Jaśkowiec, Jan; Sukumar, N. Penalty-free discontinuous Galerkin method. arXiv:2403.00125 Preprint, arXiv:2403.00125 [math.NA] (2024). BibTeX Cite \textit{J. Jaśkowiec} and \textit{N. Sukumar}, ``Penalty-free discontinuous Galerkin method'', Preprint, arXiv:2403.00125 [math.NA] (2024) Full Text: arXiv OA License
Chen, Alvin; Bishop, Joseph E.; Sukumar, N. Stress-hybrid virtual element method on six-noded triangular meshes for compressible and nearly-incompressible linear elasticity. arXiv:2401.06280 Preprint, arXiv:2401.06280 [math.NA] (2024). BibTeX Cite \textit{A. Chen} et al., ``Stress-hybrid virtual element method on six-noded triangular meshes for compressible and nearly-incompressible linear elasticity'', Preprint, arXiv:2401.06280 [math.NA] (2024) Full Text: arXiv OA License
Areias, P.; Sukumar, N.; Ambrósio, J. Continuous gap contact formulation based on the screened Poisson equation. (English) Zbl 07773244 Comput. Mech. 72, No. 4, 707-723 (2023). MSC: 74M15 74S05 PDFBibTeX XMLCite \textit{P. Areias} et al., Comput. Mech. 72, No. 4, 707--723 (2023; Zbl 07773244) Full Text: DOI arXiv OA License
Chen, Alvin; Sukumar, N. Stabilization-free virtual element method for plane elasticity. (English) Zbl 07692008 Comput. Math. Appl. 138, 88-105 (2023). MSC: 65N30 74S05 65N12 35J25 65D30 PDFBibTeX XMLCite \textit{A. Chen} and \textit{N. Sukumar}, Comput. Math. Appl. 138, 88--105 (2023; Zbl 07692008) Full Text: DOI arXiv
Chen, Alvin; Sukumar, N. Stabilization-free serendipity virtual element method for plane elasticity. (English) Zbl 07644857 Comput. Methods Appl. Mech. Eng. 404, Article ID 115784, 19 p. (2023). MSC: 74-XX 65-XX PDFBibTeX XMLCite \textit{A. Chen} and \textit{N. Sukumar}, Comput. Methods Appl. Mech. Eng. 404, Article ID 115784, 19 p. (2023; Zbl 07644857) Full Text: DOI arXiv
Dieci, Luca; Difonzo, Fabio V.; Sukumar, N. Nonnegative moment coordinates on finite element geometries. arXiv:2309.02441 Preprint, arXiv:2309.02441 [math.NA] (2023). BibTeX Cite \textit{L. Dieci} et al., ``Nonnegative moment coordinates on finite element geometries'', Preprint, arXiv:2309.02441 [math.NA] (2023) Full Text: arXiv OA License
Chen, Alvin; Sukumar, N. Stress-hybrid virtual element method on quadrilateral meshes for compressible and nearly-incompressible linear elasticity. arXiv:2304.04941 Preprint, arXiv:2304.04941 [math.NA] (2023). BibTeX Cite \textit{A. Chen} and \textit{N. Sukumar}, ``Stress-hybrid virtual element method on quadrilateral meshes for compressible and nearly-incompressible linear elasticity'', Preprint, arXiv:2304.04941 [math.NA] (2023) Full Text: arXiv OA License
Russo, Alessandro; Sukumar, N. Quantitative study of the stabilization parameter in the virtual element method. arXiv:2304.00063 Preprint, arXiv:2304.00063 [math.NA] (2023). BibTeX Cite \textit{A. Russo} and \textit{N. Sukumar}, ``Quantitative study of the stabilization parameter in the virtual element method'', Preprint, arXiv:2304.00063 [math.NA] (2023) Full Text: arXiv OA License
Sukumar, N.; Tupek, Michael R. Virtual elements on agglomerated finite elements to increase the critical time step in elastodynamic simulations. (English) Zbl 07769306 Int. J. Numer. Methods Eng. 123, No. 19, 4702-4725 (2022). MSC: 65M60 65N50 74B05 74J05 74S05 35Q74 PDFBibTeX XMLCite \textit{N. Sukumar} and \textit{M. R. Tupek}, Int. J. Numer. Methods Eng. 123, No. 19, 4702--4725 (2022; Zbl 07769306) Full Text: DOI arXiv
