Convergence of some asynchronous nonlinear multisplitting methods

Frommer's nonlinear multisplitting methods for solving nonlinear systems of equations are extended to the asynchronous setting. Block methods are extended to include overlap as well. Several specific cases are discussed. Sufficient conditions to guarantee their local convergence are given. A numerical example is presented illustrating the performance of the new approach.     

Robust Bounds for Krylov Methods

In this paper we give bounds for polynomials of operators. These bounds are robust in low rank perturbations. This problem is encountered in the study of the convergence of Krylov methods. The central idea here is to view the resolvent as a meromorphic function.     

Defect correction and a posteriori error estimation of Petrov-Galerkin methods for nonlinear Volterra integro-differential equations

We present two defect correction schemes to accelerate the Petrov-Galerkin finite element methods [19] for nonlinear Volterra integro-differential equations. Using asymptotic expansions of the errors, we show that the defect correction schemes can yield higher order approximations to either the exact solution or its derivative. One of these schemes even does not impose any extra regularity requirement on the exact solution. As by-products, all of these higher order numerical methods can also be used to form a posteriori error estimators for accessing actual errors of the Petrov-Galerkin finite element solutions. Numerical examples are also provided to illustrate the theoretical results obtained in this paper.     

Decomposition Method with a Variable Parameter for a Class of Monotone Variational Inequality Problems

In this paper, we focus on a useful modification of the decomposition method by He et al. (Ref. 1). Experience on applications has shown that the number of iterations of the original method depends significantly on the penalty parameter. The main contribution of our method is that we allow the penalty parameter to vary automatically according to some self-adaptive rules. As our numerical simulations indicate, the modified method is more flexible and efficient in practice. A detailed convergence analysis of our method is also included.     

Optimal expansion of subspaces for eigenvector approximations

We consider the problem of how to expand a given subspace for approximating an eigenvalue and eigenvector of a matrix A. Specifically, we consider which vector in the subspace, after multiplied by A, provides optimal expansion of the existing subspace for the eigenvalue problem. We determine the optimal vector, when the quality of subspace for approximation is measured by the angle between the subspace and the eigenvector. We have also derived some characterization of the angle that might lead to more practically useful choice of the expansion vector.     

An overview of advances in understanding electrostatic charge buildup in gas-solid fluidized beds

Electrostatic charging of particles in gas-solid fluidized beds often results in operational complications in commercial processes. This paper provides a comprehensive review of the advances from the last decade in three key areas, namely the fundamental understanding of triboelectric charging, methods to measure particle charge, and experiments to elucidate particle charging processes in fluidized beds. This review underscores the need for better understanding the mechanisms of triboelectric charging in granular systems, effective online charge monitoring techniques, and experiments under industrially relevant conditions to better comprehend the problems in commercial reactors that can enable strategies to mitigate charging.     

Native and substituted cyclodextrins as chiral selectors for capillary electrophoresis enantioseparations: Structures,features, application,and molecular modeling

CDs are cyclic oligosaccharides consisting of α-d -glucopyranosyl units linked through 1,4-linkages, which are obtained from enzymatic degradation of starch. The coexistence of hydrophilic and hydrophobic regions in the same structure makes these macrocycles extremely versatile as complexing host with application in food, cosmetics, environmental, agriculture, textile, pharmaceutical, and chemical industries. Due to their inherent chirality, CDs have been also successfully used as chiral selectors in enantioseparation science, in particular, for CE enantioseparations. In the last decades, multidisciplinary approaches based on CE, NMR spectroscopy, X-ray crystallography, microcalorimetry, and molecular modeling have shed light on some aspects of recognition mechanisms underlying enantiodiscrimination. With the ever growing improvement of computer facilities, hardware and software, computational techniques have become a useful tool to model at molecular level the dynamics of diastereomeric associate formation to sample low-energy conformations, the binding energies between the enantiomer and the CD, and to profile noncovalent interactions contributing to the stability of CD/enantiomer association. On this basis, the aim of this review is to provide the reader with a critical overview on the applications of CDs in CE. In particular, the contemporary theory of the electrophoretic technique and the main structural features of CDs are described, with a specific focus on techniques, methods, and approaches to model CE enantioseparations promoted by native and substituted CDs. A systematic compilation of all published literature has not been attempted.     

L2Roe: a low dissipation version of Roe's approximate Riemann solver for low Mach numbers

A modification of the Roe scheme called L²Roe for low dissipation low Mach Roe is presented. It reduces the dissipation of kinetic energy at the highest resolved wave numbers in a low Mach number test case of decaying isotropic turbulence. This is achieved by scaling the jumps in all discrete velocity components within the numerical flux function. An asymptotic analysis is used to show the correct pressure scaling at low Mach numbers and to identify the reduced numerical dissipation in that regime. Furthermore, the analysis allows a comparison with two other schemes that employ different scaling of discrete velocity jumps, namely, LMRoe and a method of Thornber et al. To this end, we present for the first time an asymptotic analysis of the last method. Numerical tests on cases ranging from low Mach number (M_∞=0.001) to hypersonic (M_∞=5) viscous flows are used to illustrate the differences between the methods and to show the correct behavior of L²Roe. No conflict is observed between the reduced numerical dissipation and the accuracy or stability of the scheme in any of the investigated test cases. Copyright © 2015 John Wiley & Sons, Ltd.