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Volumn 43, Issue 4, 2002, Pages 399-421

Additive Schwarz algorithms for solving hp-version finite element systems on triangular meshes

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; FUNCTIONS; MATRIX ALGEBRA; NUMERICAL ANALYSIS; POLYNOMIALS;

EID: 0036895124     PISSN: 01689274     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0168-9274(02)00104-6     Document Type: Article
Times cited : (7)

References (32)
  • 2
    • 0031371976 scopus 로고    scopus 로고
    • Aspects of an adaptive hp-finite element method: Adaptive strategy, conforming approximation and efficient solvers
    • Ainsworth M., Senior B. Aspects of an adaptive hp-finite element method: Adaptive strategy, conforming approximation and efficient solvers. Comput. Methods Appl. Mech. Engrg. 150:1997;65-87.
    • (1997) Comput. Methods Appl. Mech. Engrg. , vol.150 , pp. 65-87
    • Ainsworth, M.1    Senior, B.2
  • 3
    • 0026169599 scopus 로고
    • Efficient preconditioning for the p-version finite element method in two dimensions
    • Babuška I., Craig A., Mandel J., Pitkäranta J. Efficient preconditioning for the p-version finite element method in two dimensions. SIAM J. Numer. Anal. 28:1991;624-661.
    • (1991) SIAM J. Numer. Anal. , vol.28 , pp. 624-661
    • Babuška, I.1    Craig, A.2    Mandel, J.3    Pitkäranta, J.4
  • 4
    • 0000026672 scopus 로고
    • The h-p-version of the finite element method with quasiuniform meshes
    • Babuška I., Suri M. The h-p-version of the finite element method with quasiuniform meshes. Model. Math. Anal. Numer. 21:1987;199-238.
    • (1987) Model. Math. Anal. Numer. , vol.21 , pp. 199-238
    • Babuška, I.1    Suri, M.2
  • 6
    • 84966199070 scopus 로고
    • The construction of preconditioners for elliptic problems by substructuring, I
    • Bramble J., Pasciak J., Schatz A. The construction of preconditioners for elliptic problems by substructuring, I. Math. Comp. 47:1986;103-134.
    • (1986) Math. Comp. , vol.47 , pp. 103-134
    • Bramble, J.1    Pasciak, J.2    Schatz, A.3
  • 7
    • 84968495074 scopus 로고
    • The construction of preconditioners for elliptic problems by substructuring, IV
    • Bramble J., Pasciak J., Schatz A. The construction of preconditioners for elliptic problems by substructuring, IV. Math. Comp. 53:1989;1-24.
    • (1989) Math. Comp. , vol.53 , pp. 1-24
    • Bramble, J.1    Pasciak, J.2    Schatz, A.3
  • 8
    • 0027694342 scopus 로고
    • New basis functions and computational procedures for p-version finite element analysis
    • Carnevali P., Morris R.B., Tsuji Y., Taylor G. New basis functions and computational procedures for p-version finite element analysis. Internat. J. Numer. Meth. Engrg. 36:1993;3759-3779.
    • (1993) Internat. J. Numer. Meth. Engrg. , vol.36 , pp. 3759-3779
    • Carnevali, P.1    Morris, R.B.2    Tsuji, Y.3    Taylor, G.4
  • 9
    • 0000997330 scopus 로고    scopus 로고
    • Quasi-optimal Schwarz methods for the conforming spectral element discretization
    • Casarin M.A. Quasi-optimal Schwarz methods for the conforming spectral element discretization. SIAM J. Numer. Anal. 34:1997;2482-2502.
    • (1997) SIAM J. Numer. Anal. , vol.34 , pp. 2482-2502
    • Casarin, M.A.1
  • 10
    • 0000530612 scopus 로고
    • A finite element capacitance method for elliptic problems on regions partitioned into substructures
    • Dryja M. A finite element capacitance method for elliptic problems on regions partitioned into substructures. Numer. Math. 44:1984;153-168.