Kothiyal, Manuja; Kumar, Santosh; Sukumar, N. Investigation of chemical space networks using graph measures and random matrix theory. (English) Zbl 1492.92154 J. Math. Chem. 60, No. 5, 891-914 (2022). MSC: 92E10 05C92 60B20 PDFBibTeX XMLCite \textit{M. Kothiyal} et al., J. Math. Chem. 60, No. 5, 891--914 (2022; Zbl 1492.92154) Full Text: DOI
Benvenuti, E.; Chiozzi, A.; Manzini, G.; Sukumar, N. Extended virtual element method for two-dimensional linear elastic fracture. (English) Zbl 1507.74452 Comput. Methods Appl. Mech. Eng. 390, Article ID 114352, 32 p. (2022). MSC: 74S05 65N30 74A45 74B05 PDFBibTeX XMLCite \textit{E. Benvenuti} et al., Comput. Methods Appl. Mech. Eng. 390, Article ID 114352, 32 p. (2022; Zbl 1507.74452) Full Text: DOI arXiv
Sukumar, N.; Srivastava, Ankit Exact imposition of boundary conditions with distance functions in physics-informed deep neural networks. (English) Zbl 1507.65284 Comput. Methods Appl. Mech. Eng. 389, Article ID 114333, 50 p. (2022). MSC: 65N99 68T07 PDFBibTeX XMLCite \textit{N. Sukumar} and \textit{A. Srivastava}, Comput. Methods Appl. Mech. Eng. 389, Article ID 114333, 50 p. (2022; Zbl 1507.65284) Full Text: DOI arXiv
Berrone, S.; Canuto, C.; Pintore, M.; Sukumar, N. Enforcing Dirichlet boundary conditions in physics-informed neural networks and variational physics-informed neural networks. arXiv:2210.14795 Preprint, arXiv:2210.14795 [math.NA] (2022). MSC: 35A15 65L10 65L20 65K10 68T05 BibTeX Cite \textit{S. Berrone} et al., ``Enforcing Dirichlet boundary conditions in physics-informed neural networks and variational physics-informed neural networks'', Preprint, arXiv:2210.14795 [math.NA] (2022) Full Text: DOI arXiv OA License
Gladstone, Rini J.; Nabian, Mohammad A.; Sukumar, N.; Srivastava, Ankit; Meidani, Hadi FO-PINNs: A First-Order formulation for Physics Informed Neural Networks. arXiv:2210.14320 Preprint, arXiv:2210.14320 [cs.LG] (2022). BibTeX Cite \textit{R. J. Gladstone} et al., ``FO-PINNs: A First-Order formulation for Physics Informed Neural Networks'', Preprint, arXiv:2210.14320 [cs.LG] (2022) Full Text: arXiv OA License
Sukumar, N.; Bolander, John E. Virtual element method for modeling the deformation of multiphase composites. arXiv:2204.13191 Preprint, arXiv:2204.13191 [math.NA] (2022). BibTeX Cite \textit{N. Sukumar} and \textit{J. E. Bolander}, ``Virtual element method for modeling the deformation of multiphase composites'', Preprint, arXiv:2204.13191 [math.NA] (2022) Full Text: arXiv OA License
Chin, Eric B.; Mokhtari, Amir Ashkan; Srivastava, Ankit; Sukumar, N. Spectral extended finite element method for band structure calculations in phononic crystals. (English) Zbl 07510251 J. Comput. Phys. 427, Article ID 110066, 28 p. (2021). MSC: 74-XX 65-XX PDFBibTeX XMLCite \textit{E. B. Chin} et al., J. Comput. Phys. 427, Article ID 110066, 28 p. (2021; Zbl 07510251) Full Text: DOI arXiv
Chin, Eric B.; Sukumar, N. Scaled boundary cubature scheme for numerical integration over planar regions with affine and curved boundaries. (English) Zbl 1506.65047 Comput. Methods Appl. Mech. Eng. 380, Article ID 113796, 40 p. (2021). MSC: 65D30 PDFBibTeX XMLCite \textit{E. B. Chin} and \textit{N. Sukumar}, Comput. Methods Appl. Mech. Eng. 380, Article ID 113796, 40 p. (2021; Zbl 1506.65047) Full Text: DOI arXiv
