Free Access
Issue |
ESAIM: M2AN
Volume 40, Number 1, January-February 2006
|
|
---|---|---|
Page(s) | 99 - 122 | |
DOI | https://doi.org/10.1051/m2an:2006004 | |
Published online | 23 February 2006 |
- Y. Achdou, P. Le Tallec, F. Nataf and M. Vidrascu, A domain decomposition preconditioner for an advection-diffusion problem. Comput. Methods Appl Mech. Engrg. 184 (2000) 145–170. [Google Scholar]
- M. Ainsworth, A preconditioner based on domain decomposition for hp–FE approximation on quasi–uniform meshes. SIAM J. Numer. Anal. 33 (1996) 1358–1376. [CrossRef] [MathSciNet] [Google Scholar]
- B. Andersson, U. Falk, I. Babuška and T. von Petersdorff, Reliable stress and fracture mechanics analysis of complex aircraft components using a hp–version FEM. Int. J. Numer. Meth. Eng. 38 (1995) 2135–2163. [CrossRef] [Google Scholar]
- O. Axelsson, Iterative Solution Methods. Cambridge University Press (1994). [Google Scholar]
- I. Babuška and B. Guo, Approximation properties of the hp–version of the finite element method. Comput. Methods Appl. Mech. Engrg. 133 (1996) 319–346. [CrossRef] [MathSciNet] [Google Scholar]
- R. Barrett, M. Berry, T.F. Chan, J. Demmel, J. Donato, J. Dongarra, V. Eijkhout, R. Pozo, C. Romine and H. Van der Vorst, Templates for the Solution of Linear Systems: Building Blocks for Iterative Methods, 2nd edition. SIAM, Philadelphia, PA (1994). [Google Scholar]
- M. Benzi, Preconditioning techniques for large linear systems: a survey. J. Comput. Phys. 182 (2002) 418–477. [CrossRef] [MathSciNet] [Google Scholar]
- M. Benzi and M. Tuma, A parallel solver for large-scale Markov chains. Appl. Numer. Math. 41 (2002) 135–153. [CrossRef] [MathSciNet] [Google Scholar]
- C. Bernardi and Y. Maday, Spectral methods. In Handbook of Numerical Analysis, North-Holland, Amsterdam Vol. V, Part 2 (1997) 209–485. [Google Scholar]
- S. Beuchler, Multigrid solver for the inner problem in domain decomposition methods for p-fem. SIAM J. Numer. Anal. 40 (2002) 928–944. [CrossRef] [MathSciNet] [Google Scholar]
- A. Björck, Numerical methods for least-squares problems. SIAM (1996). [Google Scholar]
- R. Bridson and W.-P. Tang, Refining an approximate inverse. J. Comput. Appl. Math. 123 (2000) 293–306. [CrossRef] [MathSciNet] [Google Scholar]
- P. Brown and H. Walker, GMRES on (nearly) singular systems. SIAM J. Matrix Anal. Appl. 18 (1997) 37–51. [CrossRef] [MathSciNet] [Google Scholar]
- W. Cecot, W. Rachowicz and L. Demkowicz, An hp-adaptive finite element method for electromagnetics. III. a three-dimensional infinite element for Maxwell's equations. Internat. J. Numer. Methods Engrg. 57 (2003) 899–921. [CrossRef] [MathSciNet] [Google Scholar]
- E. Chow, A priori sparsity patterns for parallel sparse approximate inverse preconditioners. SIAM J. Sci. Comput. 21 (2000) 1804–1822. [CrossRef] [MathSciNet] [Google Scholar]
- M. Dryja and O.B. Widlund, Schwarz methods of Neumann-Neumann type for three-dimensional elliptic finite element problems. Comm. Pure Appl. Math. 48 (1995) 121–155. [CrossRef] [MathSciNet] [Google Scholar]
- M. Dryja, M.V. Sarkis and O.B. Widlund, Multilevel Schwarz methods for elliptic problems with discontinuous coefficients in three dimensions. Numer. Math. 72 (1996) 313–348. [CrossRef] [MathSciNet] [Google Scholar]
- C. Farhat and F.-X. Roux, Implicit parallel processing in structural mechanics, in Computational Mechanics Advances, J. Tinsley Oden Ed. North-Holland 2 (1994) 1–124. [Google Scholar]
- C. Farhat and F.-X. Roux, A method of finite element tearing and interconnecting and its parallel solution algorithm. Int. J. Numer. Meth. Engng. 32 (1991) 1205–1227. [Google Scholar]
- D.R. Fokkema, G.L.G. Sleijpen and H.A. Van der Vorst, Jacobi-Davidson style QR and QZ algorithms for the reduction of matrix pencils. SIAM J. Sci. Comput. 20 (1998) 94–125. [CrossRef] [MathSciNet] [Google Scholar]
