N. Sukumar's Publications Google scholar

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• 2023 • 2022 • 2021 • 2020 • 2019 • 2018 • 2017 • 2016 • 2015 • 2014 • 2013 • 2012 • 2011 • 2010 • 2009 • 2008 • 2007 • 2006 • 2005 • 2004 • 2003 • 2002 • 2001 • 2000 • 1999 • 1998 • 1997 • 1996 • 1993 • 1992 •

2023

• P. Areias, N. Sukumar, and J. Ambrósio. Continuous gap contact formulation based on the screened Poisson equation. Computational Mechanics, 2023. in press
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• A. Chen and N. Sukumar. Stress-hybrid virtual element method on quadrilateral meshes for compressible and nearly-incompressible linear elasticity. arXiv: 2304.04941, 2023.
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• A. Chen and N. Sukumar. Stabilization-free serendipity virtual element method for plane elasticity. Computer Methods in Applied Mechanics and Engineering, 138:88–105, 2023.
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• A. Chen and N. Sukumar. Stabilization-free virtual element method for plane elasticity. Computers and Mathematics with Applications, 138:88–105, 2023.
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• A. Russo and N. Sukumar. Quantitative study of the stabilization parameter in the virtual element method. arXiv: 2304.00063, 2023.
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2022

• E. Benvenuti, A. Chiozzi, G. Manzini, and N. Sukumar. Extended virtual element method for two-dimensional linear elastic fracture. Computer Methods in Applied Mechanics and Engineering, 390:114352, 2022.
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• S. Berrone, C. Canuto, M. Pintore, and N. Sukumar. Enforcing Dirichlet boundary conditions in physics-informed neural networks and variational physics-informed neural networks. arXiv: 2210.14795, 2022.
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• N. Sukumar and J. E. Bolander. Virtual element method for modeling the deformation of multiphase composites. Mechanics Research Communications, 124:103907, 2022.
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• N. Sukumar and M. R. Tupek. Virtual elements on agglomerated finite elements to increase the critical time step in elastodynamic simulations. International Journal for Numerical Methods in Engineering, 123(19):4702–4725, 2022.
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• N. Sukumar and A. Srivastava. Exact imposition of boundary conditions with distance functions in physics-informed deep neural networks. Computer Methods in Applied Mechanics and Engineering, 389:114333, 2022.
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2021

• E. B. Chin and N. Sukumar. Scaled boundary cubature scheme for numerical integration over planar regions with affine and curved boundaries. Computer Methods in Applied Mechanics and Engineering, 380:110066, 2021.
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• E. B. Chin, A. A. Mokhtari, A. Srivastava, and N. Sukumar. Spectral extended finite element method for band structure calculations in phononic crystals. Journal of Computational Physics, 427:110066, 2021.
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• J. Ja\'skowiec and N. Sukumar. Addendum to the paper “High-order symmetric cubature rules for tetrahedra and pyramids”. International Journal for Numerical Methods in Engineering, 122(7):1875–1883, 2021.
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• J. Ja\'skowiec and N. Sukumar. High-order symmetric cubature rules for tetrahedra and pyramids. International Journal for Numerical Methods in Engineering, 122(1):148–171, 2021.
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2020

• J. E. Bishop and N. Sukumar. Polyhedral finite elements for nonlinear solid mechanics using tetrahedral subdivisons and dual-cell aggregation. Computer Aided Geometric Design, 77:101812, 2020.
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• E. B. Chin and N. Sukumar. An efficient method to integrate polynomials over polytopes and curved solids. Computer Aided Geometric Design, 82:101914, 2020.
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• J. Ja\'skowiec and N. Sukumar. High-order cubature rules for tetrahedra. International Journal for Numerical Methods in Engineering, 121(11):2418–2436, 2020.
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• R. Silva-Valenzuela, A. Ortiz-Bernardin, N. Sukumar, E. Artioli, and N. Hitschfeld-Kahler. A nodal integration scheme for meshfree Galerkin methods using the virtual element decomposition. International Journal for Numerical Methods in Engineering, 121(10):2174–2205, 2020.
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2019