Chin, Eric B.; Sukumar, N. An efficient method to integrate polynomials over polytopes and curved solids. (English) Zbl 1450.65027 Comput. Aided Geom. Des. 82, Article ID 101914, 19 p. (2020). MSC: 65D30 PDFBibTeX XMLCite \textit{E. B. Chin} and \textit{N. Sukumar}, Comput. Aided Geom. Des. 82, Article ID 101914, 19 p. (2020; Zbl 1450.65027) Full Text: DOI
Floater, Michael S. (ed.); Hormann, Kai (ed.); Sukumar, N. (ed.) Special issue on “Generalized barycentric coordinates”. (English) Zbl 1490.00033 Comput. Aided Geom. Des. 77, Article ID 101818, 1 p. (2020). MSC: 00B15 65-06 PDFBibTeX XMLCite \textit{M. S. Floater} (ed.) et al., Comput. Aided Geom. Des. 77, Article ID 101818, 1 p. (2020; Zbl 1490.00033) Full Text: DOI
Bishop, Joseph E.; Sukumar, N. Polyhedral finite elements for nonlinear solid mechanics using tetrahedral subdivisions and dual-cell aggregation. (English) Zbl 1470.74061 Comput. Aided Geom. Des. 77, Article ID 101812, 24 p. (2020). MSC: 74S05 74C15 PDFBibTeX XMLCite \textit{J. E. Bishop} and \textit{N. Sukumar}, Comput. Aided Geom. Des. 77, Article ID 101812, 24 p. (2020; Zbl 1470.74061) Full Text: DOI
Benvenuti, E.; Chiozzi, A.; Manzini, G.; Sukumar, N. Extended virtual element method for the Laplace problem with singularities and discontinuities. (English) Zbl 1441.74230 Comput. Methods Appl. Mech. Eng. 356, 571-597 (2019). MSC: 74S05 65N30 74R10 PDFBibTeX XMLCite \textit{E. Benvenuti} et al., Comput. Methods Appl. Mech. Eng. 356, 571--597 (2019; Zbl 1441.74230) Full Text: DOI Link
Silva-Valenzuela, R.; Ortiz-Bernardin, A.; Sukumar, N.; Artioli, E.; Hitschfeld-Kahler, N. A nodal integration scheme for meshfree Galerkin methods using the virtual element decomposition. arXiv:1907.00303 Preprint, arXiv:1907.00303 [math.NA] (2019). BibTeX Cite \textit{R. Silva-Valenzuela} et al., ``A nodal integration scheme for meshfree Galerkin methods using the virtual element decomposition'', Preprint, arXiv:1907.00303 [math.NA] (2019) Full Text: DOI arXiv OA License
Albrecht, Clelia; Klaar, Constanze; Pask, John Ernest; Schweitzer, Marc Alexander; Sukumar, N.; Ziegenhagel, Albert Orbital-enriched flat-top partition of unity method for the Schrödinger eigenproblem. (English) Zbl 1440.65163 Comput. Methods Appl. Mech. Eng. 342, 224-239 (2018). MSC: 65N25 81Q05 PDFBibTeX XMLCite \textit{C. Albrecht} et al., Comput. Methods Appl. Mech. Eng. 342, 224--239 (2018; Zbl 1440.65163) Full Text: DOI arXiv
Cai, Yunfeng; Bai, Zhaojun; Pask, John E.; Sukumar, N. Convergence analysis of a locally accelerated preconditioned steepest descent method for Hermitian-definite generalized eigenvalue problems. (English) Zbl 1424.65039 J. Comput. Math. 36, No. 5, 739-760 (2018). MSC: 65F15 65F08 PDFBibTeX XMLCite \textit{Y. Cai} et al., J. Comput. Math. 36, No. 5, 739--760 (2018; Zbl 1424.65039) Full Text: DOI arXiv
Hormann, Kai (ed.); Sukumar, N. (ed.) Generalized barycentric coordinates in computer graphics and computational mechanics. (English) Zbl 1377.68003 Boca Raton, FL: CRC Press (ISBN 978-1-4987-6359-2/hbk; 978-1-4987-6361-5/ebook). xx, 314 p. (2018). MSC: 68-02 68-06 65-02 65-06 74-02 74-06 65D18 68U05 74S99 00B15 PDFBibTeX XMLCite \textit{K. Hormann} (ed.) and \textit{N. Sukumar} (ed.), Generalized barycentric coordinates in computer graphics and computational mechanics. Boca Raton, FL: CRC Press (2018; Zbl 1377.68003) Full Text: Link