- P. Frauenfelder and C. Lage, An object oriented software package for partial differential equations. ESAIM: M2AN 36 (2002) 937–951. [CrossRef] [EDP Sciences] [MathSciNet] [Google Scholar]
- R. Geus, The Jacobi-Davidson algorithm for solving large sparse symmetric eigenvalue problems with application to the design of accelerator cavities. Ph.D. thesis, ETH, Zürich, Institut für Wissenschaftliches Rechnen (2002). [Google Scholar]
- G. Golub and C. Van Loan, Matrix Computations. The John Hopkins University Press (1996). Third edition. [Google Scholar]
- G. Golub and Q. Ye, Inexact preconditioned conjugate gradient method with inner-outer iterations. SIAM J. Sci. Comput. 21 (1999) 1305–1320. [CrossRef] [MathSciNet] [Google Scholar]
- M. Grote and T. Huckle, Parallel preconditioning with sparse approximate inverses. SIAM J. Sci. Comput. 18 (1997) 838–853. [Google Scholar]
- W.Z. Gui and I. Babuška, The h-, p- and hp-version of the Finite Element Method in one dimension, I: The error analysis of the p-version, II: The error analysis of the h- and hp-version, III: The adaptive hp-version. Numer. Math. 49 (1986) 577–683. [Google Scholar]
- B. Guo and W. Cao, Additive Schwarz methods for the hp version of the finite element method in two dimensions. SIAM J. Scientific Comput. 18 (1997) 1267–1288. [CrossRef] [Google Scholar]
- R. Henderson, Dynamic refinement algorithms for spectral element methods. Comput. Methods Appl. Mech. Engrg. 175 (1999) 395–411. [Google Scholar]
- I.C.F. Ipsen and C.D. Meyer, The idea behind Krylov methods. Amer. Math. Monthly 105 (1998) 889–899. [Google Scholar]
- G.E. Karniadakis and S. Sherwin, Spectral/hp Element Methods for CFD. Oxford University Press (1999). [Google Scholar]
- V. Korneev, J.E. Flaherty, J.T. Oden and J. Fish, Additive Schwarz algorithms for solving hp-version finite element systems on triangular meshes. Appl. Numer. Math 43 (2002) 399–421. [CrossRef] [MathSciNet] [Google Scholar]
- V. Korneev, U. Langer and L.S. Xanthis, On fast domain decomposition solving procedures for hp-discretizations of 3d elliptic problems. Comput. Methods Appl. Math. 3 (2003) 536–559. [MathSciNet] [Google Scholar]
- P. Le Tallec and A. Patra, Non–overlapping domain decomposition methods for adaptive hp approximations of the Stokes problem with discontinuous pressure fields. Comput. Methods Appl. Mech. Engrg. 145 (1997) 361–379. [CrossRef] [MathSciNet] [Google Scholar]
- J.W. Lottes and P.F. Fischer, Hybrid Multigrid/Schwarz algorithms for the spectral element method. Technical report, Mathematics and Computer Science Division, Argonne National Laboratory (January 2003). [Google Scholar]
- J. Mandel and M. Brezina, Balancing domain decomposition for problems with large jumps in coefficients. Math. Comp. 65 (1996) 1387–1401. [CrossRef] [MathSciNet] [Google Scholar]
- J.M. Melenk and C. Schwab, hp–FEM for reaction–diffusion equations. I: Robust exponential convergence. SIAM J. Numer. Anal. 35 (1998) 1520–1557. [CrossRef] [MathSciNet] [Google Scholar]
- M. Melenk, hp-finite element methods for singular perturbations. Springer Verlag. Lect. Notes Math. 1796 (2002). [Google Scholar]
- P. Monk, Finite element methods for Maxwell's equations. Numerical Mathematics and Scientific Computation, The Clarendon Press Oxford University Press, New York, 2003. [Google Scholar]
- R. Nicolaides, Deflation of conjugate gradients with application to boundary value problems. SIAM J. Numer. Anal. 24 (1987) 355–36. [NASA ADS] [CrossRef] [MathSciNet] [Google Scholar]
- J.T. Oden, A. Patra and Y. Feng, Parallel domain decomposition solver for adaptive hp finite element methods. SIAM J. Numer. Anal. 34 (1997) 2090–2118. [CrossRef] [MathSciNet] [Google Scholar]
