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Volumn 15, Issue 2, 1999, Pages 167-199

A Note on the Complexity of Solving Poisson's Equation for Spaces of Bounded Mixed Derivatives

Author keywords

Poisson equation; complexity; sparse grids; finite element method; multilevel methods

Indexed keywords


EID: 0001335132     PISSN: 0885064X     EISSN: None     Source Type: Journal    
DOI: 10.1006/jcom.1999.0499     Document Type: Article
Times cited : (59)

References (46)
  • 1
    • 0000358863 scopus 로고
    • Approximation by trigonometric polynomials in a certain class of periodic functions of several variables
    • Babenko K. I. Approximation by trigonometric polynomials in a certain class of periodic functions of several variables. Dokl. Akad. Nauk SSSR. 132:1960;982-985.
    • (1960) Dokl. Akad. Nauk SSSR , vol.132 , pp. 982-985
    • Babenko, K.I.1
  • 3
    • 84966234195 scopus 로고
    • Parallel multilevel preconditioners
    • Bramble J., Pasciak J. P., Xu J. Parallel multilevel preconditioners. Math. Comp. 55:1990;1-22.
    • (1990) Math. Comp. , vol.55 , pp. 1-22
    • Bramble, J.1    Pasciak, J.P.2    Xu, J.3
  • 4
    • 0000000860 scopus 로고
    • Guide to multigrid development
    • W. Hackbusch, & U. Trottenberg. Berlin/Heidelberg: Springer-Verlag
    • Brandt A. Guide to multigrid development. Hackbusch W., Trottenberg U. Multigrid Methods. Lecture Notes in Mathematics. 960:1982;Springer-Verlag, Berlin/Heidelberg.
    • (1982) Multigrid Methods. Lecture Notes in Mathematics , vol.960
    • Brandt, A.1
  • 6
    • 0002655385 scopus 로고
    • An adaptive Poisson solver using hierarchical bases and sparse grids
    • P. de Groen, & R. Beauwens. Amsterdam: Elsevier
    • Bungartz H.-J. An adaptive Poisson solver using hierarchical bases and sparse grids. de Groen P., Beauwens R. Iterative Methods in Linear Algebra. 1992;293-310 Elsevier, Amsterdam.
    • (1992) Iterative Methods in Linear Algebra , pp. 293-310
    • Bungartz, H.-J.1
  • 8
    • 0006804542 scopus 로고    scopus 로고
    • Sparse grids: Recent developments for elliptic partial differential equations
    • W. Hackbusch, & G. Wittum. Berlin/Heidelberg: Springer-Verlag
    • Bungartz H.-J., Dornseifer T. Sparse grids: recent developments for elliptic partial differential equations. Hackbusch W., Wittum G. Multigrid Methods V. Lecture Notes in Computational Science and Engineering. 3:1998;45-70 Springer-Verlag, Berlin/Heidelberg.
    • (1998) Multigrid Methods V. Lecture Notes in Computational Science and Engineering , vol.3 , pp. 45-70
    • Bungartz, H.-J.1    Dornseifer, T.2
  • 10
    • 33845592412 scopus 로고
    • Multilevel preconditioning
    • Dahmen W., Kunoth A. Multilevel preconditioning. Numer. Math. 63:1992;315-344.
    • (1992) Numer. Math. , vol.63 , pp. 315-344
    • Dahmen, W.1    Kunoth, A.2
  • 11
    • 0003017186 scopus 로고
    • D-Variate Boolean interpolation
    • Delvos F.-J. d-Variate Boolean interpolation. J. Approx. Theory. 34:1982;99-114.
    • (1982) J. Approx. Theory , vol.34 , pp. 99-114
    • Delvos, F.-J.1
  • 12
    • 0042282395 scopus 로고    scopus 로고
    • Revenge of the semicoarsening frequency decomposition multigrid method
    • D. Melson, T. A. Manteuffel, S. F. McCormick, & C. C. Douglas. Hampton: NASA CP 3339
    • Dendy J. Revenge of the semicoarsening frequency decomposition multigrid method. Melson D., Manteuffel T. A., McCormick S. F., Douglas C. C. Proc. 7th Copper Mountain Conference on Multigrid Methods. 1996;227-239 NASA CP 3339, Hampton.
    • (1996) Proc. 7th Copper Mountain Conference on Multigrid Methods , pp. 227-239
    • Dendy, J.1
  • 13
    • 0040354534 scopus 로고
