Discretization in the quasi-continuum

Continuum discretization using orthogonal polynomials

A method for discretizing the continuum by using a transformed harmonic oscillator basis has recently been presented @Phys. Rev. A 63, 052111 ~2001!#. In the present paper, we propose a generalization of that formalism which does not rely on the harmonic oscillator for the inclusion of the continuum in the study of weakly bound systems. In particular, we construct wave functions that represent ...

Discretization of Continuum–of–Alleles Models

We consider models for mutation and selection of an infinitely large population of individuals that are described by real numbers, commonly called continuum-of-alleles (COA) models. It is shown that such models can be approximated arbitrarily well by models with a finite number of types, which constitutes a discretization procedure. For this purpose, two standard methods of approximation theory...

Discretization of Continuum - of - Alleles Modelsoliver Redner

Geometric, Variational Discretization of Continuum Theories

This study derives geometric, variational discretizations of continuum theories arising in fluid dynamics, magnetohydrodynamics (MHD), and the dynamics of complex fluids. A central role in these discretizations is played by the geometric formulation of fluid dynamics, which views solutions to the governing equations for perfect fluid flow as geodesics on the group of volume-preserving diffeomor...

Quasi-optimal Schwarz Methods for the Conforming Spectral Element Discretization

Fast methods are proposed for solving the system KNx = b resulting from the dis-cretization of elliptic self-adjoint equations in three dimensional domains by the spectral element method. The domain is decomposed into hexahedral elements, and in each of these elements the discretization space is formed by polynomials of degree N in each variable. Gauss-Lobatto-Legendre (GLL) quadrature rules re...