- L.F. Pavarino, Neumann-Neumann algorithms for spectral elements in three dimensions. RAIRO: Modél. Math. Anal. Numér. 31 (1997) 471–493. [MathSciNet] [Google Scholar]
- L.F. Pavarino and O.B. Widlund, Balancing Neumann-Neumann algorithms for incompressible Navier-Stokes equations. Commun. Pure Appl. Math. 55 (2002) 302–335. [CrossRef] [Google Scholar]
- A. Quarteroni and A. Valli, Numerical Approximation of Partial Differential Equations. Springer-Verlag, Berlin (1994). [Google Scholar]
- J. Ruge and K. Stüben, Algebraic multigrid, in Multigrid Methods, S. Mc Cormick Ed. SIAM Philadelphia (1987) 73–130. [Google Scholar]
- Y. Saad, A flexible inner-outer preconditioned GMRES algorithm. SIAM J. Sci. Comput. 14 (1993) 461–469. [CrossRef] [MathSciNet] [Google Scholar]
- Y. Saad and M. Schultz, GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear system. SIAM J. Sci. Statist. Comput. 7 (1986) 856–869. [Google Scholar]
- Y. Saad and B. Suchomel, Arms: an algebraic recursive multilevel solver for general sparse linear systems. Numer. Linear Algebra Appl. 9 (2002) 359–378. [CrossRef] [MathSciNet] [Google Scholar]
- M.V. Sarkis, Schwarz Preconditioners for Elliptic Problems with Discontinuous Coefficients Using Conforming and Non-Conforming Elements. Ph.D. thesis, Courant Institute, New York University, September (1994). TR671, Department of Computer Science, New York University, URL: file://cs.nyu.edu/pub/tech-reports/tr671.ps.Z. [Google Scholar]
- D. Schötzau and C. Schwab, Time discretization of parabolic problems by the hp-version of the discontinuous Galerkin finite element method. SIAM J. Numer. Anal. 38 (2000) 837–875. [CrossRef] [MathSciNet] [Google Scholar]
- C. Schwab, p– and hp– Finite Element Methods. Oxford Science Publications (1998). [Google Scholar]
- C. Schwab and M. Suri, The p and hp version of the finite element method for problems with boundary layers. Math. Comp. 65 (1996) 1403–1429. [CrossRef] [MathSciNet] [Google Scholar]
- C. Schwab, M. Suri and C.A. Xenophontos, The hp–FEM for problems in mechanics with boundary layers. Comput. Methods Appl. Mech. Engrg. 157 (1998) 311–333. [CrossRef] [MathSciNet] [Google Scholar]
- B.F. Smith, P.E. Bjørstad and W.D. Gropp, Domain Decomposition: Parallel Multilevel Methods for Elliptic Partial Differential Equations. Cambridge University Press (1996). [Google Scholar]
- P. Solin, K. Segeth and I. Dolezel, Higher-order finite element methods. Studies in Advanced Mathematics, Chapman and Hall, 2004. [Google Scholar]
- A. Toselli, FETI domain decomposition methods for scalar advection-diffusion problems. Comput. Methods Appl. Mech. Engrg. 190 (2001) 5759–5776. [Google Scholar]
- A. Toselli and X. Vasseur, Domain decomposition methods of Neumann-Neumann type for hp-approximations on geometrically refined boundary layer meshes in two dimensions. Technical Report 02–15, Seminar für Angewandte Mathematik, ETH, Zürich (September 2002). Submitted to Numerische Mathematik. [Google Scholar]
- A. Toselli and X. Vasseur, A numerical study on Neumann-Neumann and FETI methods for hp-approximations on geometrically refined boundary layer meshes in two dimensions. Comput. Methods Appl. Mech. Engrg. 192 (2003) 4551–4579. [Google Scholar]
- A. Toselli and X. Vasseur, Domain decomposition methods of Neumann-Neumann type for hp-approximations on boundary layer meshes in three dimensions. IMA J. Numer. Anal. 24 (2004) 123–156. [CrossRef] [MathSciNet] [Google Scholar]
- A. Toselli and O. Widlund, Domain Decomposition methods – Algorithms and Theory. Springer Series on Computational Mathematics, Springer 34 (2004). [Google Scholar]
- U. Trottenberg, C. Oosterlee and A. Schüller, Multigrid. Academic Press, London (2000). Guest contribution by Klaus Stüben: “An Introduction to Algebraic Multigrid”. [Google Scholar]
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.