    • Grandchild of the frequency decomposition multigrid method
    • Dendy J. Grandchild of the frequency decomposition multigrid method. SIAM J. Sci. Comput. 16:1995;307-319.
    • (1995) SIAM J. Sci. Comput. , vol.16 , pp. 307-319
    • Dendy, J.1
  • 14
    • 0006847156 scopus 로고
    • Über stetige Funktionen
    • Faber G. Über stetige Funktionen. Math. Ann. 66:1909;81-94.
    • (1909) Math. Ann. , vol.66 , pp. 81-94
    • Faber, G.1
  • 15
    • 0003002240 scopus 로고
    • Distributive lattices and the approximation of multivariate functions
    • I. J. Schoenberg. New York: Academic Press
    • Gordon W. J. Distributive lattices and the approximation of multivariate functions. Schoenberg I. J. Approximation with Special Emphasis on Spline Functions. 1969;223-277 Academic Press, New York.
    • (1969) Approximation with Special Emphasis on Spline Functions , pp. 223-277
    • Gordon, W.J.1
  • 17
    • 0007958804 scopus 로고
    • Multilevelmethoden als Iterationsverfahren über Erzeugendensystemen
    • Stuttgart: Teubner
    • Griebel M. Multilevelmethoden als Iterationsverfahren über Erzeugendensystemen. Teuber Skripten zur Numerik. 1994;Teubner, Stuttgart.
    • (1994) Teuber Skripten Zur Numerik
    • Griebel, M.1
  • 20
    • 0242503926 scopus 로고
    • On additive Schwarz preconditioners for sparse grid discretizations
    • Griebel M., Oswald P. On additive Schwarz preconditioners for sparse grid discretizations. Numer. Math. 66:1994;449-493.
    • (1994) Numer. Math. , vol.66 , pp. 449-493
    • Griebel, M.1    Oswald, P.2
  • 21
    • 0000277689 scopus 로고
    • Tensor product type subspace splittings and multilevel iterative methods for anisotropic problems
    • Griebel M., Oswald P. Tensor product type subspace splittings and multilevel iterative methods for anisotropic problems. Adv. Comput. Math. 4:1995;171-206.
    • (1995) Adv. Comput. Math. , vol.4 , pp. 171-206
    • Griebel, M.1    Oswald, P.2
  • 22
    • 0002524756 scopus 로고
    • A combination technique for the solution of sparse grid problems
    • P. de Groen, & R. Beauwens. Amsterdam: Elsevier
    • Griebel M., Schneider M., Zenger C. A combination technique for the solution of sparse grid problems. de Groen P., Beauwens R. Iterative Methods in Linear Algebra. 1992;263-281 Elsevier, Amsterdam.
    • (1992) Iterative Methods in Linear Algebra , pp. 263-281
    • Griebel, M.1    Schneider, M.2    Zenger, C.3
  • 23
    • 0001054098 scopus 로고
    • Multilevel Gauß-Seidel-algorithms for full and sparse grid problems
    • Griebel M., Zenger C., Zimmer S. Multilevel Gauß-Seidel-algorithms for full and sparse grid problems. Computing. 50:1995;127-148.
    • (1995) Computing , vol.50 , pp. 127-148
    • Griebel, M.1    Zenger, C.2    Zimmer, S.3
  • 24
    • 0003400692 scopus 로고
    • Theorie und Numerik elliptischer Differentialgleichungen
    • Stuttgart: Teubner
    • Hackbusch W. Theorie und Numerik elliptischer Differentialgleichungen. Teubner Studienbücher Mathematik. 1986;Teubner, Stuttgart.
    • (1986) Teubner Studienbücher Mathematik
    • Hackbusch, W.1
  • 26
    • 34249963996 scopus 로고
    • The frequency decomposition multi-grid method. I. Application to anisotropic problems
    • Hackbusch W. The frequency decomposition multi-grid method. I. Application to anisotropic problems. Numer. Math. 56:1989;229-245.
    • (1989) Numer. Math. , vol.56 , pp. 229-245
    • Hackbusch, W.1
  • 27
    • 21144473803 scopus 로고
    • The frequency decomposition multi-grid method. II. Analysis based on the additive Schwarz method
    • Hackbusch W. The frequency decomposition multi-grid method. II. Analysis based on the additive Schwarz method. Numer. Math. 63:1992;433-453.
