메뉴 건너뛰기




Volumn 47, Issue 2, 2009, Pages 1421-1444

On mesh geometry and stiffness matrix conditioning for general finite element spaces

Author keywords

Condition number; Finite element method; Mesh quality; Unstructured mesh

Indexed keywords

APPROXIMATION ERRORS; COMMON KNOWLEDGE; CONDITION NUMBERS; DISCRETIZATIONS; ELEMENT STIFFNESS MATRIX; FINITE ELEMENT; FINITE ELEMENT SOLUTION; FINITE ELEMENT SPACE; GEOMETRIC QUANTITIES; HIGH ORDER ELEMENT; LINEAR-ALGEBRAIC; MESH GEOMETRY; MESH QUALITY; NUMERICAL SOLUTION; SECOND-ORDER ELLIPTIC PROBLEM; SPECTRAL CONDITION NUMBER; SPECTRAL PROPERTIES; TRACE FORMULAE; UNSTRUCTURED MESHES;

EID: 70049088368     PISSN: 00361429     EISSN: None     Source Type: Journal    
DOI: 10.1137/080718486     Document Type: Article
Times cited : (53)

References (43)
  • 1
    • 51249186403 scopus 로고
    • A stable finite element for the Stokes equations
    • D. ARNOLD, F. BREZZI, AND M. FORTIN, A stable finite element for the Stokes equations, Calcolo, 12(1984), pp. 337-344.
    • (1984) Calcolo , vol.12 , pp. 337-344
    • Arnold, D.1    Brezzi, F.2    Fortin, M.3
  • 3
    • 84873260097 scopus 로고    scopus 로고
    • reprinted as, SIAM, Philadelphia
    • reprinted as Classics Appl. Math. 35, SIAM, Philadelphia, 2001.
    • (2001) Classics Appl. Math. , vol.35
  • 4
    • 0016939764 scopus 로고
    • On the angle condition in the finite element method
    • I. BABUŠKA AND A. K. AZIZ, On the angle condition in the finite element method, SIAM J. Numer. Anal., 13(1976), pp. 214-226.
    • (1976) SIAM J. Numer. Anal. , vol.13 , pp. 214-226
    • Babuška, I.1    Aziz, A.K.2
  • 6
    • 0001309061 scopus 로고    scopus 로고
    • Mesh smoothing using a posteriori error estimates
    • R. E. BANK AND R. K. SMITH, Mesh smoothing using a posteriori error estimates, SIAM J. Numer. Anal., 34(1997), pp. 979-997.
    • (1997) SIAM J. Numer. Anal. , vol.34 , pp. 979-997
    • Bank, R.E.1    Smith, R.K.2
  • 7
    • 84983134434 scopus 로고    scopus 로고
    • Computational study of the effect of unstructured and mesh quality on solution efficiency
    • AIAA, Reston, VA
    • M. BATDORF, L. FREITAG, AND C. OLLIVIER-GOOCH, Computational study of the effect of unstructured and mesh quality on solution efficiency, in Proceedings of the 13th CFD Conference, AIAA, Reston, VA, 1997.
    • (1997) Proceedings of the 13th CFD Conference
    • Batdorf, M.1    Freitag, L.2    Ollivier-Gooch, C.3
  • 8
    • 0032597987 scopus 로고    scopus 로고
    • Mesh quality: A function of geometry, error estimates or both?
    • M. BERZINS, Mesh quality: A function of geometry, error estimates or both?, Engineering with Computers, 15(1999), pp. 236-247.
    • (1999) Engineering with Computers , vol.15 , pp. 236-247
    • Berzins, M.1
  • 9
    • 0032205858 scopus 로고    scopus 로고
    • A solution-based triangular and tetrahedral mesh quality indicator
    • M. BERZINS, A solution-based triangular and tetrahedral mesh quality indicator, SIAM J. Sci. Comput., 19(1998), pp. 2051-2060.
    • (1998) SIAM J. Sci. Comput. , vol.19 , pp. 2051-2060
    • Berzins, M.1
  • 10
    • 0001326105 scopus 로고
