An adaptive discontinuous finite volume method for elliptic problems

AbstractAn adaptive discontinuous finite volume method is developed and analyzed in this paper. We prove that the adaptive procedure achieves guaranteed error reduction in a mesh-dependent energy norm and has a linear convergence rate. Numerical results are also presented to illustrate the theoretical analysis

SARS-associated Coronavirus Transmitted from Human to Pig

Severe acute respiratory syndrome–associatedcoronavirus (SARS-CoV) was isolated from a pig during a survey for possible routes of viral transmission after a SARS epidemic. Sequence and epidemiology analyses suggested that the pig was infected by a SARS-CoV of human origin

Development of CFL-Free, Explicit Schemes for Multidimensional Advection-Reaction Equations

We combine an Eulerian–Lagrangian approach and multiresolution analysis to develop unconditionally stable, explicit, multilevel methods for multidimensional linear hyperbolic equations. The derived schemes generate accurate numerical solutions even if large time steps are used. Furthermore, these schemes have the capability of carrying out adaptive compression without introducing mass balance error. Computational results are presented to show the strong potential of the numerical methods developed

Postprocessing of a finite volume element method for semilinear parabolic problems

In this paper, we study a postprocessing procedure for improving accuracy of the finite volume element approximations of semilinear parabolic problems. The procedure amounts to solve a source problem on a coarser grid and then solve a linear elliptic problem on a finer grid after the time evolution is finished. We derive error estimates in the L2 and H1 norms for the standard finite volume element scheme and an improved error estimate in the H1 norm. Numerical results demonstrate the accuracy and efficiency of the procedure

E.: An operator splitting method for nonlinear reactive transport equations and its implementation based on DLL and COM. Current trends in high performance computing and its applications

In this paper, we propose an operator splitting method for convectiondominated transport equations with nonlinear reactions, which model groundwater contaminant biodegradation and many other interesting applications. The proposed method can be efficiently implemented by applying software integration techniques such as dynamical link library (DLL) or component object model (COM). Numerical results are also included to demonstrate the performance of the method.

Curvature Concentrations on the HIV-1 Capsid

It is known that the retrovirus capsids possess a fullerene-like structure. These caged polyhedral arrangements are built entirely from hexagons and exactly 12 pentagons according to the Euler theorem. Viral capsids are composed of capsid proteins, which create the hexagon and pentagon shapes by groups of six (hexamer) and five (pentamer) proteins. Different distributions of these 12 pentamers result in icosahedral, tubular, or conical shaped capsids. These pentamer clusters introduce declination and hence curvature on the capsids. This paper provides explicit and quantitative characterization of curvature on virus capsids. The concept of curvature concentration is also introduced. For the HIV (5,7)-cone, it is shown that the curvature concentration at the narrow end is about at least four times higher than that at the broad end. Our modeling results about curvature concentrations on HIV-1 capsids echo the results in the literature that the pentamers are in the regions with the highest stress, although the connection between the two approaches (curvature concentration and stress) is to be explored. This also leads to a conjecture that “HIV-1 capsid narrow end may close last during maturation but open first during entry into a host cell"

Generating Vectors for the Lattice Structures of Tubular and Conical Viral Capsids

Retrovirus capsid is a fullerene-like lattice consisting of capsid protein hexamers and pentamers. Mathematical models for the lattice structure help understand the underlying biological mechanisms in the formation of viral capsids. It is known that viral capsids could be categorized into three major types: icosahedron, tube, and cone. While the model for icosahedral capsids is established and well-received, models for tubular and conical capsids need further investigation. This paper proposes new models for the tubular and conical capsids based on an extension of the Capser-Klug quasi-equivalence theory. In particular, two and three generating vectors are used to characterize respectively the lattice structures of tubular and conical capsids. Comparison with published HIV-1 data demonstrates a good agreement of our modeling results with experimental data