On the computation of the eigenproblems of hydrogen and helium in strong magnetic and electric fields with the sparse grid combination technique

被引:39
|
作者
Garcke, J [1 ]
Griebel, M [1 ]
机构
[1] Univ Bonn, Inst Angew Math, D-53115 Bonn, Germany
关键词
Schrodinger equation; sparse grids; combination technique; hydrogen atom; helium atom; eigenvalue solver; numerical computation; strong magnetic fields; strong electric fields;
D O I
10.1006/jcph.2000.6627
中图分类号
TP39 [计算机的应用];
学科分类号
081203 ; 0835 ;
摘要
We introduce the combination technique for the numerical solution of d-dimensional eigenproblems on sparse grids. Hen, O(d.(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(Nd) 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 Schrodinger equation for hydrogen (one-electron problem) and the six-dimensional Schrodinger equation for helium (two-electron problem) in strong magnetic and electric fields. (C) 2000 Academic Press.
引用
收藏
页码:694 / 716
页数:23
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