@Article{ Garcke.Griebel:2000,
author = {J. Garcke and M. Griebel},
title = {On the computation of the eigenproblems of hydrogen and
helium in strong magnetic and electric fields with the
sparse grid combination technique},
journal = {Journal of Computational Physics},
year = {2000},
volume = {165},
number = {2},
pages = {694--716},
note = {also as SFB 256 Preprint 670, Institut f\"ur Angewandte
Mathematik, Universit\"at Bonn, 2000},
ps = {http://wissrech.ins.uni-bonn.de/research/pub/garcke/eigen_sparse_grid.ps.gz}
,
pdf = {http://wissrech.ins.uni-bonn.de/research/pub/garcke/eigen_sparse_grid.pdf}
,
http = {http://www.idealibrary.com/links/doi/10.1006/jcph.2000.6627}
,
abstract = {We introduce the combination technique for the numerical
solution of $d$-eigenproblems on sparse grids. Here, $O(d
\cdot (\log N)^{d-1})$ different problems, each of size
$O(N)$, have to be solved independently. This is in
contrast to the one problem of size $O(N^d)$ for a
conventional finite element discretization, where $N$
denotes the number of grid points in one coordinate
direction. Therefore, also higher dimensional eigenvalue
problems can be treated by our sparse grid combination
approach. We apply this method to solve the
three-dimensional Schr\"odinger equation for hydrogen (one
electron problem) and the six-dimensional Schr\"odinger
equation for helium (two electron problem) in strong
magnetic and electric fields.},
annote = {article}
}