• E. Benvenuti, A. Chiozzi, G. Manzini, and N. Sukumar. Extended virtual element method for the Laplace problem with singularities and discontinuities. Computer Methods in Applied Mechanics and Engineering, 356:571–597, 2019.
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• E. B. Chin and N. Sukumar. Modeling curved interfaces without element-partitioning in the extended finite element method. International Journal for Numerical Methods in Engineering, 120(5):607–649, 2019.
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• C. Liu, J. H. Prévost, and N. Sukumar. Modeling branched and intersecting faults in reservoir-geomechanics models with the extended finite element method. International Journal for Numerical and Analytical Methods in Geomechanics, 43(12):2075–2089, 2019.
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• C. Liu, J. H. Prévost, and N. Sukumar. Modeling piecewise planar faults without element-partitioning in 3D reservoir-geomechanical models. International Journal for Numerical and Analytical Methods in Geomechanics, 43(2):530–543, 2019.
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2018

• C. Albrecht, C. Klaar, J. E. Pask, M. A. Schweitzer, N. Sukumar, and A. Ziegenhagel. Orbital-enriched flat-top partition of unity method for the Schrödinger eigenproblem. Computer Methods in Applied Mechanics and Engineering, 342:224–239, 2018.
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• Y. Cai, Z. Bai, J. E. Pask, and N. Sukumar. Convergence analysis of a locally accelerated preconditioned steepest descent method for Hermitian-definite generalized eigenvalue problems. Journal of Computational Mathematics, 36(5):739–760, 2018.
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• E. B. Chin, J. E. Bishop, R. V. Garimella, and N. Sukumar. Finite deformation cohesive polygonal finite elements for modeling pervasive fracture. International Journal of Fracture, 214(2):139–165, 2018.
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• N. Moës, J. E. Dolbow, and N. Sukumar. Extended finite element methods. In Encyclopedia of Computational Mechanics, John Wiley & Sons, 2018.
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2017

• S. Banerjee and N. Sukumar. Exact integration scheme for planewave-enriched partition of unity finite element method for the Helmholtz problem. Computer Methods in Applied Mechanics and Engineering, 317:619–648, 2017.
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• E. B. Chin, J. B. Lasserre, and N. Sukumar. Modeling crack discontinuities without element-partitioning in the extended finite element method. International Journal for Numerical Methods in Engineering, 86(11):1021–1048, 2017.
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• K. Hormann and N. Sukumar, editors. Generalized Barycentric Coordinates in Computer Graphics and Computational Mechanics, CRC Press, Boca Raton, FL, 2017.
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• A. Ortiz-Bernardin, A. Russo, and N. Sukumar. Consistent and stable meshfree Galerkin methods using the virtual element decomposition. International Journal for Numerical Methods in Engineering, 112(7):655–684, 2017.
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• J. E. Pask and N. Sukumar. Partition of unity finite element method for quantum mechanical materials calculations. Extreme Mechanics Letters, 11:8–17, 2017.
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• J.-H. Prévost, A. M. Rubin, and N. Sukumar. Intersecting faults for three-dimensional reservoir-geomechanical models. In Sixth Biot Conference on Poromechanics, American Society of Civil Engineers, Paris, France, 2017.
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2016

• J.-H. Prévost and N. Sukumar. Faults simulations for three-dimensional reservoir-geomechanical models with the extended finite element method. Journal of the Mechanics and Physics of Solids, 86:1–18, 2016.
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2015