    • Basis function selection and precondition high degree finite element and spectral methods
    • G. CAREY AND E. BARRAGY, Basis function selection and precondition high degree finite element and spectral methods, BIT, 29(1989), pp. 794-804.
    • (1989) BIT , vol.29 , pp. 794-804
    • Carey, G.1    Barragy, E.2
  • 11
    • 33644529423 scopus 로고    scopus 로고
    • On the error of linear interpolation and orientation, aspect ratio, and internal angles of a triangle
    • W. CAO, On the error of linear interpolation and orientation, aspect ratio, and internal angles of a triangle, SIAM J. Numer. Anal., 43(2005), pp. 19-40.
    • (2005) SIAM J. Numer. Anal. , vol.43 , pp. 19-40
    • Cao, W.1
  • 13
    • 18344378530 scopus 로고    scopus 로고
    • SIAM, Philadelphia
    • reprinted as Classics in Appl. Math. 40, SIAM, Philadelphia, 2002.
    • (2002) Appl. Math. , vol.40
  • 14
  • 15
    • 0033317391 scopus 로고    scopus 로고
    • Centroidal Voronoi tessellations: Applications and algorithms
    • Q. DU, V. FABER, AND M. GUNZBURGER, Centroidal Voronoi tessellations: Applications and algorithms, SIAM Rev., 41(1999), pp. 637-676.
    • (1999) SIAM Rev. , vol.41 , pp. 637-676
    • Du, Q.1    Faber, V.2    Gunzburger, M.3
  • 16
    • 0037114113 scopus 로고    scopus 로고
    • Grid generation and optimization based on centroidal Voronoi tessellations
    • Q. DU AND M. GUNZBURGER, Grid generation and optimization based on centroidal Voronoi tessellations, Appl. Comput. Math., 133(2002), pp. 591-607.
    • (2002) Appl. Comput. Math. , vol.133 , pp. 591-607
    • Du, Q.1    Gunzburger, M.2
  • 17
    • 23144459384 scopus 로고    scopus 로고
    • Mesh and solver co-adaptation in finite element methods for anisotropic problems
    • Q. DU, Z. HUANG, AND D. WANG, Mesh and solver co-adaptation in finite element methods for anisotropic problems, Numer. Methods Partial Differential Equations, 21(2005), pp. 859-874.
    • (2005) Numer. Methods Partial Differential Equations , vol.21 , pp. 859-874
    • Du, Q.1    Huang, Z.2    Wang, D.3
  • 18
    • 0037423969 scopus 로고    scopus 로고
    • Tetrahedral mesh generation and optimization based on centroidal Voronoi tessellations
    • Q. DU AND D. WANG, Tetrahedral mesh generation and optimization based on centroidal Voronoi tessellations, Internat. J. Numer. Methods Engrg., 56(2003), pp. 1355-1373.
    • (2003) Internat. J. Numer. Methods Engrg. , vol.56 , pp. 1355-1373
    • Du, Q.1    Wang, D.2
  • 19
    • 33745261230 scopus 로고    scopus 로고
    • Recent progress in robust and quality mesh generation
    • Q. DU AND D. WANG, Recent progress in robust and quality mesh generation, J. Comput. Appl. Math., 195(2006), pp. 8-23.
    • (2006) J. Comput. Appl. Math. , vol.195 , pp. 8-23
    • Du, Q.1    Wang, D.2
  • 20
    • 0034417405 scopus 로고    scopus 로고
    • A cost/benefit analysis of simplicial mesh improvement techniques as measured by solution efficiency
    • L. FREITAG AND C. OLLIVIER-GOOCH, A cost/benefit analysis of simplicial mesh improvement techniques as measured by solution efficiency, Internat. J. Comput. Geom. Appl., 10(2000), pp. 361-382.
    • (2000) Internat. J. Comput. Geom. Appl. , vol.10 , pp. 361-382
