메뉴 건너뛰기




Volumn 35, Issue 2, 2013, Pages

Efficient structured multifrontal factorization for general large sparse matrices

Author keywords

General sparse matrix; HSS matrix; Reduced matrix; Sparse rank relaxation; Structured multifrontal method; ULV factorization

Indexed keywords

FORESTRY; MATRIX ALGEBRA; NUMERICAL METHODS; TREES (MATHEMATICS);

EID: 84880626890     PISSN: 10648275     EISSN: 10957200     Source Type: Journal    
DOI: 10.1137/120867032     Document Type: Article
Times cited : (81)

References (42)
  • 1
    • 21644458055 scopus 로고    scopus 로고
    • Efficient inversion of Galerkin matrices of general second-order elliptic differential operators with nonsmooth coefficients
    • M. BEBENDORF, Efficient inversion of Galerkin matrices of general second-order elliptic differential operators with nonsmooth coefficients, Math. Comp., 74(2005), pp. 1179-1199.
    • (2005) Math. Comp. , vol.74 , pp. 1179-1199
    • Bebendorf, M.1
  • 2
    • 0041411652 scopus 로고    scopus 로고
    • Existence of H-matrix approximants to the inverse FE-matrix of elliptic operators with L∞-Coefficients
    • M. BEBENDORF AND W. HACKBUSCH, Existence of H-matrix approximants to the inverse FE-matrix of elliptic operators with L∞-Coefficients, Numer. Math., 95(2003), pp. 1-28.
    • (2003) Numer. Math. , vol.95 , pp. 1-28
    • Bebendorf, M.1    Hackbusch, W.2
  • 8
    • 77956413970 scopus 로고    scopus 로고
    • On the numerical rank of the off-diagonal blocks of Schur complements of discretized elliptic PDEs
    • S. CHANDRASEKARAN, P. DEWILDE, M. GU, AND N. SOMASUNDERAM, On the numerical rank of the off-diagonal blocks of Schur complements of discretized elliptic PDEs, SIAM J. Matrix Anal. Appl., 31(2010), pp. 2261-2290.
    • (2010) SIAM J. Matrix Anal. Appl. , vol.31 , pp. 2261-2290
    • Chandrasekaran, S.1    Dewilde, P.2    Gu, M.3    Somasunderam, N.4
  • 9
    • 34547225006 scopus 로고    scopus 로고
    • A fast ULV decomposition solver for hierarchically semiseparable representations
    • S. CHANDRASEKARAN, M. GU, AND T. PALS, A fast ULV decomposition solver for hierarchically semiseparable representations, SIAM J. Matrix Anal. Appl., 28(2006), pp. 603-622.
    • (2006) SIAM J. Matrix Anal. Appl. , vol.28 , pp. 603-622
    • Chandrasekaran, S.1    Gu, M.2    Pals, T.3
  • 12
    • 0020822138 scopus 로고
    • The multifrontal solution of indefinite sparse symmetric linear equations
    • I. S. DUFF AND J. K. REID, The multifrontal solution of indefinite sparse symmetric linear equations, ACM Trans. Math. Software, 9(1983), pp. 302-325.
    • (1983) ACM Trans. Math. Software , vol.9 , pp. 302-325
    • Duff, I.S.1    Reid, J.K.2
  • 14
    • 79551482511 scopus 로고    scopus 로고
    • Sweeping preconditioner for the Helmholtz equation: Hierarchical matrix representation
    • B. ENGQUIST AND L. YING, Sweeping preconditioner for the Helmholtz equation: Hierarchical matrix representation, Pure Appl. Math., LXIV (2011), pp. 697-735.
    • (2011) Pure Appl. Math. , vol.64 , pp. 697-735
    • Engquist, B.1    Ying, L.2
  • 15
    • 33746033769 scopus 로고    scopus 로고
    • A novel multigrid based preconditioner for heterogeneous Helmholtz problems
    • Y. A. ERLANGGA, C. W. OOSTERLEE, AND C. VUIK, A novel multigrid based preconditioner for heterogeneous Helmholtz problems, SIAM J. Sci. Comput., 27(2006), pp. 1471-1492.
    • (2006) SIAM J. Sci. Comput. , vol.27 , pp. 1471-1492
    • Erlangga, Y.A.1    Oosterlee, C.W.2    Vuik, C.3
  • 16
    • 0000264382 scopus 로고
    • Nested dissection of a regular finite element mesh
