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N. Sukumar
Professor, Computational Mechanics
Department of Civil & Environmental Engg
University of California
One Shields Avenue
Davis, CA 95616
Phone: +1 (530) 754-6415
Fax: +1 (530) 752-7872
E-mail: nsukumar-at-ucdavis.edu

RESEARCH INTERESTS

My research interests lie in the areas of computational solid mechanics and applied mathematics, with recent emphasis on new methods development for modeling fracture in materials, ab initio electronic-structure (Kohn-Sham equations of DFT) calculations, virtual element methods, and physics-informed neural networks to solve PDEs. Other areas of interest include computational geometry, level set methods, Bayesian probability theory, maximum-entropy methods in mechanics, convex optimization and semidefinite programming, machine (deep) learning, stochastic PDEs and UQ, and parallel computing.

EDUCATION
1998 Ph.D., Theoretical and Applied Mechanics, Northwestern University, Thesis: "The Natural Element Method in Solid Mechanics." Thesis Committee: Brian Moran, Ted Belytschko, and Vladimir Volpert
1992 M.S., Materials Science and Engineering, Oregon Graduate Institute of Science & Technology, Thesis: "Finite Element Analysis of Mixed Mode Fracture and Failure in Composite Iosipescu Specimens." Advisor: Maciej Kumosa.
1989 B. Tech., Metallurgical Engineering, Indian Institute of Technology, Bombay. Senior Project: "A Microprocessor-Based Temperature Controller for an Electrical Resistance Furnace." Advisor: Nirdosh Khosla

ACADEMIC RESEARCH EXPERIENCE
07/10–present

Professor, Department of Civil and Environmental Engineering, University of California, Davis
01/23–06/23

Visiting Scholar, Division of Applied Mathematics, Brown University
04/18–07/18

Visiting Scientist, Theoretical Division, Los Alamos National Laboratory
01/11–08/11

Visiting Professor, PULSE Institute, Photon Science, SLAC National Accelerator Laboratory
07/07–06/10

Associate Professor, Department of Civil and Environmental Engineering, University of California, Davis
09/07–12/07

Visiting Associate Professor, Sibley School of Mechanical and Aerospace Engineering, Cornell University
07/00–06/07

Assistant Professor, Department of Civil and Environmental Engineering, University of California, Davis
07/00–12/00

Research Associate, Department of Mechanical and Aerospace Engineering, Princeton University
01/99–06/00

Post-Doc, Theoretical and Applied Mechanics, Northwestern University
01/94–06/98 Research Assistant, Theoretical and Applied Mechanics, Northwestern University
09/90–10/92 Research Assistant, Department of Materials Science and Engineering, Oregon Graduate Institute

INDUSTRIAL EXPERIENCE
1992–1993 Consultant, Endochronics Inc., WA
Numerical implementation of a gradient plasticity theory (proposed by Dr. K. C. Valanis) to describe the motion of particles in granular media.
1989–1990 Systems Engineer, Tata Steel, India.
Developed and implemented software modules in Oracle for management information systems.

TEACHING EXPERIENCE
2001–present

Assistant/Associate Professor/Professor, University of California, Davis

  • Advanced Structural Mechanics (Spring 10/12)
  • Introduction to the Theory of Elasticity (Fall 11, 14/15, 19-23)
  • Finite Element Procedures in Applied Mechanics (Winter 01-10, 12-13, 15-20, 21-22, 24-) Fall 05)
  • Finite Elements: Applications to Linear and Nonlinear Structural Mechanics Problems (Spring 03/04, 07)
  • Matrix Structural Analysis and the Finite Element Method (Fall 03/05/12/17-21, Winter 14)
  • Mechanics of Materials (Fall 01/02/06/08/10/17/20, Winter 02)
  • Meshfree Methods and Partition of Unity FEM (Spring 06/10/15/24, Fall 08/18)
  • Computer Methods in Civil and Environmental Engineering (Fall 12/13, Spring 15, Winter 16)
  • Statics (Fall 04, Spring 05)
1997–1998 Teaching Assistant, Northwestern University .
Assisted in teaching, held office hours, and conducted MATLAB tutorials
  • Statics (Winter 1997)
  • Dynamic systems modeling (Spring 1998)

SHORT COURSES
  1. "Computational Methods for Nonlinear Eigenvalue Problems (with Zhaojun Bai)," International Summer School on Scientific Computing, State Key Laboratory of Scientific and Engineering Computing, Chinese Academy of Sciences, Beijing, China, July 24 - August 5, 2017.

  2. "Partition of Unity Methods," GIAN Short Course, Department of Mechanical Engineering, IIT Madras, Chennai, India, December 2016.

PRESENTATIONS
  1. "Emerging Computational Methods in Solid Mechanics," Invited Seminar, GGAM Seminar, Department of Mathematics, University of California, Davis, CA, January 2024.

  2. "Exact Imposition of Boundary Conditions in PINNs to Solve PDEs," Invited Seminar, Department of Civil and Environmental Engineering, University of Pittsburgh, Pittsburgh, PA, November 2023.

  3. "Exact Imposition of Boundary Conditions in PINNs to Solve PDEs," Invited Seminar, Department of Applied Mathematics, University of Waterloo, Ontario, Canada, October 2023.

  4. "Exact Imposition of Boundary Conditions in PINNs to Solve PDEs," Invited Lecture, BIRS Scientific Machine Learning Workshop, Banff, Canada, June 2023.

  5. "Recent Advances in Exact Imposition of Boundary Conditions in Physics-Informed Deep Neural Networks to Solve PDEs," Invited Seminar, Department of Mechanical Engineering, Boston University, Boston, MA, May 2023.

  6. "Recent Advances in Exact Imposition of Boundary Conditions in Physics-Informed Deep Neural Networks to Solve PDEs," Rhodes Information Initiative Seminar, Duke University, Durham, NC, May 2023.

