TY - GEN
T1 - On an energy minimizing basis for algebraic multigrid methods
AU - Xu, Jinchao
AU - Zikatanov, Ludmil
N1 - Generated from Scopus record by KAUST IRTS on 2023-02-15
PY - 2004/1/1
Y1 - 2004/1/1
N2 - This paper is devoted to the study of an energy minimizing basis first introduced in Wan, Chan and Smith (2000) for algebraic multigrid methods. The basis will be first obtained in an explicit and compact form in terms of certain local and global operators. The basis functions are then proved to be locally harmonic functions on each coarse grid "element". Using these new results, it is illustrated that this basis can be numerically obtained in an optimal fashion. In addition to the intended application for algebraic multigrid method, the energy minimizing basis may also be applied for numerical homogenization. © Springer-Verlag 2004.
AB - This paper is devoted to the study of an energy minimizing basis first introduced in Wan, Chan and Smith (2000) for algebraic multigrid methods. The basis will be first obtained in an explicit and compact form in terms of certain local and global operators. The basis functions are then proved to be locally harmonic functions on each coarse grid "element". Using these new results, it is illustrated that this basis can be numerically obtained in an optimal fashion. In addition to the intended application for algebraic multigrid method, the energy minimizing basis may also be applied for numerical homogenization. © Springer-Verlag 2004.
UR - http://link.springer.com/10.1007/s00791-004-0147-y
UR - http://www.scopus.com/inward/record.url?scp=33750160340&partnerID=8YFLogxK
U2 - 10.1007/s00791-004-0147-y
DO - 10.1007/s00791-004-0147-y
M3 - Conference contribution
SP - 121
EP - 127
BT - Computing and Visualization in Science
PB - Springer [email protected]
ER -