with application to fluid (2009)
K. A. Cliffe, A. Spence, Claverton Down, Bath Ba Ay, S. J. Tavener, K. A. Cliffe, ...
The numerical analysis of bifurcation problems
Two immiscible fluid layers that are subjected to a temperature gradi-ent perpendicular to their interface, exhibit a range of behaviors that is considerably richer than for the single-fluid case. We...
Two Grid Iteration With A Conjugate Gradient Smoother Applied To A Groundwater Flow Model (2007)
M. J. Hagger, K. A. Cliffe, A. Spence
. The well known two grid method is used to solve the large, sparse, linear system resulting from a finite element method discretisation of \Gammar:(krp) = 0. Several possible choices of smoother are...
Implementation of extended systems using symbolic algebra (2000)
Following the pioneering work of Keller and others in the 1970s and ’80s, numerical techniques for solving non-linear systems of equations that exhibit bifurcations have been developed to the point...
JOURNAL OF COMPUTATIONAL PHYSICS 145, 193–227 (1998) ARTICLE NO. CP985995 (1997)
Marangoni–bénard Convection, K. A. Cliffe, S. J. Tavener
Computations of Marangoni convection are usually performed in two- or threedimensional domains with rigid boundaries. In two dimensions, allowing the free surface to deform can result in a solution...
Performance Issues for Frontal Schemes on a Cache-Based High Performance Computer (1997)
K. A. Cliffe, I.S. Duff, J. A. Scott
We consider the implementation of a frontal code for the solution of large sparse unsymmetric linear systems on a high performance computer where data must be in the cache before arithmetic...
On the Equivalence of Certain Transformations of Block Matrices under Arnoldi's method (1994)
K.A. Cliffe, T.J. Garratt, J.F. Golding, A. Spence
This paper is concerned with the relationship between the eigenvalues computed by a generalisation of the standard Arnoldi's method applied to certain preconditionings of the eigenvalue problem...
Steady-state/Hopf mode interaction at a symmetry-breaking Takens-Bogdanov point (1994)
WU, W., SPENCE, P., CLIFFE, K. A.
This paper is concerned with an example of steady-state/Hopf mode interaction arising in two-parameter non-linear problems satisfying a Z2symmetry condition. Specifically we study bifurcation...
An orthogonal mapping technique for the computation of a viscous free-surface flow (1992)
Cliffe, K.A., Tavener, S.J., Wheeler, A.A.
In this paper we describe finite element computations of the free-surface flow of a viscous fluid down an undulating inclined plane. The technique developed here employs an orthogonal mapping that is...
Steady axisymmetric flows in the Taylor apparatus applying impermeable stress-free boundary conditions are computed using a finite-element technique. The unfoldings of the double singular points...