메뉴 건너뛰기




Volumn 17, Issue 1, 2010, Pages 73-96

Algebraic analysis of two-grid methods: The nonsymmetric case

Author keywords

Approximation property; Compatible relaxation; Convergence analysis; Convergence measure; Linear systems; Multigrid

Indexed keywords


EID: 72449145877     PISSN: 10705325     EISSN: None     Source Type: Journal    
DOI: 10.1002/nla.649     Document Type: Article
Times cited : (36)

References (34)
  • 4
    • 0001822668 scopus 로고
    • Multigrid methods: Fundamental algorithms, model problem analysis and applications
    • Hackbusch W, Trottenberg U (eds). Lectures Notes in Mathematics, Springer: Berlin, Heidelberg, New York
    • Stüben K, Trottenberg KU. Multigrid methods: fundamental algorithms, model problem analysis and applications. in Multigrid Methods, Hackbusch W, Trottenberg U (eds). Lectures Notes in Mathematics, vol. 960. Springer: Berlin, Heidelberg, New York, 1982; 1-176.
    • (1982) Multigrid Methods , vol.960 , pp. 1-176
    • Stüben, K.1    Trottenberg, K.U.2
  • 5
    • 21844485073 scopus 로고
    • Fourier analysis of a robust multigrid method for convection-diffusion equations
    • Reusken A. Fourier analysis of a robust multigrid method for convection-diffusion equations. Numerische Mathematik 1995; 71:365-398.
    • (1995) Numerische Mathematik , vol.71 , pp. 365-398
    • Reusken, A.1
  • 6
    • 0034397438 scopus 로고    scopus 로고
    • A robust algebraic multilevel preconditioner for non symmetric M-matrices
    • Notay Y. A robust algebraic multilevel preconditioner for non symmetric M-matrices. Numerical Linear Algebra with Applications 2000; 7:243-267.
    • (2000) Numerical Linear Algebra With Applications , vol.7 , pp. 243-267
    • Notay, Y.1
  • 7
    • 0001927250 scopus 로고
    • Algebraic multigrid theory: The symmetric case
    • Brandt A. Algebraic multigrid theory: the symmetric case. Applied Mathematics and Computation 1986; 19:23-56.
    • (1986) Applied Mathematics and Computation , vol.19 , pp. 23-56
    • Brandt, A.1
  • 11
    • 0001885411 scopus 로고
    • Algebraic multigrid (AMG)
    • McCormick SF (ed.). Frontiers in Applied Mathematics, SIAM: Philadelphia, PA
    • Ruge JW, Stüben K. Algebraic multigrid (AMG). in Multigrid Methods, McCormick SF (ed.). Frontiers in Applied Mathematics, vol. 3. SIAM: Philadelphia, PA, 1987; 73-130.
    • (1987) Multigrid Methods , vol.3 , pp. 73-130
    • Ruge, J.W.1    Stüben, K.2
  • 12
    • 0003338384 scopus 로고    scopus 로고
    • An introduction to algebraic multigrid
    • Trottenberg U, Oosterlee CW, Schüller A (eds). Academic Press: San Diego, London, Appendix A
    • Stüben K. An introduction to algebraic multigrid. in Multigrid, Trottenberg U, Oosterlee CW, Schüller A (eds). Academic Press: San Diego, London, 2001; 413-532. Appendix A.
    • (2001) Multigrid , pp. 413-532
    • Stüben, K.1
  • 14
    • 0036226531 scopus 로고    scopus 로고
    • Element-free AMGe: General algorithms for computing interpolation weights in AMG
    • Henson VE, Vassilevski PS. Element-free AMGe: general algorithms for computing interpolation weights in AMG. SIAM Journal on Scientific Computing 2002; 23:629-650.
    • (2002) SIAM Journal on Scientific Computing , vol.23 , pp. 629-650
    • Henson, V.E.1    Vassilevski, P.S.2
  • 15
    • 0030388574 scopus 로고    scopus 로고
    • Algebraic multigrid based on smoothed aggregation for second and fourth order elliptic problems
    • Vaněk P, Mandel J, Brezina M. Algebraic multigrid based on smoothed aggregation for second and fourth order elliptic problems. Computing 1996; 56:179-196.
    • (1996) Computing , vol.56 , pp. 179-196
    • Vaněk, P.1    Mandel, J.2    Brezina, M.3
  • 19
    • 51549098350 scopus 로고    scopus 로고
    • On algebraic multilevel methods for non-symmetric systems-comparison results
    • Mense C, Nabben R. On algebraic multilevel methods for non-symmetric systems-comparison results. Linear Algebra and its Applications 2008; 429:2567-2588.
    • (2008) Linear Algebra and Its Applications , vol.429 , pp. 2567-2588
    • Mense, C.1    Nabben, R.2
  • 20