    • (1984) Numer. Math. , vol.44 , pp. 153-168
    • Dryja, M.1
  • 11
    • 0011847134 scopus 로고
    • Selection of the high order coordinate functions and preconditioning in the frame of the domain decomposition method
    • in Russian
    • Ivanov S.A., Korneev V.G. Selection of the high order coordinate functions and preconditioning in the frame of the domain decomposition method. Izv. Vyssh. Uchebn. Zaved. 395:1995;62-81. (in Russian).
    • (1995) Izv. Vyssh. Uchebn. Zaved. , vol.395 , pp. 62-81
    • Ivanov, S.A.1    Korneev, V.G.2
  • 12
    • 0011806173 scopus 로고
    • On the preconditioning in the domain decomposition technique for the p-version finite element method. Part I
    • Preprint SPC 95-35
    • S.A. Ivanov, V.G. Korneev, On the preconditioning in the domain decomposition technique for the p-version finite element method. Part I, Technische Universität Chemnitz-Zwickau, Preprint SPC 95-35, 1995, 1-15.
    • (1995) Technische Universität Chemnitz-Zwickau , pp. 1-15
    • Ivanov, S.A.1    Korneev, V.G.2
  • 13
    • 0011806173 scopus 로고
    • On the preconditioning in the domain decomposition technique for the p-version finite element method. Part II
    • Preprint SPC 95-36
    • S.A. Ivanov, V.G. Korneev, On the preconditioning in the domain decomposition technique for the p-version finite element method. Part II, Technische Universität Chemnitz-Zwickau. Preprint SPC 95-36, 1995, 1-14.
    • (1995) Technische Universität Chemnitz-Zwickau , pp. 1-14
    • Ivanov, S.A.1    Korneev, V.G.2
  • 14
    • 0011881089 scopus 로고
    • Preconditioning in the domain decomposition methods for the p-version with the hierarchical bases
    • Proc. of OFEA-95. St. Petersburg, June 25-29
    • Ivanov S.A., Korneev V.G. Preconditioning in the domain decomposition methods for the p-version with the hierarchical bases. Proc. of OFEA-95. St. Petersburg, June 25-29, 1995. Math. Modeling. 8:1996;63-73.
    • (1995) Math. Modeling , vol.8 , pp. 63-73
    • Ivanov, S.A.1    Korneev, V.G.2
  • 15
    • 0031352979 scopus 로고    scopus 로고
    • Inexact solvers on element surfaces for the p and h-p finite element method
    • Guo B., Cao W. Inexact solvers on element surfaces for the p and h-p finite element method. Comput. Methods Appl. Mech. Engrg. 150:1997;173-191.
    • (1997) Comput. Methods Appl. Mech. Engrg. , vol.150 , pp. 173-191
    • Guo, B.1    Cao, W.2
  • 16
    • 0011845570 scopus 로고
    • On the construction of variational-difference schemes of higher orders of accuracy
    • in Russian; Engl. transl.: Vestnik Leningrad Univ. Math. 3 (1976) 301-316
    • Korneev V.G. On the construction of variational-difference schemes of higher orders of accuracy. Vestnik Leningrad. Univ. 25:1970;28-40. (in Russian); Engl. transl.: Vestnik Leningrad Univ. Math. 3 (1976) 301-316.
    • (1970) Vestnik Leningrad. Univ. , vol.25 , pp. 28-40
    • Korneev, V.G.1
  • 18
    • 0031357301 scopus 로고
    • Preconditioning of the p-version of the finite element method
    • Korneev V.G., Jensen S. Preconditioning of the p-version of the finite element method. Comput. Methods Appl. Mech. Engrg. 150:1977;215-238.
    • (1977) Comput. Methods Appl. Mech. Engrg. , vol.150 , pp. 215-238
    • Korneev, V.G.1    Jensen, S.2
  • 19
    • 0033117093 scopus 로고    scopus 로고
    • Domain decomposition preconditioning in the hierarchical p-version of the finite element method
    • Korneev V.G., Jensen S. Domain decomposition preconditioning in the hierarchical p-version of the finite element method. Appl. Numer. Math. 29:1999;479-518.
