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Generalized finite element method using mesh-based handbooks: application to problems in domains with many voids. (English) Zbl 1054.74059

Summary: This paper describes a new version of the generalized finite element method, originally developed [T. Strouboulis et al., Int. J. Numer. Methods Eng. 47, No. 8, 1401–1417 (2000; Zbl 0955.65080); Comput. Methods Appl. Mech. Eng. 181, No. 1-3, 43–69 (2000; Zbl 0983.65127); The design and implementation of the generalized finite element method, Ph.D. thesis, Texas A&M University, College Station, Texas, August 2000; Comput. Methods Appl. Mech. Eng. 190, No. 32-33, 4081–4193 (2001; Zbl 0997.74069)], which is well suited for problems set in domains with a large number of internal features (e.g. voids, inclusions, cracks, etc.). The main idea is to employ handbook functions constructed on subdomains resulting from the mesh-discretization of the problem domain. The proposed new version of the GFEM is shown to be robust with respect to the spacing of the features and is capable of achieving high accuracy on meshes which are rather coarse relative to the distribution of the features.

MSC:

74S05 Finite element methods applied to problems in solid mechanics
74E05 Inhomogeneity in solid mechanics
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[1] Strouboulis, T.; Babuška, I.; Copps, K., The generalized finite element method: An example of its implementation and illustration of its performance, Int. J. Numer. Methods Engrg., 47, 1401-1417 (2000) · Zbl 0955.65080
[2] Babuška, I.; Strouboulis, T.; Copps, K., The design and analysis of the generalized finite element method, Comput. Methods Appl. Mech. Engrg., 181, 1, 43-69 (2000) · Zbl 0983.65127
[3] K. Copps, The design and implementation of the generalized finite element method, Ph.D. Thesis, Texas A&M University, College Station, Texas, August 2000 (Advisor: T. Strouboulis); K. Copps, The design and implementation of the generalized finite element method, Ph.D. Thesis, Texas A&M University, College Station, Texas, August 2000 (Advisor: T. Strouboulis) · Zbl 0983.65127
[4] Strouboulis, T.; Copps, K.; Babuška, I., The generalized finite element method, Comput. Methods Appl. Mech. Engrg., 190, 4081-4193 (2001) · Zbl 0997.74069
[5] J.M. Melenk, Finite element methods with harmonic shape functions for solving Laplace’s equation, Master’s Thesis, University of Maryland, College Park, Maryland, 1992 (Advisor: I. Babuška); J.M. Melenk, Finite element methods with harmonic shape functions for solving Laplace’s equation, Master’s Thesis, University of Maryland, College Park, Maryland, 1992 (Advisor: I. Babuška)
[6] J.M. Melenk, On generalized finite element methods, Ph.D. Thesis, University of Maryland, College Park, Maryland, 1995 (Advisor: I. Babuška); J.M. Melenk, On generalized finite element methods, Ph.D. Thesis, University of Maryland, College Park, Maryland, 1995 (Advisor: I. Babuška)
[7] Babuška, I.; Melenk, J. M., The partition of unity finite element method: Basic theory and applications, Comput. Methods Appl. Mech. Engrg., 139, 289-314 (1996) · Zbl 0881.65099
[8] Babuška, I.; Melenk, J. M., The partition of unity method, Int. J. Numer. Methods Engrg., 40, 727-758 (1997) · Zbl 0949.65117
[9] Szabo, B. A.; Babuška, I., Finite Element Analysis (1991), John Wiley & Sons: John Wiley & Sons New York
[10] Babuška, I.; Strouboulis, T., The Finite Element Method and Its Reliability (2001), Oxford · Zbl 0997.74069
[11] B. Andersson, I. Babuška and P. Stehlin, Reliable multi-site damage analysis of 3d structure, Technical report, The Aeronautical Research Institute of Sweden, FFA TN 1998-18, 1998; B. Andersson, I. Babuška and P. Stehlin, Reliable multi-site damage analysis of 3d structure, Technical report, The Aeronautical Research Institute of Sweden, FFA TN 1998-18, 1998
[12] Babuška, I.; Andersson, B.; Smith, P. J.; Levin, K., Damage analysis of fiber composites. Part I: Statistical analysis on fiber scale, Comput. Methods Appl. Mech. Engrg., 172, 27-78 (1999) · Zbl 0956.74048
[13] Melenk, J. M.; Babuška, I., Approximation with harmonic and generalized harmonic polynomials in the partition of unity method, Comput. Assist. Mech. Engrg. Sci., 4, 607-632 (1997) · Zbl 0951.65128
[14] Melenk, J. M., Operator adapted spectral element methods I: harmonic and generalized harmonic polynomials, Numer. Math., 84, 35-69 (1999) · Zbl 0941.65112
[15] T. Strouboulis, L. Zhang, I. Babuška, \(p\); T. Strouboulis, L. Zhang, I. Babuška, \(p\)
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