Banerjee, Subhajit; Sukumar, N. Exact integration scheme for planewave-enriched partition of unity finite element method to solve the Helmholtz problem. (English) Zbl 1439.78016 Comput. Methods Appl. Mech. Eng. 317, 619-648 (2017). MSC: 78M10 65N30 74J20 76Q05 76M10 PDFBibTeX XMLCite \textit{S. Banerjee} and \textit{N. Sukumar}, Comput. Methods Appl. Mech. Eng. 317, 619--648 (2017; Zbl 1439.78016) Full Text: DOI
Ortiz-Bernardin, A.; Puso, M. A.; Sukumar, N. Improved robustness for nearly-incompressible large deformation meshfree simulations on Delaunay tessellations. (English) Zbl 1423.74962 Comput. Methods Appl. Mech. Eng. 293, 348-374 (2015). MSC: 74S30 65N35 74B20 PDFBibTeX XMLCite \textit{A. Ortiz-Bernardin} et al., Comput. Methods Appl. Mech. Eng. 293, 348--374 (2015; Zbl 1423.74962) Full Text: DOI
Millán, Daniel; Sukumar, N.; Arroyo, Marino Cell-based maximum-entropy approximants. (English) Zbl 1425.65172 Comput. Methods Appl. Mech. Eng. 284, 712-731 (2015). MSC: 65N30 65N50 74B05 PDFBibTeX XMLCite \textit{D. Millán} et al., Comput. Methods Appl. Mech. Eng. 284, 712--731 (2015; Zbl 1425.65172) Full Text: DOI
Cangiani, A.; Manzini, G.; Russo, A.; Sukumar, N. Hourglass stabilization and the virtual element method. (English) Zbl 1352.65475 Int. J. Numer. Methods Eng. 102, No. 3-4, 404-436 (2015). MSC: 65N30 65N12 PDFBibTeX XMLCite \textit{A. Cangiani} et al., Int. J. Numer. Methods Eng. 102, No. 3--4, 404--436 (2015; Zbl 1352.65475) Full Text: DOI
Chin, Eric B.; Lasserre, Jean B.; Sukumar, N. Numerical integration of homogeneous functions on convex and nonconvex polygons and polyhedra. (English) Zbl 1336.65020 Comput. Mech. 56, No. 6, 967-981 (2015). MSC: 65D30 PDFBibTeX XMLCite \textit{E. B. Chin} et al., Comput. Mech. 56, No. 6, 967--981 (2015; Zbl 1336.65020) Full Text: DOI HAL
Manzini, Gianmarco; Russo, Alessandro; Sukumar, N. New perspectives on polygonal and polyhedral finite element methods. (English) Zbl 1291.65322 Math. Models Methods Appl. Sci. 24, No. 8, 1665-1699 (2014). MSC: 65N06 65N12 65F05 PDFBibTeX XMLCite \textit{G. Manzini} et al., Math. Models Methods Appl. Sci. 24, No. 8, 1665--1699 (2014; Zbl 1291.65322) Full Text: DOI
Floater, Michael; Gillette, Andrew; Sukumar, N. Gradient bounds for Wachspress coordinates on polytopes. (English) Zbl 1292.65006 SIAM J. Numer. Anal. 52, No. 1, 515-532 (2014). Reviewer: Martin D. Buhmann (Gießen) MSC: 65D05 41A25 41A30 65N30 35J05 PDFBibTeX XMLCite \textit{M. Floater} et al., SIAM J. Numer. Anal. 52, No. 1, 515--532 (2014; Zbl 1292.65006) Full Text: DOI arXiv
Cai, Yunfeng; Bai, Zhaojun; Pask, John E.; Sukumar, N. Hybrid preconditioning for iterative diagonalization of ill-conditioned generalized eigenvalue problems in electronic structure calculations. (English) Zbl 1349.81204 J. Comput. Phys. 255, 16-30 (2013). MSC: 81V55 PDFBibTeX XMLCite \textit{Y. Cai} et al., J. Comput. Phys. 255, 16--30 (2013; Zbl 1349.81204) Full Text: DOI arXiv
Hattori, G.; Rojas-Díaz, R.; Sáez, A.; Sukumar, N.; García-Sánchez, F. New anisotropic crack-tip enrichment functions for the extended finite element method. (English) Zbl 1312.74029 Comput. Mech. 50, No. 5, 591-601 (2012). MSC: 74R10 74S05 74E10 74G70 PDFBibTeX XMLCite \textit{G. Hattori} et al., Comput. Mech. 50, No. 5, 591--601 (2012; Zbl 1312.74029) Full Text: DOI
Mousavi, S. E.; Pask, J. E.; Sukumar, N. Efficient adaptive integration of functions with sharp gradients and cusps in \(n\)-dimensional parallelepipeds. (English) Zbl 1253.65034 Int. J. Numer. Methods Eng. 91, No. 4, 343-357 (2012). MSC: 65D30 PDFBibTeX XMLCite \textit{S. E. Mousavi} et al., Int. J. Numer. Methods Eng. 91, No. 4, 343--357 (2012; Zbl 1253.65034) Full Text: DOI arXiv