  7. "Recent Advances in Exact Imposition of Boundary Conditions in Physics-Informed Deep Neural Networks to Solve PDEs," Joint Materials and Mechanics Seminar, Brown University, Providence, RI, May 2023.

  8. "Virtual Element Method: A Stabilized Galerkin Method on Polytopal Meshes," Invited Seminar, Applied and Computational Math Seminar, Portland State University, Portland, OR, April 2023.

  9. "Recent Advances in Exact Imposition of Boundary Conditions in Physics-Informed Deep Neural Networks to Solve PDEs," Invited Seminar, Dassault Systemes Simulia Corporation, Johnston, RI, March 2023.

  10. "Virtual Element Method: A Stabilized Galerkin Method on Polytopal Meshes," Invited Seminar, Dassault Systemes Simulia Corporation, Johnston, RI, March 2023.

  11. "Scaled Boundary Cubature Scheme in Higher Dimensions: Integration over Polytopes and Curved Regions (with E. B. Chin)," Invited Lecture, POEMS Workshop, Milano, Italy, December 2022.

  12. "Exact Imposition of Boundary Condition in Physics-Informed Deep Neural Networks to Solve PDEs," SEMM Seminar, Department of Civil & Environmental Engineering, University of California, Berkeley, CA, October 2022.

  13. "Exact Imposition of Boundary Condition in Physics-Informed Deep Neural Networks to Solve PDEs (with A. Srivastava)," USACM Thematic Conference on Meshfree and Novel Finite Element Methods, Berkeley, CA, September 2022.

  14. "Virtual Element Method: A Stabilized Galerkin Method on Polytopes," Invited Seminar, Department of Aerospace Engineering, IIT Bombay, Mumbai, India, September 2022.

  15. "Recent Advances in Exact Imposition of Boundary Condition in Physics-Informed Deep Neural Networks to Solve PDEs," Invited Seminar, Center for Machine Intelligence and Data Science, IIT Bombay, Mumbai, India, September 2022.

  16. "Modeling Cracks and Material Interfaces with the Extended Finite Element Methods," Invited Seminar, Department of Metallurgical Engineering and Materials Science, IIT Bombay, Mumbai, India, August 2022.

  17. "Recent Advances in Exact Imposition of Boundary Condition in Physics-Informed Deep Neural Networks to Solve PDEs," Invited Seminar, Department of Computational and Data Sciences, Indian Institute of Science, Bengaluru, India, July 2022.

  18. "Introduction to Virtual Element Methods, Numerical Integration over Polytopes and Extended Finite Element Methods," Invited Lectures, Department of Mechanical Engineering, Indian Institute of Science, Bengaluru, India, July 2022.

  19. "Recent Advances in Polyhedral Virtual Element Methods and Physics-Informed Deep Neural Networks to Solve PDEs," Invited Seminar, Department of Mechanical Engineering, Indian Institute of Science, Bengaluru, India, July 2022.

  20. "Numerical Integration over Polytopes and Curved Regions and use of VEM to Advance Finite Element Technology," Invited Lecture, VEM Mini-Course (SDS 2022 Meeting), Rosa Marina, Italy, June 2022.

  21. "Recent Advances in Polyhedral Virtual Element Methods and Physics-Informed Deep Neural Networks to Solve PDEs," Invited Seminar, T-3 Division, Los Alamos National Laboratory, Los Alamos, NM, May 2022.

  22. "Recent Advances in Polyhedral Virtual Element Methods and Physics-Informed Deep Neural Networks to Solve PDEs," Invited Seminar, Engineering Sciences Center, Sandia National Laboratories, Albuquerque, NM, May 2022.

  23. "Stabilization-Free Virtual Element Method for Plane Elasticity (with A. Chen)," Invited Seminar, T-3 Division, Los Alamos National Laboratory, Los Alamos, NM, March 2022.

  24. "Exact Imposition of Boundary Conditions with Distance Functions in Physics-Informed Deep Neural Networks," Invited Seminar, Mechanics and Computation Seminar, Stanford University, Stanford, CA, February 2022.

  25. "Meshfree Analysis on Complex Geometries Using Physics-Informed Deep Neural Networks," Invited Seminar, Instituto Superior Ténico, University of Lisbon, Portugal, January 2022.

  26. "Virtual Elements on Agglomerated Finite Elements to Increase the Critical Time Step in Explicit Three-Dimensional Elastodynamic Simulations," US National Congress on Computational Mechanics, Chicago, IL, July 2021.

  27. "Meshfree Analysis on Complex Geometries Using Physics-Informed Deep Neural Networks," Invited Seminar, Sandia National Laboratories, Albuquerque, NM, June 2021.

  28. "Scaled Boundary Cubature Scheme for Numerical Integration over Planar Regions with Affine and Curved Boundaries (with E. B. Chin)," Plenary Lecture, INdAM Conference on Polygonal Methods for PDEs: Theory and Applications, Rome, Italy, May 2021.

  29. "Exact Imposition of Boundary Conditions with Distance Functions in Physics-Informed Deep Neural Networks (with A. Srivastava)," CRUNCH Group Seminar, Brown University, Providence, RI, May 2021.

  30. "Spectral Extended Finite Element Method for Band Structure Calculations in Phononic Crystals (with E. B. Chin, A. A. Mokhtari and A. Srivastava)," Keynote Lecture, Society of Engineering Sciences – 56th Annual Technical Meeting, St. Louis, MO, October 2019.

  31. "Numerical Integration of Homogeneous Functions on Curved Geometries," US National Congress on Computational Mechanics, Austin, TX, July 2019.

  32. "Modeling Curved Interfaces without Element-Partitioning in the Extended Finite Element Method (with Eric B. Chin)," Invited Lecture, X-DMS 2019, Lugano, Switzerland, July 2019.

