Numerical Quadrature (numerical + quadrature)

Distribution by Scientific Domains

Selected Abstracts

Positivity-preserving, flux-limited finite-difference and finite-element methods for reactive transport

Robert J. MacKinnon
Abstract A new class of positivity-preserving, flux-limited finite-difference and Petrov,Galerkin (PG) finite-element methods are devised for reactive transport problems. The methods are similar to classical TVD flux-limited schemes with the main difference being that the flux-limiter constraint is designed to preserve positivity for problems involving diffusion and reaction. In the finite-element formulation, we also consider the effect of numerical quadrature in the lumped and consistent mass matrix forms on the positivity-preserving property. Analysis of the latter scheme shows that positivity-preserving solutions of the resulting difference equations can only be guaranteed if the flux-limited scheme is both implicit and satisfies an additional lower-bound condition on time-step size. We show that this condition also applies to standard Galerkin linear finite-element approximations to the linear diffusion equation. Numerical experiments are provided to demonstrate the behavior of the methods and confirm the theoretical conditions on time-step size, mesh spacing, and flux limiting for transport problems with and without nonlinear reaction. Copyright 2003 John Wiley & Sons, Ltd. [source]

Variational CI techniques for computing dispersion constants

Gian Luigi BendazzoliArticle first published online: 4 APR 200
Abstract We describe the computation of dispersion constants using variational subspace methods to solve the perturbation theory equations in the tensor product space of the interacting molecules, treated separately at a (full) configuration interaction (CI) level. These new techniques are more accurate than the numerical quadrature of the Casimir Polder integral at the expense of a small additional computational cost. We also show how to compute the norm of the residual of the perturbative solution in the tensor product space to check convergence. The methods are tested on LiH and BH. 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2005 [source]

Half-numerical evaluation of pseudopotential integrals

Roberto Flores-Moreno
Abstract A half-numeric algorithm for the evaluation of effective core potential integrals over Cartesian Gaussian functions is described. Local and semilocal integrals are separated into two-dimensional angular and one-dimensional radial integrals. The angular integrals are evaluated analytically using a general approach that has no limitation for the l -quantum number. The radial integrals are calculated by an adaptive one-dimensional numerical quadrature. For the semilocal radial part a pretabulation scheme is used. This pretabulation simplifies the handling of radial integrals, makes their calculation much faster, and allows their easy reuse for different integrals within a given shell combination. The implementation of this new algorithm is described and its performance is analyzed. 2006 Wiley Periodicals, Inc. J Comput Chem 27: 1009,1019, 2006 [source]

Generalization and numerical investigation of QMOM

AICHE JOURNAL, Issue 1 2007
R. Grosch
Abstract A generalized framework is developed for the quadrature method of moments (QMOM), which is a solution method for population balance models. It further evaluates the applicability of this method to industrial suspension crystallization processes. The framework is based on the concepts of generalized moments and coordinate transformations, which have been used already in earlier solution approaches. It is shown how existing approaches to QMOM are derived from the suggested unified framework. Thus, similarities and differences between the various QMOM methods are uncovered. Further, potential error sources involved in the different approaches to QMOM are discussed and assessed by means of a series of test cases. The test cases are selected to be challenging. The error in the QMOM solution is evaluated by comparison to an adaptive, error controlled solution of the population balance. The behavior of a range of different QMOM formulations is analyzed by means of numerical quadrature, dynamic simulation, as well as numerical continuation and bifurcation analysis. As a result of this detailed analysis, some general limitations of the method are detected and guidelines for its application are developed. This article is limited to lumped population balance models with one internal coordinate. 2006 American Institute of Chemical Engineers AIChE J, 2007 [source]