Pub. online:1 Jan 2019Type:Research ArticleOpen Access
Volume 30, Issue 2 (2019), pp. 243–268
We propose a fast MATLAB implementation of the mini-element (i.e. $P1$-Bubble/$P1$) for the finite element approximation of the generalized Stokes equation in 2D and 3D. We use cell arrays to derive vectorized assembling functions. We also propose a Uzawa conjugate gradient method as an iterative solver for the global Stokes system. Numerical experiments show that our implementation has an (almost) optimal time-scaling. For 3D problems, the proposed Uzawa conjugate gradient algorithm outperforms MATLAB built-in linear solvers.
Volume 9, Issue 4 (1998), pp. 437–448
This paper presents a parallel version of a Generalized Conjugate Gradient algorithm proposed by Liu and Story in which the search direction considers the effect of the inexact line search. We describe the implementation of this algorithm on a parallel architecture and analyze the related speedup ratios. Numerical results are given for a shared memory computer (Cray C92).