  33. "Numerical Integration of Homogeneous Functions on Curved Geometries," Invited Lecture, SIAM Conference on Geometric Design, Vancouver, British Columbia, Canada, June 2019.

  34. "Virtual Element Method in Computational Mechanics," Invited Seminar, Department of Mechanical, Materials and Aerospace Engineering, Illinois Institute of Technology, Chicago, IL, December 2018.

  35. "Maximum-Entropy Approximation Schemes in Computational Mechanics," Invited Seminar, Sandia National Laboratories, Livermore, CA, September 2018.

  36. "Maximum-Entropy Approximation Schemes in Computational Mechanics," Plenary Lecture, USACM Thematic Workshop on Meshfree and Particle Methods: Application and Theory, Santa Fe, NM, September 2018.

  37. "Spectral Finite Elements and Enriched Partition-of-Unity Methods for Bandstructure Calculations in Phononic Crystals (with Ankit Srivastava)," Keynote Lecture, World Congress in Computational Mechanics, New York City, NY, July 2018.

  38. "Virtual Element Method in Computational Mechanics," Invited Seminar, CSRI Seminar, Sandia National Laboratories, Albuquerque, NM, July 2018.

  39. "Virtual Element Method in Computational Mechanics," Invited Seminar, T-3 Fluid Dynamics and Solid Mechanics Seminar, Los Alamos National Laboratory, Los Alamos, NM, July 2018.

  40. "Finite Element and Enriched Partition-of-Unity Methods for Wave Problems," Invited Lecture, Department of Civil and Environmental Engineering, Duke University, Durham, NC, April 2018.

  41. "Polygonal and Polyhedral Finite Element Technology in Computational Mechanics," Invited Seminar, Department of Civil and Environmental Engineering, Carnegie Mellon University, Pittsburgh, PA, November 2017.

  42. "Polygonal and Polyhedral Finite Element Technology in Computational Mechanics," Invited Seminar, ANSYS Inc., Canonsburg, PA, November 2017.

  43. "Numerical Integration of Homogeneous Functions on Convex and Nonconvex Polytopes: Applications in the Extended Finite Element Method," Invited Seminar, Department of Mechanical Engineering, UM - Shanghai Jiao Tong University Joint Institute, Shanghai, China, August 9, 2017.

  44. "Orbital-Enriched Partition of Unity Finite Element Method for Ab Initio Density Functional Calculations," Invited Seminar, Department of Mechanical Engineering, UM - Shanghai Jiao Tong University Joint Institute, Shanghai, China, August 7, 2017.

  45. "Numerical Integration of Homogeneous Functions on Convex and Nonconvex Polytopes: Applications in the Extended Finite Element Method," Invited Seminar, State Key Laboratory of Scientific and Engineering Computing, Chinese Academy of Sciences, Beijing, China, July 31, 2017.

  46. "Numerical Integration of Homogeneous Functions on Convex and Nonconvex Polytopes: Applications in the Extended Finite Element Method," Invited Seminar, School of Mathematical Sciences, Peking University, Beijing, China, July 28, 2017.

  47. "Computational Methods for Nonlinear Eigenvalue Problems (with Zhaojun Bai)," International Summer School on Scientific Computing, State Key Laboratory of Scientific and Engineering Computing, Chinese Academy of Sciences, Beijing, China, July 24 - August 5, 2017.

  48. "Modeling Crack Discontinuities and Holes without Element Partitioning in the Extended Finite Element Method," (with Eric B. Chin), 14th U.S. National Congress on Computational Mechanics, Montreal, Canada, July 2017.

  49. "Modeling Crack Discontinuities and Holes without Element-Partitioning in the Extended Finite Element Method," Invited Lecture, POEMS 2017, Milano, Italy, July 2017.

  50. "Maximum-Entropy Approximation Schemes in Computational Mechanics," Invited Seminar, Dassault Systemes Simulia Corporation, Johnston, RI, April 2017.

  51. "Orbital-Enriched Partition of Unity Finite Element Method for Ab Initio Density Functional Calculations," Invited Seminar, PRISM/CEE Seminar, Princeton University, Princeton, NJ, April 2017.

  52. "Maximum-Entropy Approximation Schemes in Computational Mechanics," Invited Seminar, Pierce Laboratory Seminar Series, Department of Civil and Environmental Engineering, MIT, Cambridge, MA, April 2017.

  53. "Maximum-Entropy Approximation Schemes in Computational Mechanics," Invited Seminar, Joint Materials/Solid Mechanics Seminar, Brown University, Providence, RI, April 2017.

  54. "Maximum-Entropy Meshfree Methods in Computational Mechanics," Opening Lecture, 42nd Israeli Symposium on Computational Mechanics (ISCM-42), Technion, Haifa, Israel, March 2017.

  55. "Partition of Unity Finite Element Method for Quantum Mechanical Materials Calculations," Invited Seminar, Department of Mechanical Engineering and Materials Science, Duke University, Durham, NC, February 2017.

  56. "Partition of Unity Methods," GIAN Short Course, Department of Mechanical Engineering, IIT Madras, Chennai, India, December 2016.

  57. "Partition of Unity Finite Element Method for Quantum Mechanical Materials Calculations," Invited Seminar, Department of Mechanical Engineering, UC Merced, Merced, CA, October 2016.

  58. "Feasibility Constraints for Smooth Convex Data Approximations via Semidefinite Programming (with Jean B. Lasserre)," USACM Conference on Isogeometric Analysis and Meshfree Methods, San Diego, CA, October 2016.

  59. "Partition of Unity Finite Element Method for Kohn-Sham Density Functional Calculations (with J. E. Pask)," Invited Lecture, USACM Workshop on Recent Advances in Computational Methods for Nanoscale Phenomena, Ann Arbor, MI, August 2016.

  60. "Modeling Crack Discontinuities without Element Partitioning in the Extended Finite Element Method (with Eric B. Chin and Jean B. Lasserre)," WCCM XII and APCOM VI, Seoul, South Korea, July 2016.

