N. Sukumar's Publications Google scholar

• Sorted by Date • Classified by Publication Type • Classified by Research Category •

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.
  Details     BibTeX     Download: (unavailable)
• N. Sukumar and M. Kumosa. Stress singularities at sharp notches: Interpolation formulas. International Journal of Fracture, 58:R45–R49, 1992.
  Details     BibTeX     Download: (unavailable)
• 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.
  Details     BibTeX     Download: (unavailable)

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.
  Details     BibTeX     Download: [pdf] 
• N. Sukumar. Patch test in 1D: coupled FE-EFG method. Unpublished 1996.
  Details     BibTeX     Download: [pdf] 
• N. Sukumar. Application of the coupled FE-EFG method to material discontinuities in 1D and 2D. Unpublished 1996.
  Details     BibTeX     Download: [pdf] 
• N. Sukumar. SIF computations for 2D cracks using enriched basis functions. Unpublished 1996.
  Details     BibTeX     Download: [pdf] 

FEM

• P. Areias, N. Sukumar, and J. Ambrósio. Continuous gap contact formulation based on the screened Poisson equation. Computational Mechanics, 2023. in press
  Details     BibTeX     Download: [pdf] 

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.
  Details     BibTeX     Download: [pdf] 
• 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.
  Details     BibTeX     Download: [pdf] 
• C. B. Hirschberger, N. Sukumar, and P. Steinmann. Computational homogenization of material layers with micromorphic mesostructure. Philosophical Magazine, 88:3603–3631, 2008.
  Details     BibTeX     Download: [pdf] 
• 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.
  Details     BibTeX     Download: (unavailable)
• J. E. Bolander and N. Sukumar. Irregular lattice model for quasistatic crack propagation. Physical Review B, 71:094106, 2005.
  Details     BibTeX     Download: [pdf] 
• 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.
  Details     BibTeX     Download: [pdf] 

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.
  Details     BibTeX     Download: [pdf] 
• 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.
  Details     BibTeX     Download: [pdf] 
• D. Millán, N. Sukumar, and M. Arroyo. Cell-based maximum-entropy approximants. Computer Methods in Applied Mechanics and Engineering, 284:712–731, 2015.
  Details     BibTeX     Download: [pdf] 
• 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.
  Details     BibTeX     Download: [pdf] 
• 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.
  Details     BibTeX     Download: [pdf] 
• N. Sukumar. Quadratic maximum-entropy serendipity shape functions for arbitrary planar polygons. Computer Methods in Applied Mechanics and Engineering, 263:27–41, 2013.
  Details     BibTeX     Download: [pdf] 
• 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.
  Details     BibTeX     Download: [pdf] 
• 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.
  Details     BibTeX     Download: [pdf] 
• 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.
  Details     BibTeX     Download: [pdf] 
• 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.
  Details     BibTeX     Download: [pdf] 
• 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.
  Details     BibTeX     Download: [pdf] 
• 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.
  Details     BibTeX     Download: [pdf] 
• 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.
  Details     BibTeX     Download: [pdf] 
• 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.
  Details     BibTeX     Download: [pdf] 
• K. Hormann and N. Sukumar. Maximum entropy coordinates for arbitrary polytopes. Computer Graphics Forum, 27(5):1513–1520, 2008. Proceedings of SGP 2008
  Details     BibTeX     Download: [pdf] 
• 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.
  Details     BibTeX     Download: [pdf] 
• 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.
  Details     BibTeX     Download: [pdf] 
• N. Sukumar. Where do we stand on meshfree approximation schemes. Unpublished 2006.
  Details     BibTeX     Download: [HTML] 
• N. Sukumar. Maximum entropy approximation. AIP Conference Proceedings, 803(1):337–344, AIP, 2005.
  Details     BibTeX     Download: [pdf] 
• N. Sukumar. Construction of polygonal interpolants: A maximum entropy approach. International Journal for Numerical Methods in Engineering, 61(12):2159–2181, 2004.
  Details     BibTeX     Download: [pdf] 

