An efficient numerical quadrature for the calculation of the potential energy of wavefunctions expressed in the Daubechies wavelet basis

Authors:
A. I. Neelov;S. Goedecker
Affiliations:
Institute of Physics, University of Basel, Basel, Switzerland;Institute of Physics, University of Basel, Basel, Switzerland
Venue:
Journal of Computational Physics
Year:
2006

Citing 10
Cited 0

Ten lectures on wavelets

Ten lectures on wavelets
On the representation of operators in bases of compactly supported wavelets

SIAM Journal on Numerical Analysis
Using the refinement equation for evaluating integrals of wavelets

SIAM Journal on Numerical Analysis
A class of bases in L2 for the sparse representations of integral operators

SIAM Journal on Mathematical Analysis
Quadrature formulae and asymptotic error expansions for wavelet approximations of smooth functions

SIAM Journal on Numerical Analysis
A study of orthonormal multi-wavelets

Applied Numerical Mathematics - Special issue on selected keynote papers presented at 14th IMACS World Congress, Atlanta, NJ, July 1994
A dynamically adaptive multilevel wavelet collocation method for solving partial differential equations in a finite domain

Journal of Computational Physics
Numerical Solution of the Schrödinger Equation in a Wavelet Basis for Hydrogen-like Atoms

SIAM Journal on Numerical Analysis
Adaptive solution of partial differential equations in multiwavelet bases

Journal of Computational Physics
Multiwavelet moments and projection prefilters

IEEE Transactions on Signal Processing

Quantified Score

Hi-index	31.45

Visualization

Abstract

An efficient numerical quadrature is proposed for the approximate calculation of the potential energy in the context of pseudo potential electronic structure calculations with Daubechies wavelet and scaling function basis sets. Our quadrature is also applicable in the case of adaptive spatial resolution. Our theoretical error estimates are confirmed by numerical test calculations of the ground state energy and wavefunction of the harmonic oscillator in one dimension with and without adaptive resolution. As a byproduct we derive a filter, which, upon application on the scaling function coefficients of a smooth function, renders the approximate grid values of this function. This also allows for a fast calculation of the charge density from the wavefunction.