  61. "Numerical Integration of Homogeneous Functions and Polynomials on Polytopes (with Eric B. Chin and Jean B. Lasserre)," Polytopal Element Methods in Mathematics and Engineering (POEMs), Atlanta, GA, October 2015.

  62. "Modeling Crack Discontinuities without Element Partitioning in the Extended Finite Element Method (with Eric B. Chin and Jean B. Lasserre)," SES 52nd Annual Technical Meeting, College Station, TX, October 2015.

  63. "Quadrature Methods for Discontinuities and Singularities," Invited Lectures, X-DMS Short Course on Extended Discretization Methods, Ferrara, Italy, September 2015.

  64. "Comparison of Meshfree Galerkin Methods Based on MLS and Maximum-Entropy Approximation Schemes (with Mathieu Foca and Bo Li)," ECCOMAS Thematic Conference: X-DMS 2015 - eXtended Discretization Methods, Ferrara, Italy, September 2015.

  65. "Recent Developments in Maximum-Entropy Approximation Schemes," Invited Seminar, Department of Engineering Design, IIT Madras, Chennai, India, June 2015.

  66. "Recent Developments in Maximum-Entropy Approximant Schemes," Invited Seminar, Department of Mechanical and Aerospace Engineering, Case Western Reserve University, Cleveland, OH, March 2015.

  67. "Cell-Based Maximum-Entropy Approximants (with Marino Arroyo and Daniel Millan)," Invited Lecture, Workshop on Meshfree Methods for Large-Scale Computational Science and Engineering Tampa, FL, October 2014.

  68. "Cohesive Fracture Simulations on Polygonal Finite Element Meshes (with J. E. Bishop)," Invited Lecture, Symposium on Computational Fracture Mechanics, 51st Annual Technical Conference of Society of Engineering Sciences, Purdue University, West Lafayette, IN, October 2014.

  69. "Computations on Polygonal and Polyhedral Meshes with Entropy Approximants," Invited Seminar, Los Alamos National Laboratory, Los Alamos, NM, August 2014.

  70. "Computations on Polygonal and Polyhedral Meshes with Entropy Approximants," Invited Seminar, Sandia National Laboratories, Albuquerque, NM, August 2014.

  71. "Polygonal and Polyhedral Finite Element Methods in Computational Mechanics," Plenary Lecture, PACAM XIV: Fourteenth Pan-American Congress of Applied Mechanics, Santiago, Chile, March 2014.

  72. "Polygonal and Polyhedral Finite Element Methods in Computational Mechanics," Invited Seminar, Department of Civil and Environmental Engineering, Stanford University, CA, February 2014.

  73. "Maximum-Entropy Approximation Schemes: Theory and Links to B-Splines and Isogeometric Analysis (with Marino Arroyo)," Isogeometric Analysis: Integrating Design and Analysis (IGA 2014), Austin, TX, January 2014.

  74. "Polygonal and Polyhedral Finite Element Methods in Computational Mechanics," Keynote Lecture, 23rd International Workshop on Computational Mechanics of Materials, Singapore, October 2013.

  75. "Efficient Polygonal and Polyhedral Finite Element Methods (with Gianmarco Manzini and Alessandro Russo)," Invited Lecture, 7th International Workshop on Meshfree Methods for Partial Differential Equations, Bonn, Germany, September 2013.

  76. "New Perspectives on Polygonal and Polyhedral Finite Element Methods (with Gianmarco Manzini and Alessandro Russo)," Minisymposium on General Polyhedral Discretizations: Meshing, Formulations, and Applications, 12th U.S. National Congress on Computational Mechanics, Raleigh, NC, July 2013.

  77. "Quadratic Maximum-Entropy Serendipity Shape Functions for Arbitrary Planar Polygons," Invited Lecture, 1st Indian Conference on Applied Mechanics, IIT Madras, Chennai, India, July 2013.

  78. "Maximum-Entropy Approximation Schemes," Invited Seminar, Department of Mechanical Engineering, Indian Institute of Science, Bangalore, India, June 2013.

  79. "Meshfree Methods: From the Element-Free Galerkin Method to Maximum-Entropy Approximation Schemes," Invited Lecture, Advances in Computational Mechanics with Emphasis on Fracture and Multiscale Phenomena: Workshop Honoring Professor Ted Belytschko's 70th Birthday, Evanston, IL, April 2013.

  80. "Quadratic Maximum-Entropy Serendipity Shape Functions for Arbitrary Planar Polygons," Invited Lecture, Minisymposium on Meshfree and Generalized Finite Element Methods, Advances in Computational Mechanics: A Conference Celebrating the 70th Birthday of Thomas J. R. Hughes, San Diego, February 2013.

  81. "Generalized Barycentric Coordinates on Polygons and Polyhedra," Invited Seminar, Combined Applied Math and PDEs Seminar, Department of Mathematics, University of California at Davis, October 2012.

  82. "Quadratic Polygonal Finite Element Methods," Invited Seminar, Faculty of Informatics, Universita della Svizzera italiana, Lugano, Switzerland, September 21, 2012.

  83. "Polygonal Finite Element Methods," Invited Lecture, Workshop on Discretization Methods for Polygonal and Polyhedral Meshes, University of Milano-Bicocca, Milan, Italy, September 17-19, 2012.

  84. "Barycentric Finite Element Methods," Invited Lecture, Workshop on Generalized Barycentric Coordinates in Geometry Processing and Finite/Boundary Element Methods, Columbia University, New York, July 26, 2012.

  85. "Maximum-Entropy Approximants: Applications in Solid Mechanics and Structural Engineering," Invited Lecture, Department of Civil and Environmental Engineering, University of Pittsburgh, Pittsburgh, PA, February 2012.