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.
  Details     BibTeX     Download: [pdf] 
• 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.
  Details     BibTeX     Download: [pdf] 
• 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.
  Details     BibTeX     Download: [pdf] 
• 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.
  Details     BibTeX     Download: [pdf] 
• 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.
  Details     BibTeX     Download: [pdf] 
• 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.
  Details     BibTeX     Download: [pdf] 
• 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.
  Details     BibTeX     Download: [pdf] 
• 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.
  Details     BibTeX     Download: [pdf] 
• 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.
  Details     BibTeX     Download: [pdf] 
• D. Bueche, N. Sukumar, and B. Moran. Dispersive properties of the natural element method. Computational Mechanics, 25(2/3):207–219, 2000.
  Details     BibTeX     Download: [pdf] 
• N. Sukumar and B. Moran. C¹ natural neighbor interpolant for partial differential equations. Numerical Methods for Partial Differential Equations, 15(4):417–447, 1999.
  Details     BibTeX     Download: [pdf] 
• 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.
  Details     BibTeX     Download: (unavailable)
• 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.
  Details     BibTeX     Download: [pdf] 
• N. Sukumar. The Natural Element Method in Solid Mechanics. Ph.D. Thesis, Theoretical and Applied Mechanics, Northwestern University, Evanston, IL, U.S.A., 1998.
  Details     BibTeX     Download: [HTML] 
• N. Sukumar. Mixed formulation for the natural element method in linear elasticity. Unpublished 1998.
  Details     BibTeX     Download: [pdf] 
• N. Sukumar. A C¹ NEM interpolant for fourth-order PDEs. Unpublished 1997.
  Details     BibTeX     Download: [HTML] 
• N. Sukumar. A note on natural neighbor interpolation and the natural element method (NEM). Unpublished 1997.
  Details     BibTeX     Download: [HTML] 

Partition-of-Unity Methods/X-FEM

• 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.
  Details     BibTeX     Download: [pdf] 
• 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.
  Details     BibTeX     Download: [pdf] 
• 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.
  Details     BibTeX     Download: [pdf] 
• 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.
  Details     BibTeX     Download: [pdf] 
• 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.
  Details     BibTeX     Download: [pdf] 
• N. Moës, J. E. Dolbow, and N. Sukumar. Extended finite element methods. In Encyclopedia of Computational Mechanics, John Wiley & Sons, 2018.
  Details     BibTeX     Download: [pdf] 
• 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.
  Details     BibTeX     Download: [pdf] 
• 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.
  Details     BibTeX     Download: [pdf] 
• J. E. Pask and N. Sukumar. Partition of unity finite element method for quantum mechanical materials calculations. Extreme Mechanics Letters, 11:8–17, 2017.
  Details     BibTeX     Download: [pdf] 
• 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.
  Details     BibTeX     Download: [HTML] 
• 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.
  Details     BibTeX     Download: [pdf] 
• 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.
  Details     BibTeX     Download: [HTML] 
• 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.
  Details     BibTeX     Download: [pdf] 
• 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.
  Details     BibTeX     Download: [pdf] 
• 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.
  Details     BibTeX     Download: [pdf] 
• 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.
  Details     BibTeX     Download: [pdf] 
• 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.
  Details     BibTeX     Download: [pdf] 
• 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.
  Details     BibTeX     Download: [pdf] 
• 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.
  Details     BibTeX     Download: [pdf] 
• 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.
  Details     BibTeX     Download: [pdf] 
• 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.
  Details     BibTeX     Download: [pdf] 
• S. E. Mousavi and N. Sukumar. Generalized Duffy transformation for integrating vertex singularities. Computational Mechanics, 45(2--3):127–140, 2010.
  Details     BibTeX     Download: [pdf] 
• 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.
  Details     BibTeX     Download: [pdf] 
• 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.
  Details     BibTeX     Download: [pdf] 
• 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.
  Details     BibTeX     Download: [pdf] 
• 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.
  Details     BibTeX     Download: [pdf] 
• 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.
  Details     BibTeX     Download: [pdf] 
• 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
  Details     BibTeX     Download: [pdf] 
• N. Sukumar. Finite element methods in quantum mechanics. Unpublished 2009.
  Details     BibTeX     Download: [HTML] 
• 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.
  Details     BibTeX     Download: [pdf] 
• 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.
  Details     BibTeX     Download: [pdf] 
• 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.
  Details     BibTeX     Download: [pdf] 
• 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.
  Details     BibTeX     Download: [pdf] 
• 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.
  Details     BibTeX     Download: [pdf] 
• 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.
  Details     BibTeX     Download: [pdf] 
• 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.
  Details     BibTeX     Download: [pdf] 
• 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.
  Details     BibTeX     Download: [pdf] 
• 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.
  Details     BibTeX     Download: [pdf] 
• 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.
  Details     BibTeX     Download: [pdf] 
• 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.
  Details     BibTeX     Download: [pdf] 
• 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.
  Details     BibTeX     Download: [pdf] 
• 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.
  Details     BibTeX     Download: [pdf] 
• 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.
  Details     BibTeX     Download: [pdf] 
• 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.
  Details     BibTeX     Download: [pdf] 
• 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.
  Details     BibTeX     Download: [pdf] 
• N. Sukumar. Modeling crack singularities in FEM/X-FEM. Unpublished 2002.
  Details     BibTeX     Download: [pdf] 
• 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.
  Details     BibTeX     Download: [pdf] 
• 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.
  Details     BibTeX     Download: [pdf] 
• 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.
  Details     BibTeX     Download: [pdf] 
• 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.
  Details     BibTeX     Download: [pdf] 
• N. Sukumar. Partition-of-Unity Methods--Revisited. Unpublished 1996.
  Details     BibTeX     Download: [pdf] 
• N. Sukumar. Partition-of-Unity Methods in one-dimension. Unpublished 1996.
  Details     BibTeX     Download: [pdf] 