Rojas-Díaz, R.; Sukumar, N.; Sáez, A.; García-Sánchez, F. Fracture in magnetoelectroelastic materials using the extended finite element method. (English) Zbl 1242.74157 Int. J. Numer. Methods Eng. 88, No. 12, 1238-1259 (2011). MSC: 74S05 74R10 74F15 PDFBibTeX XMLCite \textit{R. Rojas-Díaz} et al., Int. J. Numer. Methods Eng. 88, No. 12, 1238--1259 (2011; Zbl 1242.74157) Full Text: DOI
Mousavi, S. E.; Grinspun, E.; Sukumar, N. Harmonic enrichment functions: a unified treatment of multiple, intersecting and branched cracks in the extended finite element method. (English) Zbl 1217.74130 Int. J. Numer. Methods Eng. 85, No. 10, 1306-1322 (2011). MSC: 74S05 74R10 74G70 PDFBibTeX XMLCite \textit{S. E. Mousavi} et al., Int. J. Numer. Methods Eng. 85, No. 10, 1306--1322 (2011; Zbl 1217.74130) Full Text: DOI Link
Mousavi, S. E.; Grinspun, E.; Sukumar, N. Higher-order extended finite elements with harmonic enrichment functions for complex crack problems. (English) Zbl 1216.74027 Int. J. Numer. Methods Eng. 86, No. 4-5, 560-574 (2011). MSC: 74S05 74R10 PDFBibTeX XMLCite \textit{S. E. Mousavi} et al., Int. J. Numer. Methods Eng. 86, No. 4--5, 560--574 (2011; Zbl 1216.74027) Full Text: DOI
Mousavi, S. E.; Sukumar, N. Numerical integration of polynomials and discontinuous functions on irregular convex polygons and polyhedrons. (English) Zbl 1221.65078 Comput. Mech. 47, No. 5, 535-554 (2011). MSC: 65D30 PDFBibTeX XMLCite \textit{S. E. Mousavi} and \textit{N. Sukumar}, Comput. Mech. 47, No. 5, 535--554 (2011; Zbl 1221.65078) Full Text: DOI
Ortiz, A.; Puso, M. A.; Sukumar, N. Maximum-entropy meshfree method for compressible and near-incompressible elasticity. (English) Zbl 1231.74491 Comput. Methods Appl. Mech. Eng. 199, No. 25-28, 1859-1871 (2010). MSC: 74S30 74B05 PDFBibTeX XMLCite \textit{A. Ortiz} et al., Comput. Methods Appl. Mech. Eng. 199, No. 25--28, 1859--1871 (2010; Zbl 1231.74491) Full Text: DOI
Mousavi, S. E.; Sukumar, N. Generalized Gaussian quadrature rules for discontinuities and crack singularities in the extended finite element method. (English) Zbl 1225.74099 Comput. Methods Appl. Mech. Eng. 199, No. 49-52, 3237-3249 (2010). MSC: 74S05 74G70 74R10 PDFBibTeX XMLCite \textit{S. E. Mousavi} and \textit{N. Sukumar}, Comput. Methods Appl. Mech. Eng. 199, No. 49--52, 3237--3249 (2010; Zbl 1225.74099) Full Text: DOI
Mousavi, S. E.; Xiao, H.; Sukumar, N. Generalized Gaussian quadrature rules on arbitrary polygons. (English) Zbl 1183.65026 Int. J. Numer. Methods Eng. 82, No. 1, 99-113 (2010). MSC: 65D32 PDFBibTeX XMLCite \textit{S. E. Mousavi} et al., Int. J. Numer. Methods Eng. 82, No. 1, 99--113 (2010; Zbl 1183.65026) Full Text: DOI
Yaw, L. L.; Sukumar, N.; Kunnath, S. K. Meshfree co-rotational formulation for two-dimensional continua. (English) Zbl 1171.74469 Int. J. Numer. Methods Eng. 79, No. 8, 979-1003 (2009). MSC: 74S30 74K10 PDFBibTeX XMLCite \textit{L. L. Yaw} et al., Int. J. Numer. Methods Eng. 79, No. 8, 979--1003 (2009; Zbl 1171.74469) Full Text: DOI
Aquino, W.; Brigham, J. C.; Earls, C. J.; Sukumar, N. Generalized finite element method using proper orthogonal decomposition. (English) Zbl 1171.76416 Int. J. Numer. Methods Eng. 79, No. 7, 887-906 (2009). MSC: 76M10 76Q05 65N30 PDFBibTeX XMLCite \textit{W. Aquino} et al., Int. J. Numer. Methods Eng. 79, No. 7, 887--906 (2009; Zbl 1171.76416) Full Text: DOI
