The construction of preconditioners for elliptic problems by substructuring. I
Mathematics of Computation
Efficient preconditioning for the p-version finite element method in two dimensions
SIAM Journal on Numerical Analysis
Schwarz methods with local refinement for the p-version finite element method
Numerische Mathematik
SIAM Journal on Numerical Analysis
Parallel Domain Decomposition Solver for Adaptive hp Finite Element Methods
SIAM Journal on Numerical Analysis
Quasi-Optimal Schwarz Methods for the Conforming Spectral Element Discretization
SIAM Journal on Numerical Analysis
Domain decomposition preconditioning in the hierarchical p-version of the finite element method
Applied Numerical Mathematics
A generic and self-optimizing polynomial library
Proceedings of the 8th workshop on Parallel/High-Performance Object-Oriented Scientific Computing
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Highly parallelizable domain decomposition Dirichlet-Dirichlet solvers for hp-version finite element methods on angular quasiuniform triangular meshes are studied under different assumptions on a reference element. The edge coordinate functions of a reference element are allowed to be either nodal with special choices of nodes, or hierarchical polynomials of several types. These coordinate functions are defined within elements as being arbitrary or discrete quasi-harmonic coordinate functions. The latter are obtained from explicit and inexpensive prolongation operators. In all situations, we are able to suggest preconditioners which are spectrally equivalent to the global stiffness matrix, which only require element-by-element and edge-by-edge operations, and which reduce computational cost. In this way, elimination is avoided when dealing with the interface problem. The domain decomposition algorithms essentially use prolongation operators from the interface boundary inside the subdomains of the decomposition according to the approach initially used for the hp-version finite element methods with quadrilateral elements [S.A. Ivanov, V.G. Korneev, Izv. Vyssh. Uchebn. Zaved. 395 (1995) 62-81; Technische Universität Chemnitz-Zwickau, Preprint SPC 95-35, 1995, 1-15, and Preprint SPC 95-36, 1995, 1-14; Math. Modeling 8 (1996) 63-73].