TY - JOUR
T1 - Matrix decomposition algorithms for the finite element Galerkin method with piecewise Hermite cubics
AU - Bialecki, Bernard
AU - Fairweather, Graeme
AU - Knudson, David B.
AU - Lipman, D. Abram
AU - Nguyen, Que N.
AU - Sun, Weiwei
AU - Weinberg, Gadalia M.
PY - 2009/8
Y1 - 2009/8
N2 - Matrix decomposition algorithms (MDAs) employing fast Fourier transforms are developed for the solution of the systems of linear algebraic equations arising when the finite element Galerkin method with piecewise Hermite bicubics is used to solve Poisson's equation on the unit square. Like their orthogonal spline collocation counterparts, these MDAs, which require O(N2logN) operations on an N×N uniform partition, are based on knowledge of the solution of a generalized eigenvalue problem associated with the corresponding discretization of a two-point boundary value problem. The eigenvalues and eigenfunctions are determined for various choices of boundary conditions, and numerical results are presented to demonstrate the efficacy of the MDAs. © Springer Science + Business Media, LLC 2008.
AB - Matrix decomposition algorithms (MDAs) employing fast Fourier transforms are developed for the solution of the systems of linear algebraic equations arising when the finite element Galerkin method with piecewise Hermite bicubics is used to solve Poisson's equation on the unit square. Like their orthogonal spline collocation counterparts, these MDAs, which require O(N2logN) operations on an N×N uniform partition, are based on knowledge of the solution of a generalized eigenvalue problem associated with the corresponding discretization of a two-point boundary value problem. The eigenvalues and eigenfunctions are determined for various choices of boundary conditions, and numerical results are presented to demonstrate the efficacy of the MDAs. © Springer Science + Business Media, LLC 2008.
KW - Eigenvalues and eigenfunctions
KW - Elliptic boundary value problems
KW - Finite element Galerkin method
KW - Generalized eigenvalue problem
KW - Matrix decomposition algorithm
KW - Piecewise Hermite cubics
UR - http://www.scopus.com/inward/record.url?scp=70350621911&partnerID=8YFLogxK
UR - https://www.scopus.com/record/pubmetrics.uri?eid=2-s2.0-70350621911&origin=recordpage
U2 - 10.1007/s11075-008-9255-y
DO - 10.1007/s11075-008-9255-y
M3 - RGC 21 - Publication in refereed journal
SN - 1017-1398
VL - 52
SP - 1
EP - 23
JO - Numerical Algorithms
JF - Numerical Algorithms
IS - 1
ER -