337 RWTH Publication No: 47148        2012        IGPM337.pdf
TITLE Integration of Products of Gaussians and Wavelets with Applications to Electronic Structure Calculations
AUTHORS Markus Bachmayr
ABSTRACT In this work, we consider a scheme for the computation of integrals of Gaussian functions with products of wavelets, which is applicable to wavelet bases given only implicitly in terms of refinement relations. The integrals under consideration arise in wavelet discretizations of operator equations involving separable approximations of Coulomb potentials. Motivated by this application, we study in particular the case of large exponents in the Gaussian terms. The numerical tests demonstrate the practical efficiency of the method.
KEYWORDS wavelets, Gaussians, Coulomb potential, exponential sum approximation, sinc quadrature, trapezoidal rule
DOI 10.1137/120874424
PUBLICATION SIAM journal on numerical analysis
51(5), 2491-2513 (2013)