Sukumar, N.; Pask, J. E. Classical and enriched finite element formulations for Bloch-periodic boundary conditions. (English) Zbl 1156.81313 Int. J. Numer. Methods Eng. 77, No. 8, 1121-1138 (2009). MSC: 81-08 35Q55 81T80 PDFBibTeX XMLCite \textit{N. Sukumar} and \textit{J. E. Pask}, Int. J. Numer. Methods Eng. 77, No. 8, 1121--1138 (2009; Zbl 1156.81313) Full Text: DOI
Giner, E.; Sukumar, N.; Fuenmayor, F. J.; Vercher, A. Singularity enrichment for complete sliding contact using the partition of unity finite element method. (English) Zbl 1195.74174 Int. J. Numer. Methods Eng. 76, No. 9, 1402-1418 (2008). MSC: 74S05 74M15 PDFBibTeX XMLCite \textit{E. Giner} et al., Int. J. Numer. Methods Eng. 76, No. 9, 1402--1418 (2008; Zbl 1195.74174) Full Text: DOI
Sukumar, N.; Chopp, D. L.; Béchet, E.; Moës, N. Three-dimensional non-planar crack growth by a coupled extended finite element and fast marching method. (English) Zbl 1195.76390 Int. J. Numer. Methods Eng. 76, No. 5, 727-748 (2008). MSC: 76S05 76R10 PDFBibTeX XMLCite \textit{N. Sukumar} et al., Int. J. Numer. Methods Eng. 76, No. 5, 727--748 (2008; Zbl 1195.76390) Full Text: DOI
Tabarraei, A.; Sukumar, N. Extended finite element method on polygonal and quadtree meshes. (English) Zbl 1169.74634 Comput. Methods Appl. Mech. Eng. 197, No. 5, 425-438 (2008). MSC: 74S05 74R10 PDFBibTeX XMLCite \textit{A. Tabarraei} and \textit{N. Sukumar}, Comput. Methods Appl. Mech. Eng. 197, No. 5, 425--438 (2008; Zbl 1169.74634) Full Text: DOI Link
Giner, E.; Sukumar, N.; Denia, F. D.; Fuenmayor, F. J. Extended finite element method for fretting fatigue crack propagation. (English) Zbl 1177.74364 Int. J. Solids Struct. 45, No. 22-23, 5675-5687 (2008). MSC: 74S05 74R10 74G70 74M15 PDFBibTeX XMLCite \textit{E. Giner} et al., Int. J. Solids Struct. 45, No. 22--23, 5675--5687 (2008; Zbl 1177.74364) Full Text: DOI
Sukumar, N.; Wright, R. W. Overview and construction of meshfree basis functions: from moving least squares to entropy approximants. (English) Zbl 1194.65149 Int. J. Numer. Methods Eng. 70, No. 2, 181-205 (2007). MSC: 65N99 65-02 PDFBibTeX XMLCite \textit{N. Sukumar} and \textit{R. W. Wright}, Int. J. Numer. Methods Eng. 70, No. 2, 181--205 (2007; Zbl 1194.65149) Full Text: DOI
Tabarraei, A.; Sukumar, N. Adaptive computations using material forces and residual-based error estimators on quadtree meshes. (English) Zbl 1173.74444 Comput. Methods Appl. Mech. Eng. 196, No. 25-28, 2657-2680 (2007). MSC: 74S05 PDFBibTeX XMLCite \textit{A. Tabarraei} and \textit{N. Sukumar}, Comput. Methods Appl. Mech. Eng. 196, No. 25--28, 2657--2680 (2007; Zbl 1173.74444) Full Text: DOI Link
Sukumar, N.; Wets, R. J.-B. Deriving the continuity of maximum-entropy basis functions via variational analysis. (English) Zbl 1157.65042 SIAM J. Optim. 18, No. 3, 914-925 (2007). Reviewer: Akrur Behera (Rourkela) MSC: 65K10 90C25 65N30 49J53 PDFBibTeX XMLCite \textit{N. Sukumar} and \textit{R. J. B. Wets}, SIAM J. Optim. 18, No. 3, 914--925 (2007; Zbl 1157.65042) Full Text: DOI
Tabarraei, A.; Sukumar, N. Application of polygonal finite elements in linear elasticity. (English) Zbl 1198.74104 Int. J. Comput. Methods 3, No. 4, 503-520 (2006). MSC: 74S05 74B05 PDFBibTeX XMLCite \textit{A. Tabarraei} and \textit{N. Sukumar}, Int. J. Comput. Methods 3, No. 4, 503--520 (2006; Zbl 1198.74104) Full Text: DOI