  86. "Efficient Numerical Integration Schemes for Singularities, Sharp Gradients and Cusps: Applications in Fracture and Quantum Mechanics (with J. E. Pask and S. E. Mousavi)," Symposium on Meshfree and Extended/Generalized Finite Element Methods, PACAM XII, Port of Spain, Trinidad, January 2012.

  87. "Maximum-Entropy Approximation Schemes," Symposium on Meshfree and Extended/Generalized Finite Element Methods, PACAM XII, Port of Spain, Trinidad, January 2012.

  88. "Maximum-Entropy Approximations in Computational Mechanics," Invited Lecture, Department of Applied Mechanics, IIT Madras, Chennai, India, December 2011.

  89. "Partition-of-Unity Enriched Finite Elements to Solve the Hartree-Fock Equations (with T. J. Martínez)," Symposium on Current Multiscale Computations and Algorithms, 48th Annual Technical Conference of Society of Engineering Sciences, Evanston, IL, October 2011.

  90. "Enriched Finite Element Solution for the All-Electron Coulomb Problem in Solids (with J. E. Pask and S. E. Mousavi)," Poster Presentation, CECAM - Jülich Summer School 2011 on Fast Methods for Long-Range Interactions in Complex Systems, Jülich, Germany, September 2011.

  91. "A New Real-Space Formulation for the All-Electron Coulomb Problem in Crystalline Solids (with J. E. Pask and S. E. Mousavi)," Symposium on Recent Developments in Nanoscale Modeling of Materials, 11th U.S. National Congress on Computational Mechanics, Minneapolis, MN, July 2011.

  92. "Partition-of-Unity Finite Elements for Large, Accurate Quantum-Mechanical Materials Calculations," Plenary Lecture, ECCOMAS Thematic Conference on the Extended Finite Element Method (XFEM 2011), Cardiff, UK, July 1, 2011.

  93. Invited Participant, Mini-Workshop: Mathematical Models, Analysis, and Numerical Methods for Dynamic Fracture, Mathematische Forschungsinstitut Oberwolfach, Germany, April 24-30, 2011.

  94. "Extended Finite Elements for Crack Modeling: Numerical Integration Issues and Harmonic Enrichment Functions," Invited Lecture, Seminar in Computational Mechanics Organized by Laboratori de Calcul Numeric, Universitat Politecnica De Catalunya, Barcelona, Spain, July 2010.

  95. "Maximum-Entropy Meshfree Method in Computational Mechanics," Invited Lecture, Universidad Politecnica de Valencia, Spain, July 2010.

  96. "Extended Finite Elements using Harmonic Enrichment Functions for Crack Modeling," Invited Lecture, Universidad Politecnica de Valencia, Spain, July 2010.

  97. "Extended Finite Element Method for Crack Modeling: Formulation and Recent Developments," Invited Seminar, Dpto. Mecanica de Estructuras, Universidad de Granada, Spain, June 2010.

  98. "Extended Finite Element Method for Crack Modeling: Formulation and Recent Developments," Invited Seminar, Universidad de Sevilla, Spain, June 2010.

  99. "Maximum-Entropy Meshfree Method," Invited Lecture, Student-Run Applied & Math Seminar, Department of Mathematics, University of California, Davis, CA, April 2010.

  100. "Partition of Unity Finite Elements for Quantum-Mechanical Calculations in Condensed Matter: Have Planewaves Finally Met Their Match," Invited Lecture, Department of Mechanical Engineering, Mechanics of Computation Seminar, Stanford University, January 2010.

  101. "Maximum-Entropy Approximation in Computational Mechanics," Invited Lecture, Department of Civil and Environmental Engineering, Structural Engineering Seminar Series, University of Illinois at Urbana-Champaign, October 2009.

  102. "Efficient Numerical Integration for Discontinuities and Vertex Singularities in the Extended Finite Element Method," Invited Lecture, Institute of Continuum Mechanics, Leibniz University Hannover, Hannover, Germany, October 6, 2009.

  103. "Linear Scaling Finite Element Solution for the All-Electron Coulomb Problem in Solids," Invited Lecture, Institute for Numerical Simulation, University of Bonn, Bonn, Germany, October 1, 2009.

  104. "Generalized Gaussian Quadrature Rules for Discontinuities and Crack Singularities in the Extended Finite Element Method (with S. E. Mousavi)," ECCOMAS Thematic Conference - XFEM 2009 The extended finite element method: Recent developments and applications, Aachen, Germany, September 28-30, 2009.

  105. "Maximum Entropy Coordinates for Arbitrary Polytopes (with Kai Hormann)," 10th US National Congress on Computational Mechanics, Symposium on Synergies in Computational Mechanics and Geometry, Columbus, OH, July 2009.

  106. "Partition of Unity Finite Element Method to Solve the Kohn-Sham Equations of Density Functional Theory (with J. E. Pask)," Keynote Lecture, Symposium on Advances in Multiscale and Multiphysics Methods: From Quantum to Continuum, 8th World Congress on Computational Mechanics WCCM8, Venice, Italy, July 2008.

  107. "A New Finite Element Method for Three-Dimensional Non-Planar Crack Growth Simulations," Invited Lecture, Department of Mechanical and Aeronautical Engineering, University of California at Davis, CA, June 2008.

  108. "Linear Scaling Enriched Finite Element Solution of the Coulomb Problem in Solids," Invited Lecture, Structural Mechanics Seminar, Georgia Institute of Technology, Atlanta, GA, March 2008.

  109. "Partition of Unity Finite Elements for Electronic-Structure Calculations in Molecules and Crystalline Solids," Invited Lecture, Department of Mechanical Engineering and Applied Mechanics, University of Pennsylvania, Philadelphia, PA, December 7, 2007.

  110. "X-FEM and FMM: A Paradigm for Planar and Non-Planar Crack Growth Simulations," Invited Presentation, Global Engineering and Materials, Inc., Baltimore, MD, December 5, 2007.