Physics-Informed Neural Networks (PINNs)

• 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.
  Details     BibTeX     Download: [pdf] 
• 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.
  Details     BibTeX     Download: [pdf] 

Polygonal/Polyhedral FE Methods

• A. Chen and N. Sukumar. Stress-hybrid virtual element method on quadrilateral meshes for compressible and nearly-incompressible linear elasticity. arXiv: 2304.04941, 2023.
  Details     BibTeX     Download: [pdf] 
• 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.
  Details     BibTeX     Download: [pdf] 
• A. Chen and N. Sukumar. Stabilization-free virtual element method for plane elasticity. Computers and Mathematics with Applications, 138:88–105, 2023.
  Details     BibTeX     Download: [pdf] 
• A. Russo and N. Sukumar. Quantitative study of the stabilization parameter in the virtual element method. arXiv: 2304.00063, 2023.
  Details     BibTeX     Download: [pdf] 
• 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.
  Details     BibTeX     Download: [pdf] 
• N. Sukumar and J. E. Bolander. Virtual element method for modeling the deformation of multiphase composites. Mechanics Research Communications, 124:103907, 2022.
  Details     BibTeX     Download: [pdf] 
• 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.
  Details     BibTeX     Download: [pdf] 
• 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. 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.
  Details     BibTeX     Download: [pdf] 
• 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.
  Details     BibTeX     Download: [pdf] 
• 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.
  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. Ja\'skowiec and N. Sukumar. High-order cubature rules for tetrahedra. International Journal for Numerical Methods in Engineering, 121(11):2418–2436, 2020.
  Details     BibTeX     Download: [pdf] 
• 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.
  Details     BibTeX     Download: [pdf] 
• 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.
  Details     BibTeX     Download: [pdf] 
• 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.
  Details     BibTeX     Download: [pdf] 
• K. Hormann and N. Sukumar, editors. Generalized Barycentric Coordinates in Computer Graphics and Computational Mechanics, CRC Press, Boca Raton, FL, 2017.
  Details     BibTeX     Download: [HTML] 
• 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.
  Details     BibTeX     Download: [pdf] 
• 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.
  Details     BibTeX     Download: [pdf] 
• 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] 
• M. Floater, A. Gillette, and N. Sukumar. Gradient bounds for Wachspress coordinates on polytopes. SIAM Journal on Numerical Analysis, 52(1):515–532, 2014.
  Details     BibTeX     Download: [pdf] 
• 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.
  Details     BibTeX     Download: [pdf] 
• N. Sukumar. Quadratic maximum-entropy serendipity shape functions for arbitrary planar polygons. Computer Methods in Applied Mechanics and Engineering, 263:27–41, 2013.
  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.
  Details     BibTeX     Download: [pdf] 
• K. Hormann and N. Sukumar. Maximum entropy coordinates for arbitrary polytopes. Computer Graphics Forum, 27(5):1513–1520, 2008. Proceedings of SGP 2008
  Details     BibTeX     Download: [pdf] 
• 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.
  Details     BibTeX     Download: [pdf] 
