TY - GEN
T1 - Fast direct solution of FEM systems using overlapped localizing modes on a shifted grid
AU - Xu, Xin
AU - Adams, Robert J.
PY - 2011
Y1 - 2011
N2 - Overlapped, localizing local-global solution (OL-LOGOS) modes have been proposed to develop fast direct solvers for low frequency electromagnetic wave problems. The efficiencies of the resulting OL-LOGOS factorization algorithms have been demonstrated for the matrix equations associated with dense three-dimensional integral equations and sparse two-dimensional partial differential equations. In both cases, approximately O(N log N) time and O(N) memory complexities have been observed. In this work, the OL-LOGOS method is applied to three-dimensional scalar FEM systems. In order to improve the factorization speed and reduce memory costs for FEM applications, a pre-factorization permutation step is incorporated into the OL-LOGOS factorization algorithm. Numerical results demonstrate factorization and memory complexities of approximately O(N log N) and O(N) as the problem size grows.
AB - Overlapped, localizing local-global solution (OL-LOGOS) modes have been proposed to develop fast direct solvers for low frequency electromagnetic wave problems. The efficiencies of the resulting OL-LOGOS factorization algorithms have been demonstrated for the matrix equations associated with dense three-dimensional integral equations and sparse two-dimensional partial differential equations. In both cases, approximately O(N log N) time and O(N) memory complexities have been observed. In this work, the OL-LOGOS method is applied to three-dimensional scalar FEM systems. In order to improve the factorization speed and reduce memory costs for FEM applications, a pre-factorization permutation step is incorporated into the OL-LOGOS factorization algorithm. Numerical results demonstrate factorization and memory complexities of approximately O(N log N) and O(N) as the problem size grows.
KW - FEM
KW - Fast Direct solver
KW - Linear equation
UR - https://www.scopus.com/pages/publications/80055023645
UR - https://www.scopus.com/pages/publications/80055023645#tab=citedBy
U2 - 10.1109/APS.2011.5997231
DO - 10.1109/APS.2011.5997231
M3 - Conference contribution
AN - SCOPUS:80055023645
SN - 9781424495634
T3 - IEEE Antennas and Propagation Society, AP-S International Symposium (Digest)
SP - 3265
EP - 3267
BT - 2011 IEEE International Symposium on Antennas and Propagation - Proceedings
T2 - 2011 IEEE International Symposium on Antennas and Propagation and USNC/URSI National Radio Science Meeting, APSURSI 2011
Y2 - 3 July 2011 through 8 July 2011
ER -