Sukumar, N.; Malsch, E. A. Recent advances in the construction of polygonal finite element interpolants. (English) Zbl 1101.65108 Arch. Comput. Methods Eng. 13, No. 1, 129-163 (2006). MSC: 65N30 65N50 65-02 65D18 35J05 65N15 PDFBibTeX XMLCite \textit{N. Sukumar} and \textit{E. A. Malsch}, Arch. Comput. Methods Eng. 13, No. 1, 129--163 (2006; Zbl 1101.65108) Full Text: DOI
Sukumar, N.; Srolovitz, D. J. Finite element-based model for crack propagation in polycrystalline materials. (English) Zbl 1213.74269 Comput. Appl. Math. 23, No. 2-3, 363-380 (2004). MSC: 74R10 74S05 PDFBibTeX XMLCite \textit{N. Sukumar} and \textit{D. J. Srolovitz}, Comput. Appl. Math. 23, No. 2--3, 363--380 (2004; Zbl 1213.74269) Full Text: Link
Sukumar, N.; Tabarraei, A. Conforming polygonal finite elements. (English) Zbl 1073.65563 Int. J. Numer. Methods Eng. 61, No. 12, 2045-2066 (2004). MSC: 65N30 65N12 65N50 35J25 PDFBibTeX XMLCite \textit{N. Sukumar} and \textit{A. Tabarraei}, Int. J. Numer. Methods Eng. 61, No. 12, 2045--2066 (2004; Zbl 1073.65563) Full Text: DOI
Sukumar, N.; Huang, Z. Y.; Prévost, J.-H.; Suo, Z. Partition of unity enrichment for bimaterial interface cracks. (English) Zbl 1041.74548 Int. J. Numer. Methods Eng. 59, No. 8, 1075-1102 (2004). MSC: 74S05 74R10 PDFBibTeX XMLCite \textit{N. Sukumar} et al., Int. J. Numer. Methods Eng. 59, No. 8, 1075--1102 (2004; Zbl 1041.74548) Full Text: DOI
Chopp, D. L.; Sukumar, N. Fatigue crack propagation of multiple coplanar cracks with the coupled extended finite element/fast marching method. (English) Zbl 1211.74199 Int. J. Eng. Sci. 41, No. 8, 845-869 (2003). MSC: 74S05 74R10 65N30 PDFBibTeX XMLCite \textit{D. L. Chopp} and \textit{N. Sukumar}, Int. J. Eng. Sci. 41, No. 8, 845--869 (2003; Zbl 1211.74199) Full Text: DOI
Sukumar, N.; Bolander, J. E. Numerical computation of discrete differential operators on non-uniform grids. (English) Zbl 1062.65112 CMES, Comput. Model. Eng. Sci. 4, No. 6, 691-705 (2003). MSC: 65N06 65N12 65N50 35J05 PDFBibTeX XMLCite \textit{N. Sukumar} and \textit{J. E. Bolander}, CMES, Comput. Model. Eng. Sci. 4, No. 6, 691--705 (2003; Zbl 1062.65112)
Cueto, E.; Sukumar, N.; Calvo, B.; Martínez, M. A.; Cegoñino, J.; Doblaré, M. Overview and recent advances in natural neighbour Galerkin methods. (English) Zbl 1050.74001 Arch. Comput. Methods Eng. 10, No. 4, 307-384 (2003). MSC: 74-02 74S30 74S05 PDFBibTeX XMLCite \textit{E. Cueto} et al., Arch. Comput. Methods Eng. 10, No. 4, 307--384 (2003; Zbl 1050.74001) Full Text: DOI
Huang, R.; Sukumar, N.; Prévost, J.-H. Modeling quasi-static crack growth with the extended finite element method. II: Numerical applications. (English) Zbl 1064.74163 Int. J. Solids Struct. 40, No. 26, 7539-7552 (2003). Reviewer: Messoud A. Efendiev (Berlin) MSC: 74S05 74R10 PDFBibTeX XMLCite \textit{R. Huang} et al., Int. J. Solids Struct. 40, No. 26, 7539--7552 (2003; Zbl 1064.74163) Full Text: DOI
Sukumar, N.; Prévost, J.-H. Modeling quasi-static crack growth with the extended finite element method. I: Computer implementation. (English) Zbl 1063.74102 Int. J. Solids Struct. 40, No. 26, 7513-7537 (2003). Reviewer: Messoud A. Efendiev (Berlin) MSC: 74S05 74R10 PDFBibTeX XMLCite \textit{N. Sukumar} and \textit{J. H. Prévost}, Int. J. Solids Struct. 40, No. 26, 7513--7537 (2003; Zbl 1063.74102) Full Text: DOI
Sukumar, N.; Srolovitz, D. J.; Baker, T. J.; Prévost, J.-H. Brittle fracture in polycrystalline microstructures with the extended finite element method. (English) Zbl 1038.74652 Int. J. Numer. Methods Eng. 56, No. 14, 2015-2037 (2003). MSC: 74S05 74R10 PDFBibTeX XMLCite \textit{N. Sukumar} et al., Int. J. Numer. Methods Eng. 56, No. 14, 2015--2037 (2003; Zbl 1038.74652) Full Text: DOI