• A. Cangiani, G. Manzini, A. Russo, and N. Sukumar. Hourglass stabilization and the virtual element method. International Journal for Numerical Methods in Engineering, 102(3--4):404–436, 2015.
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• E. B. Chin, J. B. Lasserre, and N. Sukumar. Numerical integration of homogeneous functions on convex and nonconvex polygons and polyhedra. Computational Mechanics, 56(6):967–981, 2015.
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• D. Millán, N. Sukumar, and M. Arroyo. Cell-based maximum-entropy approximants. Computer Methods in Applied Mechanics and Engineering, 284:712–731, 2015.
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• A. Ortiz-Bernardin, M. A. Puso, and N. Sukumar. Improved robustness for nearly-incompressible large deformation meshfree simulations on Delaunay tessellations. Computer Methods in Applied Mechanics and Engineering, 293:348–374, 2015.
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• J.-H. Prévost and N. Sukumar. Multi-scale X-FEM faults simulations for reservoir-geomechanical models. In 49th US Rock Mechanics/Geomechanics Symposium, American Rock Mechanics Association, San Francisco, CA, 2015.
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• N. Sukumar, J. E. Dolbow, and N. Moës. Extended finite element method in computational fracture mechanics: a retrospective examination. International Journal of Fracture, 196(1--2):189–206, 2015.
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2014

• M. Floater, A. Gillette, and N. Sukumar. Gradient bounds for Wachspress coordinates on polytopes. SIAM Journal on Numerical Analysis, 52(1):515–532, 2014.
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• G. Manzini, A. Russo, and Sukumar. New perspectives on polygonal and polyhedral finite element methods. Mathematical Methods Models and Sciences, 24(8):1665–1699, 2014.
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2013

• Y. Cai, Z. Bai, J. E. Pask, and N. Sukumar. Hybrid preconditioning for iterative diagonalization of ill-conditioned generalized eigenvalue problems in electronic structure calculations. Journal of Computational Physics, 255:16–30, 2013.
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• F. Greco and N. Sukumar. Derivatives of maximum-entropy basis functions on the boundary: Theory and computations. International Journal for Numerical Methods in Engineering, 94(12):1123–1149, 2013.
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• J. O. Royset, N. Sukumar, and R. J-B Wets. Uncertainty quantification using exponential epi-splines. In Proceedings of the 11th International Conference on Structural Safety and Reliability, New York, NY, 2013.
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• N. Sukumar. Quadratic maximum-entropy serendipity shape functions for arbitrary planar polygons. Computer Methods in Applied Mechanics and Engineering, 263:27–41, 2013.
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2012

• G. Hattori, R. Rojas-Díaz, A. Sáez, N. Sukumar, and F. García-Sánchez. New anisotropic crack-tip enrichment functions for the extended finite element method. Computational Mechanics, 50(5):591–601, 2012.
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• S. E. Mousavi, J. E. Pask, and N. Sukumar. Efficient adaptive integration of functions with sharp gradients and cusps in n-dimensional parallelepipeds. International Journal for Numerical Methods in Engineering, 91(4):343–357, 2012.
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• J. E. Pask, N. Sukumar, and S. E. Mousavi. Linear scaling solution of the all-electron Coulomb problem in solids. International Journal for Multiscale Computational Engineering, 10(1):83–99, 2012.
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• G. Quaranta, S. K. Kunnath, and N. Sukumar. Maximum-entropy meshfree method for nonlinear static analysis of planar reinforced concrete structures. Engineering Structures, 42:179–189, 2012.
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2011

• G. Hattori, R. Rojas-Díaz, A. Sáez, F. García-Sánchez, and N. Sukumar. El Método de los Elementos Finitos Extendidos (X-FEM) para Medios Bidimensionales Fisurados Totalmente Anisótropos. Anales de Mecánica de la Fractura, 28(2):451–455, 2011.
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• S. E. Mousavi and N. Sukumar. Numerical integration of polynomials and discontinous functions on irregular convex polygons and polyhedrons. Computational Mechanics, 47(5):535–554, 2011.
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• S. E. Mousavi, E. Grinspun, and N. Sukumar. Higher-order extended finite element with harmonic enrichment functions for complex crack problems. International Journal for Numerical Methods in Engineering, 86(4--5):560–574, 2011.
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• S. E. Mousavi, E. Grinspun, and N. Sukumar. Harmonic enrichment functions: A unified treatment of multiple, intersecting and branched cracks in the extended finite element method. International Journal for Numerical Methods in Engineering, 85(10):1306–1322, 2011.
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• A. Ortiz, M. A. Puso, and N. Sukumar. Maximum-entropy meshfree method for incompressible media problems. Finite Elements in Analysis and Design, 47(6):572–585, 2011.
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• J. E. Pask, N. Sukumar, M. Guney, and W. Hu. Partition-of-unity finite-element method for large scale quantum molecular dynamics on massively parallel computational platforms. Technical Report LLNL-TR-470692, Department of Energy LDRD Grant 08-ERD-052, 2011.
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• R. Rojas-Díaz, N. Sukumar, A. Sáez, and F. García-Sánchez. Fracture in magnetoelectroelastic materials using the extended finite element method. International Journal for Numerical Methods in Engineering, 88(12):1238–1259, 2011.
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2010