    • (1992) Numer. Math. , vol.63 , pp. 433-453
    • Hackbusch, W.1
  • 28
    • 85067973190 scopus 로고
    • Iterative Solution of Large Sparse Systems of Equations
    • New York: Springer-Verlag
    • Hackbusch W. Iterative Solution of Large Sparse Systems of Equations. Applied Mathematical Sciences. 95:1993;Springer-Verlag, New York.
    • (1993) Applied Mathematical Sciences , vol.95
    • Hackbusch, W.1
  • 29
    • 0039391863 scopus 로고
    • Sparse-grid finite-volume multigrid for 3D-problems
    • Hemker P. W. Sparse-grid finite-volume multigrid for 3D-problems. Adv. Comput. Math. 4:1995;83-110.
    • (1995) Adv. Comput. Math. , vol.4 , pp. 83-110
    • Hemker, P.W.1
  • 30
    • 0012178599 scopus 로고
    • On the h- And p-versions of the extrapolated Gordon's projector with applications to elliptic equations
    • Hennart J. P., Mund E. H. On the h- and p-versions of the extrapolated Gordon's projector with applications to elliptic equations. SIAM J. Sci. Stat. Comput. 9:1988;773-791.
    • (1988) SIAM J. Sci. Stat. Comput. , vol.9 , pp. 773-791
    • Hennart, J.P.1    Mund, E.H.2
  • 31
    • 3643135186 scopus 로고
    • On the design of nested iterations for elliptic difference equations
    • Kronsjö L., Dahlquist G. On the design of nested iterations for elliptic difference equations. BIT. 11:1971;63-71.
    • (1971) BIT , vol.11 , pp. 63-71
    • Kronsjö, L.1    Dahlquist, G.2
  • 33
    • 0001233373 scopus 로고
    • A new multigrid approach to convection problems
    • Mulder W. A. A new multigrid approach to convection problems. J. Comput. Phys. 83:1989;303-323.
    • (1989) J. Comput. Phys. , vol.83 , pp. 303-323
    • Mulder, W.A.1
  • 35
    • 0004139365 scopus 로고
    • Multilevel Finite Element Approximation: Theory and Applications
    • Stuttgart: Teubner
    • Oswald P. Multilevel Finite Element Approximation: Theory and Applications. Teubner Skripten zur Numerik. 1994;Teubner, Stuttgart.
    • (1994) Teubner Skripten Zur Numerik
    • Oswald, P.1
  • 37
    • 0001048298 scopus 로고
    • Quadrature and interpolation formulas for tensor products of certain classes of functions
    • Smolyak S. A. Quadrature and interpolation formulas for tensor products of certain classes of functions. Dokl. Akad. Nauk SSSR. 148:1963;1042-1045.
    • (1963) Dokl. Akad. Nauk SSSR , vol.148 , pp. 1042-1045
    • Smolyak, S.A.1
  • 40
    • 38249007011 scopus 로고
    • On approximate recovery of functions with bounded mixed derivative
    • Temlyakov V. N. On approximate recovery of functions with bounded mixed derivative. J. Complexity. 9:1993;41-59.
    • (1993) J. Complexity , vol.9 , pp. 41-59
    • Temlyakov, V.N.1
  • 42
    • 46449084805 scopus 로고
    • Explicit cost bounds of algorithms for multivariate tensor products
    • Wasilkowski G. W., Wozniakowski H. Explicit cost bounds of algorithms for multivariate tensor products. J. Complexity. 11:1995;1-56.
    • (1995) J. Complexity , vol.11 , pp. 1-56
    • Wasilkowski, G.W.1    Wozniakowski, H.2
  • 44
    • 34250126304 scopus 로고
    • On the multi-level splitting of finite element spaces
    • Yserentant H. On the multi-level splitting of finite element spaces. Numer. Math. 49:1986;379-412.
    • (1986) Numer. Math. , vol.49 , pp. 379-412
    • Yserentant, H.1
  • 45
    • 0141936336 scopus 로고
    • Hierarchical bases
    • R. E. Jr. O'Malley. Philadelphia: SIAM
    • Yserentant H. Hierarchical bases. O'Malley R. E. Jr. Proc. ICIAM91, Washington, 1991. 1992;SIAM, Philadelphia.
    • (1992) Proc. ICIAM91, Washington, 1991
    • Yserentant, H.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.