    • Freitag, L.1    Ollivier-Gooch, C.2
  • 21
    • 85003413406 scopus 로고
    • Condition of finite element matrices generated from nonuniform meshes
    • I. FRIED, Condition of finite element matrices generated from nonuniform meshes, AIAA Journal, 10(1972), pp. 219-221.
    • (1972) AIAA Journal , vol.10 , pp. 219-221
    • Fried, I.1
  • 22
    • 0015667999 scopus 로고
    • Bounds on the spectral and maximum norms of the finite element stiffness, flexibility and mass matrices
    • I. FRIED, Bounds on the spectral and maximum norms of the finite element stiffness, flexibility and mass matrices, Int. J. Solids Structures, 9(1973), pp. 1013-1034.
    • (1973) Int. J. Solids Structures , vol.9 , pp. 1013-1034
    • Fried, I.1
  • 25
    • 0032367243 scopus 로고    scopus 로고
    • Bounds for eigenvalues and condition number in the p-version of the finite element methods
    • N. HU, X. GUO, AND I. KATZ, Bounds for eigenvalues and condition number in the p-version of the finite element methods, Math. Comp., 67(1998), pp. 1423-1450.
    • (1998) Math. Comp. , vol.67 , pp. 1423-1450
    • Hu, N.1    Guo, X.2    Katz, I.3
  • 26
    • 39549119675 scopus 로고    scopus 로고
    • Conforming centroidal Voronoi Delaunay triangulation for quality mesh generation
    • L. JU, Conforming centroidal Voronoi Delaunay triangulation for quality mesh generation, Intern. J. Numer. Anal. Model., 4(2007), pp. 531-547.
    • (2007) Intern. J. Numer. Anal. Model. , vol.4 , pp. 531-547
    • Ju, L.1
  • 27
    • 36348997658 scopus 로고    scopus 로고
    • Adaptive finite element methods for elliptic PDEs based on conforming centroidal Voronoi-Delaunay triangulations
    • L. JU, M. GUNZBURGER, AND W. ZHAO, Adaptive finite element methods for elliptic PDEs based on conforming centroidal Voronoi-Delaunay triangulations, SIAM J. Sci. Comput., 28(2006), pp. 2023-2053.
    • (2006) SIAM J. Sci. Comput. , vol.28 , pp. 2023-2053
    • Ju, L.1    Gunzburger, M.2    Zhao, W.3
  • 28
    • 0023542111 scopus 로고
    • Finite-element grid improvement by minimization of stiffness matrix trace
    • Glenn Research Center, Cleveland, OH
    • M. KITTUR, R. HUSTON, AND F. OSWALD, Finite-Element Grid Improvement by Minimization of Stiffness Matrix Trace, NASA Tech. Report 87-C-4, Glenn Research Center, Cleveland, OH, 1987.
    • (1987) NASA Tech. Report 87-C-4
    • Kittur, M.1    Huston, R.2    Oswald, F.3
  • 29
    • 0002212314 scopus 로고    scopus 로고
    • Matrix norms and the condition number: A general framework to improve mesh quality via node-movement
    • Lake Tahoe, CA
    • P. KNUPP, Matrix norms and the condition number: A general framework to improve mesh quality via node-movement, in Proceedings of the 8th International Meshing Roundtable (Lake Tahoe, CA), 1999, pp. 13-22.
    • (1999) Proceedings of the 8th International Meshing Roundtable , pp. 13-22
    • Knupp, P.1
  • 30
    • 0141750723 scopus 로고    scopus 로고
    • Hexahedral and tetrahedral mesh shape optimization
    • P. KNUPP, Hexahedral and tetrahedral mesh shape optimization, Internat. J. Numer. Methods Engrg., 58(2003), pp. 319-332.
    • (2003) Internat. J. Numer. Methods Engrg. , vol.58 , pp. 319-332