• S. E. Mousavi and N. Sukumar. Generalized Gaussian quadrature rules for discontinuities and crack singularities in the extended finite element method. Computer Methods in Applied Mechanics and Engineering, 199(49--52):3237–3249, 2010.
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• S. E. Mousavi, H. Xiao, and N. Sukumar. Generalized Gaussian quadrature rules on arbitrary polygons. International Journal for Numerical Methods in Engineering, 82(1):99–113, 2010.
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• S. E. Mousavi and N. Sukumar. Generalized Duffy transformation for integrating vertex singularities. Computational Mechanics, 45(2--3):127–140, 2010.
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• A. Ortiz, M. A. Puso, and N. Sukumar. Maximum-entropy meshfree method for compressible and near-incompressible elasticity. Computer Methods in Applied Mechanics and Engineering, 199(25--28):1859–1871, 2010.
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• J. X. Shi, D. Chopp, J. Lua, N. Sukumar, and T. Belytschko. Abaqus implementation of extended finite element using a level set representation for three-dimensional fatigue crack growth and life predictions. Engineering Fracture Mechanics, 77(14):2840–2863, 2010.
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2009

• W. Aquino, J. C. Brigham, C. J. Earls, and N. Sukumar. Generalized finite element method using proper orthogonal decomposition. International Journal for Numerical Methods in Engineering, 79(7):887–906, 2009.
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• E. Giner, N. Sukumar, J. E. Tarancón, and F. J. Fuenmayor. An Abaqus implementation of the extended finite element method. Engineering Fracture Mechanics, 76(3):347–368, 2009.
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• C. B. Hirschberger, S. Ricker, P. Steinmann, and N. Sukumar. Computational multiscale modelling of heterogeneous material layers. Engineering Fracture Mechanics, 76(6):793–812, 2009.
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• A. Rajagopal, M. Scherer, P. Steinmann, and N. Sukumar. Smooth conformal α-NEM for gradient elasticity. The International Journal of Structural Changes in Solids -- Mechanics and Applications, 1(1):83–109, 2009.
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• R. Rojas-Díaz, N. Sukumar, A. Sáez, and F. García-Sánchez. Crack analysis in magnetoelectroelastic media using the extended finite element method. In Proceedings of the International Conference on Extended Finite Element Methods -- Recent Developments and Applications, pp. 181–186, Aachen, Germany, 2009.
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• J. Shi, J. Lua, L. Chen, D. Chopp, and N. Sukumar. X-FEM for Abaqus (XFA) toolkit for automated crack onset and growth simulation: New development, validation, and demonstration. In 2009 SIMULIA Customer Conference, 2009.
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• N. Sukumar and J. E. Bolander. Voronoi-based interpolants for fracture modelling. In Tessellations in the Sciences: Virtues, Techniques and Applications of Geometric Tilings, Springer Verlag, 2009.
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• N. Sukumar and J. E. Pask. Classical and enriched finite element formulations for Bloch-periodic boundary conditions. International Journal for Numerical Methods in Engineering, 77(8):1121–1138, 2009. Errata: a = 5.7 bohr for the harmonic oscillator problem in Sec. 4.2.1; a = 4 bohr and σ = 1.5 for the periodic Gaussian problem in Sec. 4.2.2
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• N. Sukumar. Finite element methods in quantum mechanics. Unpublished 2009.
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• L. L. Yaw, N. Sukumar, and S. K. Kunnath. Meshfree co-rotational formulation for two-dimensional continua. International Journal for Numerical Methods in Engineering, 79(8):979–1003, 2009.
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• L. L. Yaw, S. K. Kunnath, and N. Sukumar. Meshfree method for inelastic frame analysis. ASCE Journal of Structural Engineering, 135(6):676–684, 2009.
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2008

