Crotalus enyo

Number of Pages: 6Integrative BiologyGeological Science

Parameter-robust discretization and preconditioning of Biot's consolidation model

Biot's consolidation model in poroelasticity has a number of applications in science, medicine, and engineering. The model depends on various parameters, and in practical applications these parameters ranges over several orders of magnitude. A current challenge is to design discretization techniques and solution algorithms that are well behaved with respect to these variations. The purpose of this paper is to study finite element discretizations of this model and construct block diagonal preconditioners for the discrete Biot systems. The approach taken here is to consider the stability of the problem in non-standard or weighted Hilbert spaces and employ the operator preconditioning approach. We derive preconditioners that are robust with respect to both the variations of the parameters and the mesh refinement. The parameters of interest are small time-step sizes, large bulk and shear moduli, and small hydraulic conductivity.Comment: 24 page

Sauromalus hispidus

Number of Pages: 4Integrative BiologyGeological Science

Weakly imposed symmetry and robust preconditioners for Biot's consolidation model

We discuss the construction of robust preconditioners for finite element approximations of Biot's consolidation model in poroelasticity. More precisely, we study finite element methods based on generalizations of the Hellinger-Reissner principle of linear elasticity, where the stress tensor is one of the unknowns. The Biot model has a number of applications in science, medicine, and engineering. A challenge in many of these applications is that the model parameters range over several orders of magnitude. Therefore, discretization procedures which are well behaved with respect to such variations are needed. The focus of the present paper will be on the construction of preconditioners, such that the preconditioned discrete systems are well-conditioned with respect to variations of the model parameters as well as refinements of the discretization. As a byproduct, we also obtain preconditioners for linear elasticity that are robust in the incompressible limit.Comment: 21 page

Foundations of Programming Languages

This clearly written textbook provides an accessible introduction to the three programming paradigms of object-oriented/imperative, functional, and logic programming. Highly interactive in style, the text encourages learning through practice, offering test exercises for each topic covered. Review questions and programming projects are also presented, to help reinforce the concepts outside of the classroom. This updated and revised new edition features new material on the Java implementation of the JCoCo virtual machine

Scan Data : An alternative source of data for consumer demand research

Scan data have recently become a more popular source of data for use in consumer demand research. Previous studies have used scan data to measure the effects of promotional actives and their effects on consumer demand. Before scan data were available, researchers most frequent sources of data were government survey publications. These data sets are creditable and useful but they do not contain all the desirable characteristics needed in consumer demand research. There are also private corporations that collect and supply data, but there interest lies with the needs of industry not academia. The government surveys are briefly described and comments regarding their usefulness in consumer demand follows. The public data sets are also described and a word is said about their effectiveness in consumer demand research at the academic level. The empirical analysis is centered around estimation the demand for beef hotdogs using scan data plus data that contain advertising information from television, radio, and newspaper. The null hypotheses that holidays, television, and radio advertising do not have an impact on demand can all be rejected, since the respective parameter estimates are significantly by different from zero. Newspaper advertising on the other hand has proven to be insignificant

A mixed finite element method for nearly incompressible multiple-network poroelasticity

In this paper, we present and analyze a new mixed finite element formulation of a general family of quasi-static multiple-network poroelasticity (MPET) equations. The MPET equations describe flow and deformation in an elastic porous medium that is permeated by multiple fluid networks of differing characteristics. As such, the MPET equations represent a generalization of Biot's equations, and numerical discretizations of the MPET equations face similar challenges. Here, we focus on the nearly incompressible case for which standard mixed finite element discretizations of the MPET equations perform poorly. Instead, we propose a new mixed finite element formulation based on introducing an additional total pressure variable. By presenting energy estimates for the continuous solutions and a priori error estimates for a family of compatible semi-discretizations, we show that this formulation is robust in the limits of incompressibility, vanishing storage coefficients, and vanishing transfer between networks. These theoretical results are corroborated by numerical experiments. Our primary interest in the MPET equations stems from the use of these equations in modelling interactions between biological fluids and tissues in physiological settings. So, we additionally present physiologically realistic numerical results for blood and tissue fluid flow interactions in the human brain