  111. "A New Real-Space Finite Element Method to Solve the Kohn-Sham Equations of Density Functional Theory," Invited Lecture, Numerical Analysis and Scientific Computing Seminar, Courant Institute of Mathematical Sciences, New York University, New York, NY, November 16, 2007.

  112. "Partition of Unity Finite Elements for Electronic-Structure Calculations in Molecules and Crystalline Solids," Invited Lecture, Joint Mechanical Engineering/Civil Engineering Seminar, Columbia University, New York, NY, November 9, 2007. [PDF]

  113. "Barycentric Finite Element Methods," Invited Lecture, Symposium on Barycentric Coordinates and Transfinite Interpolation, Tenth SIAM Conference on Geometric Design & Computing, San Antonio, TX, November 5, 2007.

  114. "Three-Dimensional Non-Planar Crack Growth by a Coupled Extended Finite Element and Fast Marching Method," Invited Lecture, Department of Civil and Environmental Engineering, Cornell University, Ithaca, NY, October 29, 2007.

  115. "Mesh-Independent Crack Modeling using the Extended Finite Element Method," Invited Presentation, Cornell Fracture Group, Cornell University, Ithaca, September 27, 2007.

  116. "Three-Dimensional Non-Planar Crack Growth by a Coupled Extended Finite Element and Fast Marching Method (with D. L. Chopp, N. Moës, E. Bechet)," 9th U.S. National Congress on Computational Mechanics, San Francisco, CA, July 25, 2007.

  117. "Finite Element and Meshfree Methods in Mechanics," Invited Lecture, GGAM Mini-Conference, Department of Mathematics, University of California, Davis, CA, March 31, 2007.

  118. "Linking Geometry and Approximation for Computational Mechanics," Invited Lecture, Mechanics Colloquium, Technical University of Kaiserslautern, Germany, September 18, 2006.

  119. "Partition of Unity Finite Elements in Quantum Mechanical Materials Calculations," Invited Lecture, Seminar in Computational Mechanics Organized by Laboratori de Calcul Numeric and CIMNE, Universitat Politecnica De Catalunya, Barcelona, Spain, September 15, 2006.

  120. "Meshfree Methods and Partition of Unity Finite Elements," Short Course at Universidad Politecnica De Valencia, Valencia, Spain, September 5-11, 2006.

  121. "Partition of Unity Finite Element Method for Large-Scale Electronic Structure Calculations (with J. E. Pask)," Seventh World Congress on Computational Mechanics, Symposium on Enriched Finite Element Methods for Evolving Discontinuities and Interfaces, Los Angeles, CA, July 2006.

  122. "Continuity of Maximum-Entropy Basis Functions via Variational Analysis (with R. J-B Wets)," Seventh World Congress on Computational Mechanics, Symposium on Computational Geometry and Analysis, Los Angeles, CA, July 2006.

  123. "Recent Advances in Polygonal Finite Element Methods," Invited Lecture, Mathematical Modeling and Analysis Group, Los Alamos National Laboratory, Los Alamos, New Mexico, April 2006.

  124. "Natural Neighbors and Voronoi Tessellations in Computational Solid Mechanics," Keynote Lecture, The World a Jigsaw: Tessellations in the Sciences, Lorent Center, Leiden University, The Netherlands, March 6-10, 2006 [PDF] [HTML] [PDF]

  125. "Scattered Data Approximation and Meshfree Methods," Invited Lecture, Applied Math Seminar, Department of Mathematics, University of California, Davis, CA, October 2005 [PDF]

  126. "Adaptive Computations using Conforming Quadtree Meshes," (with A. Tabarraei), Invited Lecture, Mechanics Colloquium, Technical University of Kaiserslautern, Germany, September 2005

  127. "Construction of Meshfree Approximation Schemes: Use of Information-Theoretic Variational Principles," Invited Lecture, Technical University of Kaiserslautern, Germany, September 2005

  128. "Meshfree Methods and Partition of Unity Finite Elements: Basic Principles and Applications," Invited Lecture, Technical University of Kaiserslautern, Germany, September 2005

  129. "Adaptive Computations using Residual-Based Error Estimators on Conforming Quadtree Meshes," (with A. Tabarraei), Third International Workshop on Meshfree Methods for Partial Differential Equations, Bonn, Germany, September 2005

  130. "Maximum Entropy Approximation," 25th International Workshop on Bayesian Inference and Maximum Entropy Methods in Science and Engineering, San Jose State University, CA, August 2005

  131. "Maximum Entropy Approximation," Symposium on Meshfree and Particle Methods, Keynote Lecture, Eight U.S. National Congress on Computational Mechanics, Austin, TX, July 2005 [PDF]

  132. "Scattered Data Approximation using the Maximum Entropy Principle," Invited Lecture, Department of Civil and Environmental Engineering, Cornell University, Ithaca, NY, May 2005.

  133. "Scattered Data Approximation using the Maximum Entropy Principle," Invited Lecture, Department of Mechanical and Aeronautical Engineering, University of California, Davis, CA, December 2004.

  134. "Modeling Arbitrary Crack Discontinuities in Finite Elements," Invited Lecture, Rockwell Scientific Company, Thousand Oaks, CA, November 2004

  135. "Recent Advances in Polygonal Finite Elements: Construction and Applications to PDEs,", Keynote Lecture, International Workshops on Advances in Computational Mechanics (Meshfree/Particle Methods), Hosei University, Tokyo, Japan, November 2004.

  136. "Construction and Application of Polygonal Finite Element Approximations," (with A. Tabarraei), Sixth World Congress on Computational Mechanics, Symposium on Meshfree and Extended/Fictitious FEM, Beijing, China, September 2004.

  137. "Polygonal Interpolants: Construction and Adaptive Computations on Quadtree Meshes," (with A. Tabarraei), European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS 2004), Symposium on Computational Fracture Mechanics, Jyvskyla, Finland, July 2004.