    • A. GEORGE, Nested dissection of a regular finite element mesh, SIAM J. Numer. Anal., 10(1973), pp. 345-363.
    • (1973) SIAM J. Numer. Anal. , vol.10 , pp. 345-363
    • George, A.1
  • 19
    • 84880346087 scopus 로고    scopus 로고
    • Domain-decomposition based H-LU preconditioners
    • O. B. Widlund and D. E. Keyes, eds., Lect. Notes Comput. Sci. Eng, Springer, Berlin
    • L. GRASEDYCK, R. KRIEMANN, AND S. LE BORNE, Domain-decomposition based H-LU preconditioners, in Domain Decomposition Methods in Science and Engineering XVI, O. B. Widlund and D. E. Keyes, eds., Lect. Notes Comput. Sci. Eng. 55, Springer, Berlin, 2006, pp. 661-668.
    • (2006) Domain Decomposition Methods in Science and Engineering XVI , vol.55 , pp. 661-668
    • Grasedyck, L.1    Kriemann, R.2    Le Borne, S.3
  • 20
    • 2342579516 scopus 로고    scopus 로고
    • An algebraic multigrid method for linear elasticity
    • M. GRIEBEL, D. OELTZ, AND M. A. SCHWEITZER, An algebraic multigrid method for linear elasticity, SIAM J. Sci. Comput., 25(2003), pp. 385-407.
    • (2003) SIAM J. Sci. Comput. , vol.25 , pp. 385-407
    • Griebel, M.1    Oeltz, D.2    Schweitzer, M.A.3
  • 21
    • 79251503935 scopus 로고    scopus 로고
    • Direction-preserving and Schur-monotonic semiseparable approximations of symmetric positive definite matrices
    • M. GU, X. S. LI, AND P. S. VASSILEVSKI, Direction-preserving and Schur-monotonic semiseparable approximations of symmetric positive definite matrices, SIAM. J. Matrix Anal. Appl., 31(2010), pp. 2650-2664.
    • (2010) SIAM. J. Matrix Anal. Appl. , vol.31 , pp. 2650-2664
    • Gu, M.1    Li, X.S.2    Vassilevski, P.S.3
  • 22
    • 0032637646 scopus 로고    scopus 로고
    • A sparse matrix arithmetic based on H-matrices. Part I: Introduction to H-matrices
    • W. HACKBUSCH, A sparse matrix arithmetic based on H-matrices. Part I: Introduction to H-matrices, Computing, 62(1999), pp. 89-108.
    • (1999) Computing , vol.62 , pp. 89-108
    • Hackbusch, W.1
  • 23
    • 0001675181 scopus 로고
    • A graph theoretic approach to matrix inversion by partitioning
    • F. HARARY, A graph theoretic approach to matrix inversion by partitioning, Numer. Math., 4(1962), pp. 128-135.
    • (1962) Numer. Math. , vol.4 , pp. 128-135
    • Harary, F.1
  • 24
    • 0039236804 scopus 로고
    • Complexity bounds for regular finite difference and finite element grids
    • A. J. HOFFMAN, M. S. MARTIN, AND D. J. ROSE, Complexity bounds for regular finite difference and finite element grids, SIAM J. Numer. Anal., 10(1973), pp. 364-369.
    • (1973) SIAM J. Numer. Anal. , vol.10 , pp. 364-369
    • Hoffman, A.J.1    Martin, M.S.2    Rose, D.J.3
  • 25
    • 0026840122 scopus 로고
    • The multifrontal method for sparse matrix solution: Theory and practice
    • J. W. H. LIU, The multifrontal method for sparse matrix solution: Theory and practice, SIAM Rev., 34(1992), pp. 82-109.
    • (1992) SIAM Rev. , vol.34 , pp. 82-109
    • Liu, J.W.H.1
  • 27
    • 64949123438 scopus 로고    scopus 로고
    • A fast direct solver for a class of elliptic partial differential equations
    • P. G. MARTINSSON, A fast direct solver for a class of elliptic partial differential equations, J. Sci. Comput., 3, 2009, pp. 316-330
    • (2009) J. Sci. Comput. , vol.3 , pp. 316-330
    • Martinsson, P.G.1
  • 28
    • 16844371628 scopus 로고    scopus 로고
    • A fast direct solver for boundary integral equations in two dimensions
    • P. G. MARTINSSON AND V. ROKHLIN, A fast direct solver for boundary integral equations in two dimensions, J. Comput. Phys., 205(2005), pp. 1-23.
