N. Sukumar's Publications Google scholar

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Classified by Research Category

• Elastic Fracture (FEM) • Element-Free Galerkin Method • FEM • Lattice Models and Multiscale Mechanics • Maximum-Entropy Approximants • Natural Element Method (NEM) • Partition-of-Unity Methods/X-FEM • Physics-Informed Neural Networks (PINNs) • Polygonal/Polyhedral FE Methods • Phononics • Quadrature/Cubature Rules • Quantum Mechanics • Structural Engineering • UQ and Stochastic Methods •

Elastic Fracture (FEM)

• 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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• 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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Element-Free Galerkin Method

• 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. 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 Unpublished 1996.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 Unpublished 1996.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 Unpublished 1996.
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FEM

• P. Areias, N. Sukumar, and J. Ambrósio. Continuous gap contact formulation based on the screened Poisson equation. Computational Mechanics, 72(4):707–723, 2023.
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Lattice Models and Multiscale Mechanics

• 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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• 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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• 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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• 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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• J. E. Bolander and N. Sukumar. Irregular lattice model for quasistatic crack propagation. Physical Review B, 71:094106, 2005.
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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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Maximum-Entropy Approximants

• 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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• 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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• 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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• 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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• 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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• 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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• 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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• 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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• 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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• 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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• 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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• 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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• 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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• N. Sukumar. Where do we stand on meshfree approximation schemes. Unpublished 2006.
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• N. Sukumar. Maximum entropy approximation. AIP Conference Proceedings, 803(1):337–344, AIP, 2005.
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• 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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Natural Element Method (NEM)

• 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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• 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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• 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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• 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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• 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. 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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• 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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• 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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• 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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• 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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• 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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Partition-of-Unity Methods/X-FEM

• O. Certik, J. E. Pask, I. Fernando, R. Goswami, N. Sukumar, L. A. Collins, G. Manzini, and J. Vackar. High-order finite element method for atomic structure calculations. Computer Physics Communications, 297:109051, 2024.
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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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• 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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• 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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• 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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• 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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• 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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• 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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• 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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• 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. 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, 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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• 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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• 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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• 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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• 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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• 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. 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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• 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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• 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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• 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, 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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• 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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• 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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• 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. Modeling crack singularities in FEM/X-FEM. Unpublished 2002.
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• 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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• 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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• 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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Physics-Informed Neural Networks (PINNs)

• N. Sukumar and R. Roy. A Wachspress-based transfinite formulation for exactly enforcing Dirichlet boundary conditions on convex polygonal domains in physics-informed neural networks. , 2026. arXiv Preprint: 2601.01756
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• R. J. Gladstone, M. A. Nabian, N. Sukumar, A. Srivastava, and H. Meidani. FO-PINNs: A first-order formulation for physics informed neural networks. Engineering Analysis with Boundary Elements, 174:106161, 2025.
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• N. Sukumar and A. Acharya. Variational formulation based on duality to solve partial differential equations: Use of B-splines and machine learning approximants. Computer Methods in Applied Mechanics and Engineering, 441:117909, 2025.
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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. Heliyon, 9:e18820, 2023.
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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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Polygonal/Polyhedral FE Methods

• R. Rangarajan and N. Sukumar. CutVEM: Conforming virtual element method on embedded domains with shape-agnostic element agglomeration. Computer Methods in Applied Mechanics and Engineering, 449:118540, 2026.
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• A. Chen, J. E. Bishop, and N. Sukumar. Stress-hybrid virtual element method on six-noded triangular meshes for compressible and nearly-incompressible linear elasticity. Computer Methods in Applied Mechanics and Engineering, 426:116971, 2024.
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• A. Chen and N. Sukumar. Stress-hybrid virtual element method on quadrilateral meshes for compressible and nearly-incompressible linear elasticity. International Journal for Numerical Methods in Engineering, 125(3):e7384, 2024.
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• L. Dieci, F. V. Difonzo, and N. Sukumar. Nonnegative moment coordinates on finite element geometries. Mathematics in Engineering, 6(1):81–99, 2024.
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• J. Jaskowiec and N. Sukumar. Penalty-free discontinuous Galerkin method. International Journal for Numerical Methods in Engineering, 125(12):e7472, 2024.
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• A. Russo and N. Sukumar. Quantitative study of the stabilization parameter in the virtual element method. In Nonlinear Differential Equations and Applications (PICNDEA 2022), Volume 7, CIM Series in Mathematical Sciences, Springer, Cham, 2024.
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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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• 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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• 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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• 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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• J. Jaskowiec 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. Jaskowiec 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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• 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. Jaskowiec 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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• 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, 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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• 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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• 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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• 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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• 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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• 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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• 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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• 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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• 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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• 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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• 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 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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Phononics

• 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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Quadrature/Cubature Rules

• 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.
  Details     BibTeX     Download: [pdf] 
• J. Jaskowiec 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.
  Details     BibTeX     Download: [pdf] 
• J. Jaskowiec and N. Sukumar. High-order symmetric cubature rules for tetrahedra and pyramids. International Journal for Numerical Methods in Engineering, 122(1):148–171, 2021.
  Details     BibTeX     Download: [pdf] 
• E. B. Chin and N. Sukumar. An efficient method to integrate polynomials over polytopes and curved solids. Computer Aided Geometric Design, 82:101914, 2020.
  Details     BibTeX     Download: [pdf] 
• J. Jaskowiec 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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• 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. Numerical integration of homogeneous functions on convex and nonconvex polygons and polyhedra. Computational Mechanics, 56(6):967–981, 2015.
  Details     BibTeX     Download: [pdf] 
• 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, 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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Quantum Mechanics

• O. Certik, J. E. Pask, I. Fernando, R. Goswami, N. Sukumar, L. A. Collins, G. Manzini, and J. Vackar. High-order finite element method for atomic structure calculations. Computer Physics Communications, 297:109051, 2024.
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• 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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• 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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• 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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• 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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• 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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• 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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Structural Engineering

• 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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• 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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UQ and Stochastic Methods

• 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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