    • 58449096398 scopus 로고    scopus 로고
    • On algebraic multilevel methods for non-symmetric systems-convergence results
    • Mense C, Nabben R. On algebraic multilevel methods for non-symmetric systems-convergence results. Electronic Transactions on Numerical Analysis 2008; 20:323-345.
    • (2008) Electronic Transactions on Numerical Analysis , vol.20 , pp. 323-345
    • Mense, C.1    Nabben, R.2
  • 21
    • 22144438010 scopus 로고    scopus 로고
    • Algebraic multigrid and algebraic multilevel methods: A theoretical comparison
    • Notay Y. Algebraic multigrid and algebraic multilevel methods: a theoretical comparison. Numerical Linear Algebra with Applications 2005; 12:419-451.
    • (2005) Numerical Linear Algebra With Applications , vol.12 , pp. 419-451
    • Notay, Y.1
  • 24
    • 0000555209 scopus 로고
    • Black box multigrid for nonsymmetric problems
    • Dendy JE. Black box multigrid for nonsymmetric problems. Applied Mathematics and Computation 1983; 13:261-283.
    • (1983) Applied Mathematics and Computation , vol.13 , pp. 261-283
    • Dendy, J.E.1
  • 26
    • 72449122329 scopus 로고    scopus 로고
    • Towards adaptive smoothed aggregation (αSA) for nonsymmetric problems
    • University of Colorado at Boulder
    • Brezina M, Manteuffel T, McCormick S, Ruge J, Sanders G. Towards adaptive smoothed aggregation (αSA) for nonsymmetric problems. Technical Report, University of Colorado at Boulder, 2008.
    • (2008) Technical Report
    • Brezina, M.1    Manteuffel, T.2    McCormick, S.3    Ruge, J.4    Sanders, G.5
  • 27
    • 34249296232 scopus 로고    scopus 로고
    • AMG strategies for PDE systems with applications in industrial semiconductor simulation
    • University of Cologne, Germany
    • Clees T. AMG strategies for PDE systems with applications in industrial semiconductor simulation. Ph.D. Dissertation, University of Cologne, Germany, 2004.
    • (2004) Ph.d. Dissertation
    • Clees, T.1
  • 28
    • 72449124673 scopus 로고    scopus 로고
    • An aggregation-based algebraic multigrid method
    • Université Libre de Bruxelles, Brussels, Belgium, Available from
    • Notay Y. An aggregation-based algebraic multigrid method. Technical Report GANMN 08-02, Université Libre de Bruxelles, Brussels, Belgium, 2008. Available from: http://homepages.ulb.ac.be/~ynotay.
    • (2008) Technical Report Ganmn 08-02
    • Notay, Y.1
  • 29
    • 51449106109 scopus 로고    scopus 로고
    • Two-sided bounds on the convergence rate of two-level methods
    • Zikatanov LT. Two-sided bounds on the convergence rate of two-level methods. Numerical Linear Algebra with Applications 2007; 15:439-454.
    • (2007) Numerical Linear Algebra With Applications , vol.15 , pp. 439-454
    • Zikatanov, L.T.1
  • 30
    • 84878786891 scopus 로고    scopus 로고
    • Algebraic multigrid methods based on compatible relaxation and energy minimization
    • Widlund OB, Keyes DE (eds). Lecture Notes in Computational Science and Engineering, Springer: Berlin, Heidelberg
    • Brannick J, Zikatanov L. Algebraic multigrid methods based on compatible relaxation and energy minimization. in Domain Decomposition Methods in Science and Engineering XVI, Widlund OB, Keyes DE (eds). Lecture Notes in Computational Science and Engineering, vol. 55. Springer: Berlin, Heidelberg, 2007; 15-26.
    • (2007) Domain Decomposition Methods in Science and Engineering Xvi , vol.55 , pp. 15-26
    • Brannick, J.1    Zikatanov, L.2
  • 32
    • 4043101775 scopus 로고    scopus 로고
    • A survey of algebraic multilevel iterations (AMLI) methods
    • Axelsson O. A survey of algebraic multilevel iterations (AMLI) methods. BIT 2003; 43:863-879.
    • (2003) BIT , vol.43 , pp. 863-879
    • Axelsson, O.1
  • 33
    • 0026219648 scopus 로고
    • The role of the strengthened c.b.s. inequality in multilevel methods
    • Eijkhout V, Vassilevski PS. The role of the strengthened c.b.s. inequality in multilevel methods. SIAM Review 1991; 33:405-419.
    • (1991) SIAM Review , vol.33 , pp. 405-419
    • Eijkhout, V.1    Vassilevski, P.S.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.