Title

An improved XFEM for the Poisson equation with discontinuous coefficients

Journal title

Archive of Mechanical Engineering

Yearbook

2017

Volume

vol. 64

Issue

No 1

Affiliation

Stąpór, Paweł : Faculty of Management and Computer Modelling, Kielce University of Technology, Poland

Authors

Stąpór, Paweł

Keywords

Poisson equation ; weak discontinuity ; XFEM

Divisions of PAS

Nauki Techniczne

Coverage

123-144

Publisher

Polish Academy of Sciences, Committee on Machine Building

Bibliography

[1] T.P. Fries and H.G. Matthies. Classification and overview of meshfree methods. Informatikbericht Nr.: 2003-3. Technical University Braunschweig, Brunswick, Germany, 2004.
[2] M.A. Schweitzer. Meshfree and generalized finite element methods. Postdoctoral dissertation. Mathematisch–Naturwissenschaftlichen Fakultat der Rheinischen Friedrich-Wilhelms-Universitat, Bonn, Germany, 2008.
[3] Vinh Phu Nguyen, C. Anitescu, S. Bordas, and T. Rabczuk. Isogeometric analysis: An overview and computer implementation aspects. Mathematics and Computers in Simulation, 117:89–116, 2015. doi: 10.1016/j.matcom.2015.05.008.
[4] T. Belytschko and T. Black. Elastic crack growth in finite elements with minimal remeshing. International Journal for Numerical Methods in Engineering, 45(5):601–620, 1999.
[5] R. Merle and J. Dolbow. Solving thermal and phase change problems with the eXtended finite element method. Computational Mechanics, 28(5):339–350, 2002. doi: 10.1007/s00466-002-0298-y.
[6] J. Chessa, P. Smolinski, and T. Belytschko. The extended finite element method (XFEM) for solidification problems. International Journal for Numerical Methods in Engineering, 53(8):1959–1977, 2002. doi: 10.1002/nme.386.
[7] P. Stapór. The XFEM for nonlinear thermal and phase change problems. International Journal of Numerical Methods for Heat & Fluid Flow, 25(2):400–421, 2015. doi: 10.1108/HFF-02-2014-0052.
[8] J.Y. Wu and F.B. Li. An improved stable XFEM (Is-XFEM) with a novel enrichment function for the computational modeling of cohesive cracks. Computer Methods in Applied Mechanics and Engineering, 295:77–107, 2015. doi: 10.1016/j.cma.2015.06.018.
[9] P. Hansbo, M.G. Larson, and S. Zahedi. A cut finite element method for a stokes interface problem. Applied Numerical Mathematics, 85:90–114, 2014. doi: 10.1016/j.apnum.2014.06.009.
[10] E. Wadbro, S. Zahedi, G. Kreiss, and M. Berggren. A uniformly well-conditioned, unfitted Nitsche method for interface problems. BIT Numerical Mathematics, 53(3):791–820, 2013. doi: 10.1007/s10543-012-0417-x.
[11] I. Babuška and U. Banerjee. Stable generalized finite element method (SGFEM). Computer Methods in Applied Mechanics and Engineering, 201:91–111, 2012. doi: 10.1016/j.cma.2011.09.012.
[12] K. Kergrene, I. Babuška, and U. Banerjee. Stable generalized finite element method and associated iterative schemes; application to interface problems. Computer Methods in Applied Mechanics and Engineering, 305:1–36, 2016. doi: 10.1016/j.cma.2016.02.030.
[13] G. Zi and T. Belytschko. New crack-tip elements for XFEM and applications to cohesive cracks. International Journal for Numerical Methods in Engineering, 57(15):2221–2240, 2003. doi: 10.1002/nme.849.
[14] G. Ventura, E. Budyn, and T. Belytschko. Vector level sets for description of propagating cracks in finite elements. International Journal for Numerical Methods in Engineering, 58(10):1571–1592, 2003. doi: 10.1002/nme.829.
[15] J.E. Tarancón, A.Vercher, E. Giner, and F.J. Fuenmayor. Enhanced blending elements for XFEM applied to linear elastic fracture mechanics. International Journal for Numerical Methods in Engineering, 77(1):126–148, 2009. doi: 10.1002/nme.2402.
[16] T.P. Fries. A corrected XFEM approximation without problems in blending elements. International Journal for Numerical Methods in Engineering, 75(5):503–532, 2008. doi: 10.1002/nme.2259.
[17] P. Stąpór. Application of XFEM with shifted-basis approximation to computation of stress intensity factors. Archive of Mechanical Engineering, 58(4):447–483, 2011. doi: 10.2478/v10180-011-0028-0.
[18] N. Moës, M. Cloirec, P. Cartraud, and J.-F. Remacle. A computational approach to handle complex microstructure geometries. Computer Methods in Applied Mechanics and Engineering, 192(28):3163–3177, 2003. doi: 10.1016/S0045-7825(03)00346-3.
[19] J. Dolbow, N. Moës, and T. Belytschko. Discontinuous enrichment in finite elements with a partition of unity method. Finite Elements in Analysis and Design, 36(3):235–260, 2000. doi: 10.1016/S0168-874X(00)00035-4.
[20] B.A. Saxby. High-order XFEM with applications to two-phase flows. PhD thesis, The University of Manchester, Manchester, UK, 2014. www.escholar.manchester.ac.uk/uk-ac-manscw:234445.