    • (2005) J. Comput. Phys. , vol.205 , pp. 1-23
    • Martinsson, P.G.1    Rokhlin, V.2
  • 30
    • 0001241033 scopus 로고
    • The use of linear graphs in Gauss elimination
    • S. PARTER, The use of linear graphs in Gauss elimination, SIAM Rev., 3(1961), pp. 119-130.
    • (1961) SIAM Rev. , vol.3 , pp. 119-130
    • Parter, S.1
  • 31
    • 3142698698 scopus 로고    scopus 로고
    • A simple mesh generator in MATLAB
    • P.-O. PERSSON AND G. STRANG, A simple mesh generator in MATLAB, SIAM Rev., 46(2004), pp. 329-345.
    • (2004) SIAM Rev. , vol.46 , pp. 329-345
    • Persson, P.-O.1    Strang, G.2
  • 32
    • 84855187884 scopus 로고    scopus 로고
    • A fast direct solver for elliptic problems on general meshes in 2D
    • P. G. SCHMITZ AND L. YING, A fast direct solver for elliptic problems on general meshes in 2D, J. Comput. Phys., 231(2012), pp. 1314-1338.
    • (2012) J. Comput. Phys. , vol.231 , pp. 1314-1338
    • Schmitz, P.G.1    Ying, L.2
  • 33
    • 70350331539 scopus 로고
    • The product form of inverses of sparse matrices and graph theory
    • R. P. TEWARSON, The product form of inverses of sparse matrices and graph theory, SIAM Rev., 9(1967), pp. 91-99.
    • (1967) SIAM Rev. , vol.9 , pp. 91-99
    • Tewarson, R.P.1
  • 35
    • 77956415161 scopus 로고    scopus 로고
    • Acoustic inverse scattering via Helmholtz operator factorization and optimization
    • S. WANG, M. V. DE HOOP, AND J. XIA, Acoustic inverse scattering via Helmholtz operator factorization and optimization, J. Comput. Phys., 229(2010), pp. 8445-8462.
    • (2010) J. Comput. Phys. , vol.229 , pp. 8445-8462
    • Wang, S.1    De Hoop, M.V.2    Xia, J.3
  • 36
    • 84880613404 scopus 로고    scopus 로고
    • Efficient scalable algorithms for hierarchically semiseparable matrices
    • submitted
    • S. WANG, X. S. LI, J. XIA, M. V. DE HOOP, AND Y. SITU, Efficient scalable algorithms for hierarchically semiseparable matrices, SIAM J. Sci. Comput., submitted.
    • SIAM J. Sci. Comput.
    • Wang, S.1    Li, X.S.2    Xia, J.3    De Hoop, M.V.4    Situ, Y.5
  • 37
    • 84877338334 scopus 로고    scopus 로고
    • Robust and efficient multifrontal solver for large discretized PDEs
    • M. W. Berry et al., eds., Springer, London
    • J. XIA, Robust and efficient multifrontal solver for large discretized PDEs, High-Perform. Sci. Comput., M. W. Berry et al., eds., Springer, London, 2012, pp. 199-217.
    • (2012) High-Perform. Sci. Comput. , pp. 199-217
    • Xia, J.1
  • 38
    • 84869127788 scopus 로고    scopus 로고
    • A robust inner-outer HSS preconditioner
    • J. XIA, A robust inner-outer HSS preconditioner, Numer. Linear Algebra Appl., 19(2012), pp. 992-1016.
    • (2012) Numer. Linear Algebra Appl. , vol.19 , pp. 992-1016
    • Xia, J.1
  • 39
    • 77956417875 scopus 로고    scopus 로고
    • Superfast multifrontal method for large structured linear systems of equations
    • J. XIA, S. CHANDRASEKARAN, M. GU, AND X. S. LI, Superfast multifrontal method for large structured linear systems of equations, SIAM J. Matrix Anal. Appl., 31(2010), pp. 1382-1411.
    • (2010) SIAM J. Matrix Anal. Appl. , vol.31 , pp. 1382-1411
    • Xia, J.1    Chandrasekaran, S.2    Gu, M.3    Li, X.S.4
  • 42
    • 84865452975 scopus 로고    scopus 로고
    • On the complexity of some hierarchical structured matrix algorithms
    • J. XIA, On the complexity of some hierarchical structured matrix algorithms, SIAM J. Matrix Anal. Appl., 33(2012), pp. 388-410.
    • (2012) SIAM J. Matrix Anal. Appl. , vol.33 , pp. 388-410
    • Xia, J.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.