    • (1999) Appl. Numer. Math. , vol.29 , pp. 479-518
    • Korneev, V.G.1    Jensen, S.2
  • 21
    • 0000587379 scopus 로고
    • Relévements de traces polynômiales et interpolations hilbertiennes entre espaces de polynômes
    • Maday Y. Relévements de traces polynômiales et interpolations hilbertiennes entre espaces de polynômes. C. R. Acad. Sci. Paris Sér. I Math. 309:1989;463-468.
    • (1989) C. R. Acad. Sci. Paris Sér. I Math. , vol.309 , pp. 463-468
    • Maday, Y.1
  • 22
    • 0030189140 scopus 로고
    • Iterative methods for p-version finite elements: Preconditioning thin solids
    • Mandel J. Iterative methods for p-version finite elements: preconditioning thin solids. Comput. Methods Appl. Mech. Engrg. 133:1977;247-257.
    • (1977) Comput. Methods Appl. Mech. Engrg. , vol.133 , pp. 247-257
    • Mandel, J.1
  • 23
    • 0002943819 scopus 로고    scopus 로고
    • Polynomial liftings on a tetrahedron and applications to the h-p version of the finite element method in three dimensions
    • Munos-Sola R. Polynomial liftings on a tetrahedron and applications to the h-p version of the finite element method in three dimensions. SIAM J. Numer. Anal. 34:1997;282-314.
    • (1997) SIAM J. Numer. Anal. , vol.34 , pp. 282-314
    • Munos-Sola, R.1
  • 24
    • 84861731976 scopus 로고
    • Method of splitting into subspaces for solving elliptic boundary value problems in complex-form domains
    • Nepomnyaschikh S.V. Method of splitting into subspaces for solving elliptic boundary value problems in complex-form domains. Russian J. Numer. Anal. Math. Modeling. 6:1991;151-168.
    • (1991) Russian J. Numer. Anal. Math. Modeling , vol.6 , pp. 151-168
    • Nepomnyaschikh, S.V.1
  • 25
    • 0001238122 scopus 로고    scopus 로고
    • Parallel domain decomposition solver for adaptive hp finite element methods
    • Oden J.T., Patra A., Feng Y.S. Parallel Domain decomposition solver for adaptive hp finite element methods. SIAM J. Numer. Anal. 34:1997;2090-2118.
    • (1997) SIAM J. Numer. Anal. , vol.34 , pp. 2090-2118
    • Oden, J.T.1    Patra, A.2    Feng, Y.S.3
  • 26
    • 21344476056 scopus 로고
    • Additive Schwartz methods for the p-version finite element method
    • Pavarino L.F. Additive Schwartz methods for the p-version finite element method. Numer. Math. 66:1994;493-515.
    • (1994) Numer. Math. , vol.66 , pp. 493-515
    • Pavarino, L.F.1
  • 27
    • 0024885663 scopus 로고
    • Toward a universal hp adaptive finite element strategy, Part 3. Design of hp meshes
    • Rackowicz W., Oden J.T., Demkowicz L. Toward a universal hp adaptive finite element strategy, Part 3. Design of hp meshes. Comput. Methods Appl. Mech. Engrg. 77:1989;181-212.
    • (1989) Comput. Methods Appl. Mech. Engrg. , vol.77 , pp. 181-212
    • Rackowicz, W.1    Oden, J.T.2    Demkowicz, L.3
  • 29
    • 0031554686 scopus 로고    scopus 로고
    • A straight-forward structure to construct shape functions for variable p-order meshes
    • Shephard M.S., Dey S., Flaherty J.E. A straight-forward structure to construct shape functions for variable p-order meshes. Comput. Methods Appl. Mech. Engrg. 147:1997;209-234.
    • (1997) Comput. Methods Appl. Mech. Engrg. , vol.147 , pp. 209-234
    • Shephard, M.S.1    Dey, S.2    Flaherty, J.E.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.