Carmen Rodrigo

A Simple and Efficient Segregated Smoother for the Discrete Stokes Equations

We consider the multigrid solution of the generalized Stokes equations with a segregated (i.e., equationwise) Gauss--Seidel smoother based on a Uzawa-type iteration. We analyze the smoother in the framework of local Fourier analysis, and obtain an analytic bound on the smoothing factor showing uniform performance for a family of Stokes problems. These results are confirmed by the numerical computation of the two-grid convergence factor for different types of grids and discretizations. Numerical results also show that the actual convergence of the W-cycle is approximately the same as that obtained by a Vanka smoother, despite this latter smoother being significantly more costly per iteration step.

Accuracy Measures and Fourier Analysis for the Full Multigrid Algorithm

The full multigrid (FMG) algorithm is often claimed to achieve so-called discretization-level accuracy. In this paper, this notion is formalized by defining a worst-case relative accuracy measure, denoted

Multigrid finite element methods on semi‐structured triangular grids for planar elasticity

E_{FMG}^{\ell}

Multigrid fourier analysis on semi‐structured anisotropic meshes for vector problems

, which compares the total error of the

Efficient geometric multigrid implementation for triangular grids

\ell

A nonconforming finite element method for the Biot's consolidation model in poroelasticity

-level FMG solution against the inherent discretization error. This measure can be used for tuning algorithmic components so as to obtain discretization-level accuracy. A Fourier analysis is developed for estimating

On an Uzawa smoother in multigrid for poroelasticity equations

E_{FMG}^{\ell}

Performance‐influence models of multigrid methods: A case study on triangular grids

, and the resulting estimates are confirmed by numerical tests.

Multigrid methods for cell-centered discretizations on triangular meshes

Multigrid methods for a stencil-based implementation of a finite element method for planar elasticity, using semi-structured triangular grids, are presented. Local Fourier Analysis (LFA) is applied to identify the correct multigrid components. To this end, LFA for multigrid methods on regular triangular grids is extended to the case of the problem of planar elasticity, although its application to other systems is straightforward. For the discrete elasticity operator obtained with linear finite elements, different collective smoothers such as three-color smoother and some zebra-type smoothers are analyzed, and LFA results for these smoothers are shown. The multigrid method is constructed in block-wise form. In particular, different smoothers and different numbers of preand postsmoothing steps are considered in each triangle of the coarsest triangulation of the domain. Some numerical experiments are presented to illustrate the efficiency of this multigrid algorithm.

Multicolor Fourier analysis of the multigrid method for quadratic FEM discretizations

Abstract An efficient multigrid finite element method for vector problems on triangular anisotropic semi‐structured grids is proposed. This algorithm is based on zebra line‐type smoothers to overcome the difficulties arising when multigrid is applied on stretched meshes. In order to choose the type of multigrid cycle and the number of pre‐ and post‐smoothing steps, a three‐grid Fourier analysis is done. To this end, local Fourier analysis (LFA) on triangular grids for scalar problems is extended to the vector case. To illustrate the good performance of the method, a system of reaction‐diffusion is considered as model problem. A very satisfactory global convergence factor is obtained by using a V(0,2)‐cycle for domains triangulated with highly anisotropic meshes.