• E. Giner, N. Sukumar, F. J. Fuenmayor, and A. Vercher. Singularity enrichment for complete sliding contact using the partition of unity finite element method. International Journal for Numerical Methods in Engineering, 76(9):1402–1418, 2008.
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• E. Giner, N. Sukumar, F. D. Denia, and F. J. Fuenmayor. Extended finite element method for fretting fatigue crack propagation. International Journal of Solids and Structures, 45(22--23):5675–5687, 2008.
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• C. B. Hirschberger, N. Sukumar, and P. Steinmann. Computational homogenization of material layers with micromorphic mesostructure. Philosophical Magazine, 88:3603–3631, 2008.
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• K. Hormann and N. Sukumar. Maximum entropy coordinates for arbitrary polytopes. Computer Graphics Forum, 27(5):1513–1520, 2008. Proceedings of SGP 2008
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• J. Shi, J. Lua, H. Waisman, P. Liu, T. Belytschko, N. Sukumar, and Y. Liang. X-FEM toolkit for automated crack onset and growth prediction. In 49th AIAA Conference, pp. 1–22, Schaumburg IL, April 2008.
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• N. Sukumar, D. L. Chopp, E. Béchet, and N. Moës. Three-dimensional non-planar crack growth by a coupled extended finite element and fast marching method. International Journal for Numerical Methods in Engineering, 76(5):727–748, 2008.
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• A. Tabarraei and N. Sukumar. Extended finite element method on polygonal and quadtree meshes. Computer Methods in Applied Mechanics and Engineering, 197(5):425–438, 2008.
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2007

• C. B. Hirschberger, S. Ricker, P. Steinmann, and N. Sukumar. A computational homogenisation approach for cohesive interfaces. In Proceedings of the International Conference on Computational Plasticity, Computational Plasticity IX: Fundamentals and Applications, pp. 442–445, Barcelona, Spain, 2007.
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• N. Sukumar and R. J-B Wets. Deriving the continuity of maximum-entropy basis functions via variational analysis. SIAM Journal on Optimization, 18(3):914–925, 2007.
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• N. Sukumar and R. W. Wright. Overview and construction of meshfree basis functions: From moving least squares to entropy approximants. International Journal for Numerical Methods in Engineering, 70(2):181–205, 2007.
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• A. Tabarraei and N. Sukumar. Adaptive computations using material forces and residual-based error estimators on quadtree meshes. Computer Methods in Applied Mechanics and Engineering, 196(25--28):2657–2680, 2007.
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2006

• N. Sukumar. Where do we stand on meshfree approximation schemes. Unpublished 2006.
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• N. Sukumar and E. A. Malsch. Recent advances in the construction of polygonal finite element interpolants. Archives of Computational Methods in Engineering, 13(1):129–163, 2006.
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• A. Tabarraei and N. Sukumar. Application of polygonal finite elements in linear elasticity. International Journal of Computational Methods, 3(4):503–520, 2006.
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2005

• J. E. Bolander and N. Sukumar. Irregular lattice model for quasistatic crack propagation. Physical Review B, 71:094106, 2005.
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• Z. Huang, Z. Suo, G. Xu, J. He, J. H. Prévost, and N. Sukumar. Initiation and arrest of an interfacial crack in a four-point bend test. Engineering Fracture Mechanics, 72:2584–2601, 2005.
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• N. Sukumar. Maximum entropy approximation. AIP Conference Proceedings, 803(1):337–344, AIP, 2005.
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• N. Sukumar, J. Dolbow, A. Devan, J. Yvonnet, F. Chinesta, D. Ryckelynck, Ph. Lorong, I. Alfaro, M. A. Martínez, E. Cueto, and M. Doblaré. Meshless methods and partition of unity finite elements. International Journal of Forming Processes, 8(4):409–427, 2005.
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• A. Tabarraei and N. Sukumar. Adaptive computations on conforming quadtree meshes. Finite Elements in Analysis and Design, 41(7--8):686–702, 2005.
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2004

