TY - BOOK AU - Wachspress, E. PY - 1971 DA - 1971// TI - A rational basis for function approximation PB - Springer CY - New York UR - https://doi.org/10.1007/BFb0069458 DO - 10.1007/BFb0069458 ID - Wachspress1971 ER - TY - JOUR AU - Alwood, R. AU - Cornes, G. PY - 1969 DA - 1969// TI - A polygonal finite element for plate bending problems using the assumed stress approach JO - Int J Numer Methods Eng VL - 1 UR - https://doi.org/10.1002/nme.1620010202 DO - 10.1002/nme.1620010202 ID - Alwood1969 ER - TY - JOUR AU - Sukumar, N. AU - Tabarraei, A. PY - 2004 DA - 2004// TI - Conforming polygonal finite elements JO - Int J Numer Methods Eng VL - 61 UR - https://doi.org/10.1002/nme.1141 DO - 10.1002/nme.1141 ID - Sukumar2004 ER - TY - JOUR AU - Dasgupta, G. PY - 2003 DA - 2003// TI - Interpolants within convex polygons: Wachspress’ shape functions JO - J Aerosp Eng (ASCE) VL - 16 UR - https://doi.org/10.1061/(ASCE)0893-1321(2003)16:1(1) DO - 10.1061/(ASCE)0893-1321(2003)16:1(1) ID - Dasgupta2003 ER - TY - JOUR AU - Rjasanow, S. AU - Weißer, S. PY - 2012 DA - 2012// TI - Higher order BEM-based FEM on polygonal meshes JO - SIAM J Numer Anal VL - 50 UR - https://doi.org/10.1137/110849481 DO - 10.1137/110849481 ID - Rjasanow2012 ER - TY - JOUR AU - Barros, F. B. AU - Barcellos, C. S. AU - Duarte, C. A. PY - 2007 DA - 2007// TI - p-Adaptive C k generalized finite element method for arbitrary polygonal clouds JO - Comput Mech VL - 41 UR - https://doi.org/10.1007/s00466-007-0177-7 DO - 10.1007/s00466-007-0177-7 ID - Barros2007 ER - TY - JOUR AU - Veiga, L. B. AU - Brezzi, F. AU - Cangiani, A. AU - Manzini, G. AU - Marini, L. AU - Russo, A. PY - 2013 DA - 2013// TI - Basic principles of virtual element methods JO - Maths Models Methods Appl Sci VL - 23 UR - https://doi.org/10.1142/S0218202512500492 DO - 10.1142/S0218202512500492 ID - Veiga2013 ER - TY - JOUR AU - Bishop, J. PY - 2013 DA - 2013// TI - A displacement-based finite element formulation for general polyhedra using harmonic shape functions JO - Int J Numer Methods Eng VL - 97 UR - https://doi.org/10.1002/nme.4562 DO - 10.1002/nme.4562 ID - Bishop2013 ER - TY - JOUR AU - Biabanaki, S. AU - Khoei, A. PY - 2012 DA - 2012// TI - A polygonal finite element method for modeling arbitrary interfaces in large deformation problems JO - Comput Mech VL - 50 UR - https://doi.org/10.1007/s00466-011-0668-4 DO - 10.1007/s00466-011-0668-4 ID - Biabanaki2012 ER - TY - JOUR AU - Biabanaki, S. AU - Khoei, A. AU - Wriggers, P. PY - 2013 DA - 2013// TI - Polygonal finite element methods for contact-impact problems on non-conformal meshes JO - Comput Methods Appl Mech Eng VL - 269 UR - https://doi.org/10.1016/j.cma.2013.10.025 DO - 10.1016/j.cma.2013.10.025 ID - Biabanaki2013 ER - TY - JOUR AU - Sukumar, N. AU - Moran, B. AU - Belytschko, T. PY - 1998 DA - 1998// TI - The natural element method in solid mechanics JO - Int J Numer Methods Eng VL - 43 UR - https://doi.org/3.0.CO;2-R DO - 3.0.CO;2-R ID - Sukumar1998 ER - TY - JOUR AU - Sukumar, N. PY - 2013 DA - 2013// TI - Quadratic maximum-entropy serendipity shape functions for arbitrary planar polygons JO - Comput Methods Appl Mech Eng VL - 263 UR - https://doi.org/10.1016/j.cma.2013.04.009 DO - 10.1016/j.cma.2013.04.009 ID - Sukumar2013 ER - TY - JOUR AU - Natarajan, S. AU - Bordas, S. AU - Mahapatra, D. R. PY - 2009 DA - 2009// TI - Numerical integration over arbitrary polygonal domains based on Schwarz-Christoffel conformal mapping JO - Int J Numer Methods Eng VL - 80 UR - https://doi.org/10.1002/nme.2589 DO - 10.1002/nme.2589 ID - Natarajan2009 ER - TY - JOUR AU - Mousavi, S. AU - Xiao, H. AU - Sukumar, N. PY - 2010 DA - 2010// TI - Generalized Gaussian quadrature rules on arbitrary polygons JO - Int J Numer Methods Eng VL - 82 ID - Mousavi2010 ER - TY - STD TI - Talischi C, Paulino GH (2013) http://arxiv.org/pdf/1307.4423v1.pdf. (In review) UR - http://arxiv.org/pdf/1307.4423v1.pdf ID - ref15 ER - TY - STD TI - Fries T, Matthies H (2003) Classification and overview of meshfree methods. Tech. Rep. D38106, Institute of Scientific Computing, Technical University, Braunschweig, Hans-Sommer-Strasse ID - ref16 ER - TY - JOUR AU - Sukumar, N. AU - Malsch, E. PY - 2006 DA - 2006// TI - Recent advances in the construction of polygonal finite element interpolants JO - Arch Comput Methods Eng VL - 13 UR - https://doi.org/10.1007/BF02905933 DO - 10.1007/BF02905933 ID - Sukumar2006 ER - TY - JOUR AU - Sukumar, N. PY - 2003 DA - 2003// TI - Voronoi cell finite difference method for the diffusion operator on arbitrary unstructured grids JO - Int J Numer Methods Eng VL - 57 UR - https://doi.org/10.1002/nme.664 DO - 10.1002/nme.664 ID - Sukumar2003 ER - TY - JOUR AU - Rashid, M. AU - Gullet, P. PY - 2000 DA - 2000// TI - On a finite element method with variable element topology JO - Comput Methods Appl Mech Eng VL - 190 UR - https://doi.org/10.1016/S0045-7825(00)00175-4 DO - 10.1016/S0045-7825(00)00175-4 ID - Rashid2000 ER - TY - JOUR AU - Moorthy, S. AU - Ghosh, S. PY - 2000 DA - 2000// TI - Adaptivity and convergence in the Voronoi cell finite element model for analyzing heterogeneous materials JO - Comput Methods Appl Mech Eng VL - 185 UR - https://doi.org/10.1016/S0045-7825(99)00349-7 DO - 10.1016/S0045-7825(99)00349-7 ID - Moorthy2000 ER - TY - JOUR AU - Tiwary, A. AU - Hu, C. AU - Ghosh, S. PY - 2007 DA - 2007// TI - Numerical conformal mapping method based Voronoi cell finite element model for analyzing microstructures with irregular heterogeneities JO - Finite Elem Anal Design VL - 43 UR - https://doi.org/10.1016/j.finel.2006.12.005 DO - 10.1016/j.finel.2006.12.005 ID - Tiwary2007 ER - TY - JOUR AU - Liu, G. AU - Nguyen, T. AU - Dai, K. AU - Lam, K. PY - 2007 DA - 2007// TI - Theoretical aspects of the smoothed finite element method (SFEM) JO - Int J Numer Methods Eng VL - 71 UR - https://doi.org/10.1002/nme.1968 DO - 10.1002/nme.1968 ID - Liu2007 ER - TY - JOUR AU - Dai, K. AU - Liu, G. AU - Nguyen, T. PY - 2007 DA - 2007// TI - An n-sided polygonal smoothed finite element method (nSFEM) for solid mechanics JO - Finite Elem Anal Design VL - 43 UR - https://doi.org/10.1016/j.finel.2007.05.009 DO - 10.1016/j.finel.2007.05.009 ID - Dai2007 ER - TY - JOUR AU - Nguyen-Thoi, T. AU - Liu, G. AU - Nguyen-Xuan, H. PY - 2011 DA - 2011// TI - An n-sided polygonal edge-based smoothed finite element method (nES-FEM) for solid mechanics JO - Int J Numer Methods Eng VL - 27 ID - Nguyen-Thoi2011 ER - TY - JOUR AU - Wolf, J. AU - Song, C. PY - 2001 DA - 2001// TI - The scaled boundary finite-element method—a fundamental solution-less boundary—element method JO - Comput Methods Appl Mech Eng VL - 190 UR - https://doi.org/10.1016/S0045-7825(01)00183-9 DO - 10.1016/S0045-7825(01)00183-9 ID - Wolf2001 ER - TY - JOUR AU - Ooi, E. T. AU - Song, C. AU - Tin-Loi, F. AU - Yang, Z. PY - 2012 DA - 2012// TI - Polygon scaled boundary finite elements for crack propagation modelling JO - Int J Numer Methods Eng VL - 91 UR - https://doi.org/10.1002/nme.4284 DO - 10.1002/nme.4284 ID - Ooi2012 ER - TY - JOUR AU - Tang, X. AU - Wu, S. AU - Zheng, C. AU - Zhang, J. PY - 2009 DA - 2009// TI - A novel virtual node method for polygonal elements JO - Appl Math Mech VL - 30 UR - https://doi.org/10.1007/s10483-009-1003-3 DO - 10.1007/s10483-009-1003-3 ID - Tang2009 