  138. "Polygonal Finite Elements: Construction and Applications to PDEs," Invited Lecture, Ecole Centrale de Nantes, Nantes, France, July 2004

  139. "Partition of Unity and Polygonal Finite Element Methods," Invited Lecture, Universidad Politecnica de Valencia, Spain, April 2004

  140. "Numerical Formulation and Application of Polygonal Finite Elements" (with A. Tabarraei), 7th International ESAFORM Conference on Material Forming, Trondheim, Norway, April 2004

  141. "Conforming Polygonal Finite Elements," Invited Lecture, Laboratoire de Mecanique des Systemes et des Procedes, ENSAM, Paris, France, April 2004

  142. "Modeling Strong and Weak Discontinuities within Displacement Based Finite Elements," Invited Lecture, Department of Applied Mechanics, Indian Institute of Technology Madras, Chennai, India, March 2004

  143. "Modeling Arbitrary Discontinuities in Finite Elements," Invited Lecture, Department of Mechanical Engineering, Indian Institute of Technology Bombay, Mumbai, India, March 2004

  144. "Partition of Unity Enrichment for Bimaterial Interface Cracks," (with J. H. Prévost, Z. Suo, and Z. Y. Huang) Seventh U.S. National Congress on Computational Mechanics, Albuquerque, NM, July 2003 [PDF]

  145. "Irregular Lattice Models for Diffusion Processes and Crack Propagation," (with J. E. Bolander) Invited Presentation, Mimetic Discretizations of Continuum Mechanics, San Diego, CA, July 2003

  146. "Meshless Methods and Partition of Unity Finite Elements" Keynote Lecture, 6th International ESAFORM Conference on Material Forming, Salerno, Italy, April 28-30, 2003

  147. "Finite Element-Based Model for Crack Propagation in Polycrystalline Materials" Invited Lecture, 2nd Symposium on Computational Modeling of Multi-Scale Phenomena, Petropolis, Brazil, August 2002 [PDF]

  148. "Modeling Discontinuities and their Evolution within Finite Elements: Application to Material Interfaces, 3-D Cracks, and Microstructures," Invited Lecture, Department of Mechanical and Aerospace Engineering, Rutgers University, Piscataway, NJ, September 2001

  149. "Enriched Natural Neighbor Interpolants for Two-Dimensional Crack Modeling," Sixth U.S. National Congress on Computational Mechanics, Dearborn, MI (August 2001) [PDF]

  150. "Microstructural Effects in Brittle Fracture with the Extended Finite Element Method," (with D. J. Srolovitz, J. H. Prévost, and T. J. Baker) Sixth U.S. National Congress on Computational Mechanics, Dearborn, MI, August 2001 [PDF]

  151. "Sibson and Non-Sibsonian Interpolants for Elliptic Partial Differential Equations," First MIT Conference on Fluid and Solid Mechanics, Cambridge, MA, June 2001

  152. "Extended Finite Element Method: Introduction and Applications," MAE Material Group Seminar, Princeton University, NJ, December 2000

  153. "Natural Neighbor Galerkin Methods," (with Brian Moran) ICTAM 2000, Chicago, IL, October 2000

  154. "Modeling Holes and Inclusions by Level Sets in the Extended Finite Element Method," Mechanics Club Seminar, Northwestern University, Evanston, IL, February 2000

  155. "The Natural Element Method," Number Crunch Seminar, Engineering Sciences and Applied Mathematics, Northwestern University, Evanston, IL, October 1999

  156. "Galerkin Methods for Elliptic Partial Differential Equations," Number Crunch Seminar, Engineering Sciences and Applied Mathematics, Northwestern University, Evanston, IL, October 1999

  157. "An Element-Free Galerkin Method for 3D Crack Growth," (with T. Belytschko, B. Moran, and T. Black) Joint ASME, ASCE, and SES Conference (McNU 97), Northwestern University, Evanston, IL (July 1997)

