Research Group of Prof. Dr. M. Griebel
Institute for Numerical Simulation

  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 = { 1},
  pdf = { 1},
  http = {},
  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}