stability and its relation to the approximation property of the test space. We design online basis functions, which accelerate convergence in the test space, and consequently, improve stability. We present several numerical examples and show that one needs a few test functions to achieve an error similar to the projection error in the primal variable irrespective of the Peclet number

Variational Formulations for Explicit Runge-Kutta Methods

Variational space-time formulations for partial di fferential equations have been of great interest in the last decades, among other things, because they allow to develop mesh-adaptive algorithms. Since it is known that implicit time marching schemes have variational structure, they are often employed for adaptivity. Previously, Galerkin formulations of explicit methods were introduced for ordinary di fferential equations employing speci fic inexact quadrature rules. In this work, we prove that the explicit Runge-Kutta methods can be expressed as discontinuous-in-time Petrov-Galerkin methods for the linear di ffusion equation. We systematically build trial and test functions that, after exact integration in time, lead to one, two, and general stage explicit Runge-Kutta methods. This approach enables us to reproduce the existing time-domain (goal-oriented) adaptive algorithms using explicit methods in time

Forward-in-Time Goal-Oriented Adaptivity

In goal-oriented adaptive algorithms for partial differential equations, we adapt the finite element mesh in order to reduce the error of the solution in some quantity of interest. In time-dependent problems, this adaptive algorithm involves solving a dual problem that runs backward in time. This process is, in general, computationally expensive in terms of memory storage. In this work, we define a pseudo-dual problem that runs forward in time. We also describe a forward-in-time adaptive algorithm that works for some specific problems. Although it is not possible to define a general dual problem running forwards in time that provides information about future states, we provide numerical evidence via one-dimensional problems in space to illustrate the efficiency of our algorithm as well as its limitations. Finally, we propose a hybrid algorithm that employs the classical backward-in-time dual problem once and then performs the adaptive process forwards in time

Secure dynamic community establishment in coalitions

Accepted versio

A model of discriminant analysis on the basis of descriptor variables for the ampelography of Vitis sp.

Use of descriptor variables in ampelography is recommended to simplify recording of data and to enable useful comparisons. Parametric assumptions are, however, poorly satisfied especially with regard to statistical interference. In the paper some statistical procedures to improve the discriminant ability of descriptor variables are considered. The use of variances and covariances of variety by year interactions is suggested for the error matrix within a multiple discriminant analysis procedure. The adequacy of this model is verified in a 3-year experiment with Italian wine varieties. The discriminant power, as evaluated on the basis of the estimated distances among varieties, is satisfactory

hp-HGS strategy for inverse 3D DC resistivity logging measurement simulations

In this paper we present a twin adaptive strategy hp-HGS for solving inverse problems related to 3D DC borehole resistivity measurement simulations. The term "simulation of measurements" is widely used by the geophysical community. A quantity of interest, voltage, is measured at a receiver electrode located in the logging instrument. We use the self-adaptive goal-oriented hp-Finite Element Method (hp-FEM) computer simulations of the process of measurements in deviated wells (when the angle between the borehole and formation layers are < 90 deg). We also employ the hierarchical genetic search (HGS) algorithm to solve the inverse problem. Each individual in the population represents a single configuration of the formation layers. The evaluation of the individual is performed by solving the direct problem by means of the hp-FEM algorithm and by comparison with measured logging curve. We conclude the paper with some discussion on the parallelization of the algorithm. © 2012 Published by Elsevier Ltd

Numerical simulation of spheres moving and colliding close to bed streams, with a complete characterization of turbulence

River morphodynamics and sediment transportMechanics of sediment transpor

GENETIC ASPECTS OF BEEF PRODUCTION AMONG HOLSTEIN-FRIESIANS PEDIGREE SELECTED FOR MILK PRODUCTION

To explore the potential of cattle to produce both milk and beef, the genetic aspects of beef production among Holstein-Friesian bulls pedigree selected for milk were studied. The data included growth records of 504 bulls (DPT) by 120 sires (SPT) pedigree selected for progeny testing by American Breeders Service, 1964 to 1971. DPT bulls with proofs had an average predicted difference for milk (PMD) of +180 kilograms. The daughter average was 7,273 kg per lactation under varying herd conditions. Sires accounted for 10% of the variation in average daily gain (ADG), 10% in daily gain per 100 kg body weight (DG/100) and 16% in body weight, indicating substantial genetic variability in beef traits. Sire variance components for beef traits varied with age. There were wide ranges in estimated breeding value (EBV) and estimated transmitting ability (ETA) for beef traits among DPT and SPT bulls, respectively. Ranking EBV among DPT bulls and ETA among SPT bulls for beef traits and selecting the top 10% and 20%, respectively, showed high selection differentials, empirically reflecting the potential for genetic improvement from selection

Dendrite formation in rechargeable lithium-metal batteries: Phase-field modeling using open-source finite element library

We describe a phase-field model for the electrodeposition process that forms dendrites within metal-anode batteries. We derive the free energy functional model, arriving at a system of partial differential equations that describe the evolution of a phase field, the lithium-ion concentration, and an electric potential. We formulate, discretize, and solve the set of partial differential equations describing the coupled electrochemical interactions during a battery charge cycle using an open-source finite element library. The open-source library allows us to use parallel solvers and time-marching adaptivity. We describe two- and three-dimensional simulations; these simulations agree with experimentally-observed dendrite growth rates and morphologies reported in the literature.Comment: Under Revie