    • Knupp, P.1
  • 31
    • 0026841003 scopus 로고
    • On the maximum angle condition for linear tetrahedral elements
    • M. KŘÍŽEK, On the maximum angle condition for linear tetrahedral elements, SIAM J. Numer. Anal., 29(1992), pp. 513-520.
    • (1992) SIAM J. Numer. Anal. , vol.29 , pp. 513-520
    • Křížek, M.1
  • 32
    • 0000714820 scopus 로고
    • Relationship between tetrahedron shape measures
    • A. LIU AND B. JOE, Relationship between tetrahedron shape measures, BIT, 34(1994), pp. 268-287.
    • (1994) BIT , vol.34 , pp. 268-287
    • Liu, A.1    Joe, B.2
  • 35
    • 10444254656 scopus 로고    scopus 로고
    • Optimal finite element mesh for elliptic equation of divergence form
    • S. OH AND J. YIM, Optimal finite element mesh for elliptic equation of divergence form, Appl. Math. Comput., 162(2005), pp. 969-989.
    • (2005) Appl. Math. Comput. , vol.162 , pp. 969-989
    • Oh, S.1    Yim, J.2
  • 37
    • 21844498639 scopus 로고
    • Bounds on spectral condition numbers of matrices arising in the p-version of the finite element method
    • E. OLSEN AND J. DOUGLAS, Bounds on spectral condition numbers of matrices arising in the p-version of the finite element method, Numer. Math., 69(1995), pp. 333-352.
    • (1995) Numer. Math. , vol.69 , pp. 333-352
    • Olsen, E.1    Douglas, J.2
  • 38
    • 21344477231 scopus 로고
    • On preconditioning for finite element equations on irregular grids
    • A. RAMAGE AND A. J. WATHEN, On preconditioning for finite element equations on irregular grids, SIAM J. Matrix Anal. Appl., 15(1994), pp. 909-921.
    • (1994) SIAM J. Matrix Anal. Appl. , vol.15 , pp. 909-921
    • Ramage, A.1    Wathen, A.J.2
  • 39
    • 12844256736 scopus 로고    scopus 로고
    • What is a good linear finite element? Interpolation, conditioning, anisotropy and quality measures
    • University of California, Berkeley, CA
    • J. SHEWCHUK, What is a Good Linear Finite Element? Interpolation, Conditioning, Anisotropy and Quality Measures, Tech. report, Department of Computer Science, University of California, Berkeley, CA, 2003.
    • (2003) Tech. Report, Department of Computer Science
    • Shewchuk, J.1
  • 41
    • 85037534165 scopus 로고    scopus 로고
    • A general accuracy criterion for finite element approximation
    • I. TSUKERMAN, A general accuracy criterion for finite element approximation, IEEE Trans. Magnetics, 35(1998), pp. 1-4.
    • (1998) IEEE Trans. Magnetics , vol.35 , pp. 1-4
    • Tsukerman, I.1
  • 42
    • 0000021772 scopus 로고
    • Realistic eigenvalue bounds for the Galerkin mass matrix
    • A. WATHEN, Realistic eigenvalue bounds for the Galerkin mass matrix, IMA J. Numer. Anal., 7(1987), pp. 449-457.
    • (1987) IMA J. Numer. Anal. , vol.7 , pp. 449-457
    • Wathen, A.1
  • 43
    • 0035148185 scopus 로고    scopus 로고
    • Orthogonal polynomials and cubature formulae on balls, simplices, and spheres
    • Y. XU, Orthogonal polynomials and cubature formulae on balls, simplices, and spheres, J. Comput. Appl. Math., 127(2001), pp. 349-368.
    • (2001) J. Comput. Appl. Math. , vol.127 , pp. 349-368
    • Xu, Y.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.