Flow Field Clustering via Algebraic Multigrid
VIS '04 Proceedings of the conference on Visualization '04
Variations on algebraic recursive multilevel solvers (ARMS) for the solution of CFD problems
Applied Numerical Mathematics
An application of multigrid methods for a discrete elastic model for epitaxial systems
Journal of Computational Physics
Journal of Computational and Applied Mathematics
A damping preconditioner for time-harmonic wave equations in fluid and elastic material
Journal of Computational Physics
An efficient multigrid method for the simulation of high-resolution elastic solids
ACM Transactions on Graphics (TOG)
From Functional Analysis to Iterative Methods
SIAM Review
Fast iterative solvers for thin structures
Finite Elements in Analysis and Design
Journal of Computational and Applied Mathematics
Algebraic multilevel methods with aggregations: an overview
LSSC'05 Proceedings of the 5th international conference on Large-Scale Scientific Computing
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We present an algebraic multigrid (AMG) method for the efficient solution of linear block-systems stemming from a discretization of a system of partial differential equations (PDEs). It generalizes the classical AMG approach for scalar problems to systems of PDEs in a natural blockwise fashion. We apply this approach to linear elasticity and show that the block interpolation, described in this paper, reproduces the rigid body modes, i.e., the kernel elements of the discrete linear elasticity operator. It is well known from geometric multigrid methods that this reproduction of the kernel elements is an essential property to obtain convergence rates which are independent of the problem size. We furthermore present results of various numerical experiments in two and three dimensions. They confirm that the method is robust with respect to variations of the Poisson ratio $\nu$. We obtain rates $\rho