Domain decomposition preconditioning for p-version finite elements with high aspect rations
Applied Numerical Mathematics - II on Domain decomposition; Guest Editor: W. Proskurowski
Convergence of a Nonconforming Multiscale Finite Element Method
SIAM Journal on Numerical Analysis
An energy-minimizing interpolation for robust multigrid methods
SIAM Journal on Scientific Computing
The method of subspace corrections
Journal of Computational and Applied Mathematics - Special issue on numerical analysis 2000 Vol. VII: partial differential equations
Multigrid
Element-Free AMGe: General Algorithms for Computing Interpolation Weights in AMG
SIAM Journal on Scientific Computing
AMGE Based on Element Agglomeration
SIAM Journal on Scientific Computing
Algebraic Multigrid Based on Element Interpolation (AMGe)
SIAM Journal on Scientific Computing
Molecular simulations of electroosmotic flows in rough nanochannels
Journal of Computational Physics
Algebraic Multigrid for High-Order Hierarchical $H(curl)$ Finite Elements
SIAM Journal on Scientific Computing
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In this paper, we will design and analyze a class of new algebraic multigrid methods for algebraic systems arising from the discretization of second order elliptic boundary value problems by high-order finite element methods. For a given sparse stiffness matrix from a quadratic or cubic Lagrangian finite element discretization, an algebraic approach is carefully designed to recover the stiffness matrix associated with the linear finite element disretization on the same underlying (but nevertheless unknown to the user) finite element grid. With any given classical algebraic multigrid solver for linear finite element stiffness matrix, a corresponding algebraic multigrid method can then be designed for the quadratic or higher order finite element stiffness matrix by combining with a standard smoother for the original system. This method is designed under the assumption that the sparse matrix to be solved is associated with a specific higher order, quadratic for example, finite element discretization on a finite element grid but the geometric data for the underlying grid is unknown. The resulting new algebraic multigrid method is shown, by numerical experiments, to be much more efficient than the classical algebraic multigrid method which is directly applied to the high-order finite element matrix. Some theoretical analysis is also provided for the convergence of the new method.