Belytschko, Ted; Parimi, Chandu; Moës, Nicolas; Sukumar, N.; Usui, Shuji Structured extended finite element methods for solids defined by implicit surfaces. (English) Zbl 1038.74041 Int. J. Numer. Methods Eng. 56, No. 4, 609-635 (2003). MSC: 74S05 PDFBibTeX XMLCite \textit{T. Belytschko} et al., Int. J. Numer. Methods Eng. 56, No. 4, 609--635 (2003; Zbl 1038.74041) Full Text: DOI
Sukumar, N.; Chopp, D. L.; Moës, N.; Belytschko, T. Modeling holes and inclusions by level sets in the extended finite element method. (English) Zbl 1029.74049 Comput. Methods Appl. Mech. Eng. 190, No. 46-47, 6183-6200 (2001). MSC: 74S05 74B05 74E05 PDFBibTeX XMLCite \textit{N. Sukumar} et al., Comput. Methods Appl. Mech. Eng. 190, No. 46--47, 6183--6200 (2001; Zbl 1029.74049) Full Text: DOI
Sukumar, N.; Moran, B.; Semenov, A. Yu.; Belikov, V. V. Natural neighbor Galerkin methods. (English) Zbl 1082.74554 Int. J. Numer. Methods Eng. 50, No. 1, 1-27 (2001). MSC: 74S05 74K99 65D05 PDFBibTeX XMLCite \textit{N. Sukumar} et al., Int. J. Numer. Methods Eng. 50, No. 1, 1--27 (2001; Zbl 1082.74554) Full Text: DOI
Daux, Christophe; Moës, Nicolas; Dolbow, John; Sukumar, Natarajan; Belytschko, Ted Arbitrary branched and intersecting cracks with the extended finite element method. (English) Zbl 0989.74066 Int. J. Numer. Methods Eng. 48, No. 12, 1741-1760 (2000). MSC: 74S05 74R10 74G70 PDFBibTeX XMLCite \textit{C. Daux} et al., Int. J. Numer. Methods Eng. 48, No. 12, 1741--1760 (2000; Zbl 0989.74066) Full Text: DOI
Sukumar, N.; Moës, N.; Moran, B.; Belytschko, T. Extended finite element method for three-dimensional crack modelling. (English) Zbl 0963.74067 Int. J. Numer. Methods Eng. 48, No. 11, 1549-1570 (2000). MSC: 74S05 74R10 74G70 PDFBibTeX XMLCite \textit{N. Sukumar} et al., Int. J. Numer. Methods Eng. 48, No. 11, 1549--1570 (2000; Zbl 0963.74067) Full Text: DOI
Bueche, D.; Sukumar, N.; Moran, B. Dispersive properties of the natural element method. (English) Zbl 0969.74075 Comput. Mech. 25, No. 2-3, 207-219 (2000). MSC: 74S30 74S05 74H15 74K10 74J05 PDFBibTeX XMLCite \textit{D. Bueche} et al., Comput. Mech. 25, No. 2--3, 207--219 (2000; Zbl 0969.74075) Full Text: DOI
Sukumar, N.; Moran, B. \(C^1\) natural neighbor interpolant for partial differential equations. (English) Zbl 0943.74080 Numer. Methods Partial Differ. Equations 15, No. 4, 417-447 (1999). Reviewer: Ladislav Prášek (Plzeň) MSC: 74S30 65D05 65N55 PDFBibTeX XMLCite \textit{N. Sukumar} and \textit{B. Moran}, Numer. Methods Partial Differ. Equations 15, No. 4, 417--447 (1999; Zbl 0943.74080) Full Text: DOI
Sukumar, N.; Moran, B.; Belytschko, T. The natural element method in solid mechanics. (English) Zbl 0940.74078 Int. J. Numer. Methods Eng. 43, No. 5, 839-887 (1998). Reviewer: Ladislav Prasek (Plzeň) MSC: 74S30 74S05 PDFBibTeX XMLCite \textit{N. Sukumar} et al., Int. J. Numer. Methods Eng. 43, No. 5, 839--887 (1998; Zbl 0940.74078) Full Text: DOI
Sukumar, N.; Moran, B.; Black, T.; Belytschko, T. An element-free Galerkin method for three-dimensional fracture mechanics. (English) Zbl 0888.73066 Comput. Mech. 20, No. 1-2, 170-175 (1997). MSC: 74S05 74R99 PDFBibTeX XMLCite \textit{N. Sukumar} et al., Comput. Mech. 20, No. 1--2, 170--175 (1997; Zbl 0888.73066) Full Text: DOI