• N. Sukumar. Construction of polygonal interpolants: A maximum entropy approach. International Journal for Numerical Methods in Engineering, 61(12):2159–2181, 2004.
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• N. Sukumar and A. Tabarraei. Conforming polygonal finite elements. International Journal for Numerical Methods in Engineering, 61(12):2045–2066, 2004.
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• N. Sukumar, Z. Y. Huang, J.-H. Prévost, and Z. Suo. Partition of unity enrichment for bimaterial interface cracks. International Journal for Numerical Methods in Engineering, 59(8):1075–1102, 2004.
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• N. Sukumar and D. J. Srolovitz. Finite element-based model for crack propagation in polycrystalline materials. Computational & Applied Mathematics, 23(2--3):363–380, 2004.
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• N. Sukumar and A. Tabarraei. Polygonal interpolants: Construction and adaptive computations on quadtree meshes. In Proceedings of the European Congress on Computational Methods in Applied Science and Engineering (ECCOMAS 2004), Jyvaskyla, Finland, 2004.
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• N. Sukumar and A. Tabarraei. Numerical formulation and application of polygonal finite elements. In Proceedings of the Seventh International ESAFORM Conference on Material Forming, pp. 73–76, Trondheim, Norway, 2004.
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2003

• T. Belytschko, C. Parimi, N. Moës, N. Sukumar, and S. Usui. Structured extended finite element methods for solids defined by implicit surfaces. International Journal for Numerical Methods in Engineering, 56(4):609–635, 2003.
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• D. L. Chopp and N. Sukumar. Fatigue crack propagation of multiple coplanar cracks with the coupled extended finite element/fast marching method. International Journal of Engineering Science, 41(8):845–869, 2003.
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• E. Cueto, N. Sukumar, B. Calvo, M. A. Martínez, J. Cegoñino, and M. Doblaré. Overview and recent advances in natural neighbour Galerkin methods. Archives of Computational Methods in Engineering, 10(4):307–384, 2003.
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• R. Huang, N. Sukumar, and J.-H. Prévost. Modeling quasi-static crack growth with the extended finite element method. Part II: Numerical applications. International Journal of Solids and Structures, 40(26):7539–7552, 2003.
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• N. Sukumar and J.-H. Prévost. Modeling quasi-static crack growth with the extended finite element method. Part I: Computer implementation. International Journal of Solids and Structures, 40(26):7513–7537, 2003.
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• N. Sukumar. Meshless methods and partition of unity finite elements. In Proceedings of the Sixth International ESAFORM Conference on Material Forming, pp. 603–606, Salerno, Italy, 2003.
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• N. Sukumar, D. J. Srolovitz, T. J. Baker, and J.-H. Prévost. Brittle fracture in polycrystalline microstructures with the extended finite element method. International Journal for Numerical Methods in Engineering, 56(14):2015–2037, 2003.
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• N. Sukumar, D. L. Chopp, and B. Moran. Extended finite element method and fast marching method for three dimensional fatigue crack propagation. Engineering Fracture Mechanics, 70(1):29–48, 2003.
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• N. Sukumar. Voronoi cell finite difference method for the diffusion operator on arbitrary unstructured grids. International Journal for Numerical Methods in Engineering, 57(1):1–34, 2003.
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• N. Sukumar and J. E. Bolander. Numerical computation of discrete differential operators on non-uniform grids. CMES: Computer Modeling in Engineering & Sciences, 4(6):691–706, 2003.
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2002

• N. Sukumar. Modeling crack singularities in FEM/X-FEM. Unpublished 2002.
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2001