Date

2017

Type

Artykuły / Articles

Identifier

DOI: 10.1515/meceng-2017-0008 ; ISSN 0004-0738, e-ISSN 2300-1895

Source

Archive of Mechanical Engineering; 2017; vol. 64; No 1; 123-144

References

Vinh Phu Nguyen (2015), Isogeometric analysis : An overview and computer implementation aspects and in, Mathematics Computers Simulation, 117, doi.org/10.1016/j.matcom.2015.05.008 ; Tarancón (2009), Enhanced blending elements for XFEM applied to linear elastic fracture mechanics for in, International Journal Numerical Methods Engineering, 77, 126, doi.org/10.1002/nme.2402 ; Merle (2002), Solving thermal and phase change problems with the eXtended finite element method, Computational mechanics, 28, 339, doi.org/10.1007/s00466-002-0298-y ; Babuška (2012), Stable generalized finite element method in and, Computer Methods Applied Mechanics Engineering, 201, doi.org/10.1016/j.cma.2011.09.012 ; Belytschko (1999), Elastic crack growth in finite elements with minimal remeshing for numerical methods in engineering, International journal, 45, 601. ; Wadbro (2013), A uniformly well - conditioned , unfitted nitsche method for interface problems Numerical, BIT Mathematics, 53, 791, doi.org/10.1007/s10543-012-0417-x ; Chessa (2002), The extended finite element method for solidification problems for in, International Journal Numerical Methods Engineering, 53, 1959, doi.org/10.1002/nme.386 ; Zi (2003), New crack - tip elements for xfem and applications to cohesive cracks for in, International Journal Numerical Methods Engineering, 57, 2221, doi.org/10.1002/nme.849 ; Moës (2003), A computational approach to handle complex microstructure geometries in and, Computer methods applied mechanics engineering, 28, 192, doi.org/10.1016/S0045-7825(03)00346-3 ; Wu (2015), An improved stable XFEM ( Is with a novel enrichment function for the computational modeling of cohesive cracks in and, Computer Methods Applied Mechanics Engineering, 295, doi.org/10.1016/j.cma.2015.06.018 ; Kergrene (2016), Stable generalized finite element method and associated iterative schemes ; application to interface problems in and, Computer Methods Applied Mechanics Engineering, 305, doi.org/10.1016/j.cma.2016.02.030 ; Stapór (2015), The XFEM for nonlinear thermal and phase change problems of Numerical Methods for Heat & Fluid, International Journal Flow, 25, 400, doi.org/10.1108/HFF-02-2014-0052 ; Stąpór (2011), Application of xfem with shifted - basis approximation to computation of stress intensity factors Archive of Mechanical, Engineering, 58, 447, doi.org/10.2478/v10180-011-0028-0 ; Fries (2008), A corrected XFEM approximation without problems in blending elements for in, International Journal Numerical Methods Engineering, 75, 503, doi.org/10.1002/nme.2259 ; Ventura (2003), Vector level sets for description of propagating cracks in finite elements for in, International Journal Numerical Methods Engineering, 58, 1571, doi.org/10.1002/nme.829 ; Hansbo (2014), A cut finite element method for a stokes interface problem Numerical, Applied Mathematics, 85, doi.org/10.1016/j.apnum.2014.06.009