ER - TY - JOUR AU - Veiga, L. AU - Brezzi, F. AU - Cangiani, A. AU - Manzini, G. AU - Marini, L. AU - Russo, A. PY - 2013 DA - 2013// TI - Basic principles of virtual element methods JO - Math Models Methods Appl Sci VL - 23 UR - https://doi.org/10.1142/S0218202512500492 DO - 10.1142/S0218202512500492 ID - Veiga2013 ER - TY - JOUR AU - Qin, Q. PY - 2005 DA - 2005// TI - Trefftz finite element method and its applications JO - Appl Mech Rev VL - 58 UR - https://doi.org/10.1115/1.1995716 DO - 10.1115/1.1995716 ID - Qin2005 ER - TY - STD TI - Copeland D, Langer U, Pusch D (2009) In: Bercovier M, Gander M, Komhuber R, Widlund O (eds). Lecture notes in Computational Science and Engineering, vol. 70 ID - ref30 ER - TY - JOUR AU - Hofreither, C. AU - Langer, U. AU - Pechstein, C. PY - 2010 DA - 2010// TI - Analysis of a non-standard finite element method based on boundary integral operators JO - Elect Trans Num Anal VL - 37 ID - Hofreither2010 ER - TY - JOUR AU - Weißer, S. PY - 2011 DA - 2011// TI - Residual error estimate for BEM-based FEM on polygonal meshes JO - Numerische Math VL - 118 UR - https://doi.org/10.1007/s00211-011-0371-6 DO - 10.1007/s00211-011-0371-6 ID - Weißer2011 ER - TY - STD TI - Weißer S (2012) Finite element methods with local trefftz trial functions. Ph.D. thesis, Universität des Saarlandes, Saarbrücken ID - ref33 ER - TY - JOUR AU - Zienkiewicz, O. C. PY - 1997 DA - 1997// TI - Trefftz type approximation and the generalized finite element method—history and development JO - Comput Assis Mech Eng Sci VL - 4 ID - Zienkiewicz1997 ER - TY - JOUR AU - Piltner, R. PY - 1985 DA - 1985// TI - Special finite elements with holes and internal cracks JO - Int J Numer Methods Eng VL - 21 UR - https://doi.org/10.1002/nme.1620210809 DO - 10.1002/nme.1620210809 ID - Piltner1985 ER - TY - JOUR AU - Qin, Q. H. AU - He, X. Q. PY - 2009 DA - 2009// TI - Special elliptic hole elements of Trefftz FEM in stress concentration analysis JO - J Mech MEMS VL - 1 ID - Qin2009 ER - TY - JOUR AU - Jirousek, J. AU - Wróblewski, A. AU - Qin, Q. AU - He, X. PY - 1995 DA - 1995// TI - A family of quadrilateral hybrid-Trefftz p-elements for thick plate analysis JO - Comput Methods Appl Mech Eng VL - 127 UR - https://doi.org/10.1016/0045-7825(95)00842-5 DO - 10.1016/0045-7825(95)00842-5 ID - Jirousek1995 ER - TY - JOUR AU - Qin, Q. PY - 1995 DA - 1995// TI - Hybrid-Trefftz finite element method for Reissner plates on an elastic foundation JO - Comput Methods Appl Mech Eng VL - 122 UR - https://doi.org/10.1016/0045-7825(94)00730-B DO - 10.1016/0045-7825(94)00730-B ID - Qin1995 ER - TY - JOUR AU - Choo, Y. S. AU - Choi, N. AU - Lee, B. C. PY - 2010 DA - 2010// TI - A new hybrid-Trefftz triangular and quadrilateral plate elements JO - Appl Math Model VL - 34 UR - https://doi.org/10.1016/j.apm.2009.03.022 DO - 10.1016/j.apm.2009.03.022 ID - Choo2010 ER - TY - JOUR AU - Du, Q. AU - Wang, D. PY - 2005 DA - 2005// TI - Anisotropic centroidal Voronoi tessellations and their applications JO - SIAM J Sci Comput VL - 26 UR - https://doi.org/10.1137/S1064827503428527 DO - 10.1137/S1064827503428527 ID - Du2005 ER - TY - STD TI - Sieger D, Alliez P, Botsch M (2010) In: Proceedings of the 19th International Meshing Roundtable, pp. 335–350 ID - ref41 ER - TY - JOUR AU - Talischi, C. AU - Paulino, G. H. AU - Pereira, A. AU - Menezes, I. F. PY - 2012 DA - 2012// TI - PolyTop: a Matlab implementation of a general topology optimization framework using unstructured polygonal finite element meshes JO - Struct Multidiscip Optim VL - 45 UR - https://doi.org/10.1007/s00158-011-0696-x DO - 10.1007/s00158-011-0696-x ID - Talischi2012 ER -