Algebraic multilevel preconditioning methods, II
SIAM Journal on Numerical Analysis
Algebraic multilevel preconditioning of anisotropic elliptic problems
SIAM Journal on Scientific Computing
SIAM Journal on Scientific Computing
AMLI Preconditioning of Pure Displacement Non-conforming Elasticity FEM Systems
NAA '00 Revised Papers from the Second International Conference on Numerical Analysis and Its Applications
A simple preconditioner for the SIPG discretization of linear elasticity equations
NMA'10 Proceedings of the 7th international conference on Numerical methods and applications
Multilevel preconditioning of crouzeix-raviart 3d pure displacement elasticity problems
LSSC'09 Proceedings of the 7th international conference on Large-Scale Scientific Computing
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Preconditioning techniques based on various multilevel extensions of two-level splittings of finite element (FE) spaces lead to iterative methods which have an optimal rate of convergence and computational complexity with respect to the number of degrees of freedom. This article deals with the construction of algebraic two-level and multilevel preconditioning algorithms for the Lamé equations of elasticity, which are discretized by Crouzeix-Raviart non-conforming linear finite elements on triangles. An important point to note is that in the non-conforming case the FE spaces corresponding to two successive levels of mesh refinements are not nested. To handle this, a proper aggregation-based two-level basis is considered, which enables us to fit the general framework of the two-level preconditioners and to generalize the method to the multilevel case. The derived estimate of the constant in the strengthened Cauchy-Bunyakowski-Schwarz (CBS) inequality is uniform with respect to both, mesh anisotropy and Poisson ratio, including the almost incompressible case.