• 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.
  Details     BibTeX     Download: [pdf] 
• A. Tabarraei and N. Sukumar. Application of polygonal finite elements in linear elasticity. International Journal of Computational Methods, 3(4):503–520, 2006.
  Details     BibTeX     Download: [pdf] 
• A. Tabarraei and N. Sukumar. Adaptive computations on conforming quadtree meshes. Finite Elements in Analysis and Design, 41(7--8):686–702, 2005.
  Details     BibTeX     Download: [pdf] 
• N. Sukumar. Construction of polygonal interpolants: A maximum entropy approach. International Journal for Numerical Methods in Engineering, 61(12):2159–2181, 2004.
  Details     BibTeX     Download: [pdf] 
• N. Sukumar and A. Tabarraei. Conforming polygonal finite elements. International Journal for Numerical Methods in Engineering, 61(12):2045–2066, 2004.
  Details     BibTeX     Download: [pdf] 
• 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.
  Details     BibTeX     Download: [pdf] 
• 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.
  Details     BibTeX     Download: [pdf] 

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.
  Details     BibTeX     Download: [pdf] 

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. 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.
  Details     BibTeX     Download: [pdf] 
• 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.
  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. Ja\'skowiec and N. Sukumar. High-order cubature rules for tetrahedra. International Journal for Numerical Methods in Engineering, 121(11):2418–2436, 2020.
  Details     BibTeX     Download: [pdf] 
• 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.
  Details     BibTeX     Download: [pdf] 
• 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.
  Details     BibTeX     Download: [pdf] 
• 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.
  Details     BibTeX     Download: [pdf] 
• S. E. Mousavi and N. Sukumar. Generalized Duffy transformation for integrating vertex singularities. Computational Mechanics, 45(2--3):127–140, 2010.
  Details     BibTeX     Download: [pdf] 

Quantum Mechanics

• 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.
  Details     BibTeX     Download: [pdf] 
• 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.
  Details     BibTeX     Download: [pdf] 
• J. E. Pask and N. Sukumar. Partition of unity finite element method for quantum mechanical materials calculations. Extreme Mechanics Letters, 11:8–17, 2017.
  Details     BibTeX     Download: [pdf] 
• 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.
  Details     BibTeX     Download: [pdf] 
• 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.
  Details     BibTeX     Download: [pdf] 
• 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.
  Details     BibTeX     Download: [pdf] 
• 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
  Details     BibTeX     Download: [pdf] 
• N. Sukumar. Finite element methods in quantum mechanics. Unpublished 2009.
  Details     BibTeX     Download: [HTML] 

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.
  Details     BibTeX     Download: [pdf] 
• 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.
  Details     BibTeX     Download: [pdf] 
• 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.
  Details     BibTeX     Download: [pdf] 

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.
  Details     BibTeX     Download: [pdf] 

Generated by bib2html.pl (written by Patrick Riley ) on Mon Apr 17, 2023 12:46:38