• N. Sukumar, D. L. Chopp, N. Moës, and T. Belytschko. Modeling holes and inclusions by level sets in the extended finite-element method. Computer Methods in Applied Mechanics and Engineering, 190(46--47):6183–6200, 2001.
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• N. Sukumar, B. Moran, A. Yu. Semenov, and V. V. Belikov. Natural neighbor Galerkin methods. International Journal for Numerical Methods in Engineering, 50(1):1–27, 2001.
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• N. Sukumar. Sibson and non-Sibsonian interpolants for elliptic partial differential equations. In Proceedings of the first MIT Conference on Fluid and Solid Mechanics, pp. 1665–1667, 2, Elsevier Press, Amsterdam, The Netherlands, 2001.
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2000

• D. Bueche, N. Sukumar, and B. Moran. Dispersive properties of the natural element method. Computational Mechanics, 25(2/3):207–219, 2000.
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• C. Daux, N. Moës, J. Dolbow, N. Sukumar, and T. Belytschko. Arbitrary branched and intersecting cracks with the extended finite element method. International Journal for Numerical Methods in Engineering, 48(12):1741–1760, 2000.
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• N. Moës, N. Sukumar, B. Moran, and T. Belytschko. An extended finite element method (X-FEM) for two- and three-dimensional crack modeling. In Proceedings of the European Congress on Computational Methods in Applied Sciences and Engineering, ECCOMAS 2000, Barcelona, Spain, 2000.
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• N. Sukumar, N. Moës, B. Moran, and T. Belytschko. Extended finite element method for three-dimensional crack modelling. International Journal for Numerical Methods in Engineering, 48(11):1549–1570, 2000.
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1999

• N. Sukumar and B. Moran. C¹ natural neighbor interpolant for partial differential equations. Numerical Methods for Partial Differential Equations, 15(4):417–447, 1999.
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1998

• B. Moran, N. Sukumar, and T. Belytschko. Application of the natural element method in elastostatics. In Modeling and Simulation Based Engineering, 1, Tech. Science Press, 1998.
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• N. Sukumar, B. Moran, and T. Belytschko. The natural element method in solid mechanics. International Journal for Numerical Methods in Engineering, 43(5):839–887, 1998.
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• N. Sukumar. The Natural Element Method in Solid Mechanics. Ph.D. Thesis, Theoretical and Applied Mechanics, Northwestern University, Evanston, IL, U.S.A., 1998.
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• N. Sukumar. Mixed formulation for the natural element method in linear elasticity. Unpublished 1998.
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1997

• N. Sukumar, B. Moran, T. Black, and T. Belytschko. An element-free Galerkin method for three-dimensional fracture mechanics. Computational Mechanics, 20(1/2):170–175, 1997.
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• N. Sukumar. A C¹ NEM interpolant for fourth-order PDEs. Unpublished 1997.
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• N. Sukumar. A note on natural neighbor interpolation and the natural element method (NEM). Unpublished 1997.
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1996

• N. Sukumar. Partition-of-Unity Methods--Revisited. Unpublished 1996.
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• N. Sukumar. Partition-of-Unity Methods in one-dimension. Unpublished 1996.
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• N. Sukumar. Patch test in 1D: coupled FE-EFG method. Unpublished 1996.
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• N. Sukumar. Application of the coupled FE-EFG method to material discontinuities in 1D and 2D. Unpublished 1996.
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• N. Sukumar. SIF computations for 2D cracks using enriched basis functions. Unpublished 1996.
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1993

• N. Sukumar and M. Kumosa. Finite element analysis of axial splits in composite Iosipescu specimens. International Journal of Fracture, 62:55–85, 1993.
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1992

• N. Sukumar and M. Kumosa. Stress singularities at sharp notches: Interpolation formulas. International Journal of Fracture, 58:R45–R49, 1992.
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• N. Sukumar and M. Kumosa. Application of the Finite Element Iterative Method to cracks and sharp notches in orthotropic media. International Journal of Fracture, 58:177–192, 1992.
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