Korneev, V.; Flaherty, J. E.; Oden, T.; Fish, J. \(hp\)-version additive Schwarz algorithms on triangular meshes. (English) Zbl 1038.65134 Mat. Model. 14, No. 2, 61-94 (2002). 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. Edge coordinate functions are allowed to be either nodal, with special choices of nodes, or hierarchical polynomials of several types.Two kinds of interior coordinate functions are studied: arbitrary and so-called discrete quasi-harmonic functions. In all situations, preconditioners are suggested which are (almost) spectrally equivalent to the global stiffness matrix, which require only element-by-element and edge-by edge operations, thus providing a high level of parallelization. They also considerably reduce the computational cost. Reviewer: I. N. Katz (St. Louis) Cited in 2 Documents MSC: 65N55 Multigrid methods; domain decomposition for boundary value problems involving PDEs 35J25 Boundary value problems for second-order elliptic equations 65F10 Iterative numerical methods for linear systems 65F35 Numerical computation of matrix norms, conditioning, scaling 65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs 65N50 Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs 65Y05 Parallel numerical computation Keywords:finite elements; \(hp\)-version; Domain decomposition; discrete quasi-harmonic functions; preconditioners; quasiuniform triangular meshes; additive Schwarz algorithms; parallel computation PDFBibTeX XMLCite \textit{V. Korneev} et al., Mat. Model. 14, No. 2, 61--94 (2002; Zbl 1038.65134) Full Text: MNR