PUBLICATIONS

Refereed Journal and Conference Publications, and Books

  1. O. Čertík, J. E. Pask, I. Fernando, R. Goswami, N. Sukumar, N. Sukumar, L. A. Collins, G. Manzini and J. Vackář (2023), "High-Order Finite Element Method for Atomic Structure Calculations," arXiv:2307.05856. [HTML]
  2. A. Chen and N. Sukumar (2023) "Stress-Hybrid Virtual Element Method on Quadrilateral Meshes for Compressible and Nearly-Incompressible Linear Elasticity," arXiv: 2304.04941 [HTML]
  3. S. Berrone, C. Canuto, M. Pintore and N. Sukumar (2022), "Enforcing Dirichlet Boundary Conditions in Physics-Informed Neural Networks and Variational Physics-Informed Neural Networks," arXiv: 2210.14795 [HTML]
  4. A. Chen and N. Sukumar (2023) "Stabilization-Free Serendipity Virtual Element Method for Plane Elasticity," Computer Methods in Applied Mechanics and Engineering, Vol. 404, Article 115784. [HTML]
  5. A. Chen and N. Sukumar (2023) "Stabilization-Free Virtual Element Method for Plane Elasticity," Computers and Mathematics with Applications, Vol. 138, pp. 88–105. [HTML]
  6. N. Sukumar and J. E. Bolander (2022) "Virtual Element Method for Modeling the Deformation of Multiphase Composites," Mechanics Research Communications, Vol. 124, Article 103907 [HTML]
  7. N. Sukumar and M. R. Tupek (2022) "Virtual Elements on Agglomerated Finite Elements to Increase the Critical Time Step in Elastodynamic Simulations," International Journal for Numerical Methods in Engineering, Vol. 123, Number 19, pp. 4702–4725. [HTML]
  8. N. Sukumar and A. Srivastava (2022) "Exact Imposition of Boundary Conditions with Distance Functions in Physics-Informed Deep Neural Networks," Computer Methods in Applied Mechanics and Engineering, Vol. 389, Article 114333. Available at arXiv: 2104.08426
  9. E. Benvenuti, A. Chiozzi, G. Manzini and N. Sukumar (2022), "Extended Virtual Element Method for Two-Dimensional Linear Elastic Fracture," Computer Methods in Applied Mechanics and Engineering, Vol. 390, Article 114352. [PDF] Available at arXiv: 2111.04150
  10. E. B. Chin and N. Sukumar (2021), "Scaled Boundary Cubature Scheme for Numerical Integration over Planar Regions with Affine and Curved Boundaries," Computer Methods in Applied Mechanics and Engineering, Vol. 380, Article 113796. [PDF]
  11. E. B. Chin, A. A. Mokhtari, A. Srivastava, and N. Sukumar (2021), "Spectral Extended Finite Element Method for Band Structure Calculations in Phononic Crystals," Journal of Computational Physics, Vol. 427, Article 110066. [PDF]
  12. J. Jaśkowiec and N. Sukumar (2021), "Addendum to the Paper "High-Order Symmetric Cubature Rules for Tetrahedra and Pyramids," International Journal for Numerical Methods in Engineering, Vol. 122, Number 7, pp. 1875–1883. [PDF] [Cubature Rules]
  13. J. Jaśkowiec and N. Sukumar (2021), "High-Order Symmetric Cubature Rules for Tetrahedra and Pyramids," International Journal for Numerical Methods in Engineering, Vol. 122, Number 1, pp. 148–171. [PDF] [Cubature Rules]
  14. E. B. Chin and N. Sukumar (2020), "An Efficient Method to Integrate Polynomials Over Polytopes and Curved Solids," Computer Aided Geometric Design, Vol. 82, 101914. [PDF] [C++ Code]
  15. J. Jaśkowiec and N. Sukumar (2020), "High-Order Cubature Rules for Tetrahedra," International Journal for Numerical Methods in Engineering, Vol. 121, Number 11, pp. 2418–2436. [PDF] [Cubature Rules]
  16. R. Silva-Valenzuela, A. Ortiz-Bernardin, N. Sukumar, E. Artioli and N. Hitschfeld-Kahler (2020), "A Nodal Integration Scheme for Meshfree Galerkin Methods using the Virtual Element Decomposition," International Journal for Numerical Methods in Engineering, Vol. 121, Number 10, pp. 2174–2205. [PDF]
  17. J. E. Bishop and N. Sukumar (2020), "Polyhedral Finite Elements for Nonlinear Solid Mechanics using Tetrahedral Subdivisions and Dual-Cell Aggregation," Computer Aided Geometric Design, Vol. 77, Article 101812. [PDF]
  18. E. Benvenuti, A. Chiozzi, G. Manzini and N. Sukumar (2019), "Extended Virtual Element Method for the Laplace Problem with Singularities and Discontinuities," Computer Methods in Applied Mechanics and Engineering, Vol. 356, pp. 571–597. [PDF]
  19. E. B. Chin and N. Sukumar (2019), "Modeling Curved Interfaces without Element-Partitioning in the Extended Finite Element Method," International Journal for Numerical Methods in Engineering, Vol. 120, Number 5, pp. 607–649. [PDF]
  20. C. Liu, J. H. Prévost and N. Sukumar (2019), "Modeling Branched and Intersecting Faults in Reservoir-Geomechanics Models with the Extended Finite Element Method," International Journal for Numerical and Analytical Methods in Geomechanics, Vol. 43, Number 12, pp. 2075–2089. [PDF]
  21. C. Liu, J. H. Prévost and N. Sukumar (2019), "Modeling Piecewise Planar Faults without Element-Partitioning in 3D Reservoir-Geomechanical Models," International Journal for Numerical and Analytical Methods in Geomechanics, Vol. 43, Number 2, pp. 530–543. [PDF]
  22. E. B. Chin, J. E. Bishop, R. V. Garimella and N. Sukumar (2018) "Finite Deformation Cohesive Polygonal Finite Elements for Modeling Pervasive Fracture," International Journal of Fracture, Vol. 214, Number 2, pp. 139–165. [PDF]
  23. C. Albrecht, C. Klaar, J. E. Pask, M. A. Schweitzer, N. Sukumar and A. Ziegenhagel (2018), "Orbital-enriched Flat-top Partition of Unity Method for the Schrödinger Eigenproblem," Computer Methods in Applied Mechanic and Engineering, Vol. 342, pp. 224–239. [PDF] Available at arXiv:1801.09596
  24. Y. Cai, Z. Bai, J. E. Pask and N. Sukumar (2018), "Convergence Analysis of a Locally Accelerated Preconditioned Steepest Descent Method for Hermitian-Definite Generalized Eigenvalue Problems," Journal of Computational Mathematics, Vol. 36, Number 5, pp. 739–760. [PDF]
  25. N. Moës, J. E. Dolbow and N. Sukumar (2018), "Extended Finite Element Methods," in Encyclopedia of Computational Mechanics, Second Edition, E. Stein, R. de Borst and T. J. R. Hughes (Editors), John Wiley & Sons, New York.
  26. K. Hormann and N. Sukumar (Eds.) (2017), "Generalized Barycentric Coordinates in Computer Graphics and Computational Mechanics," CRC Press, Boca Raton, FL. [HTML] COVER [Taylor & Francis]
  27. J.-H. Prévost, A. M. Rubin and N. Sukumar (2017), "Intersecting Fault Simulations for Three-Dimensional Reservoir-Geomechanical Models," Sixth Biot Conference on Poromechanics, Paris, France, American Society of Civil Engineers. [HTML]
  28. A. Ortiz-Bernardin, A. Russo and N. Sukumar (2017), "Consistent and Stable Meshfree Galerkin Methods using the Virtual Element Decomposition," International Journal for Numerical Methods in Engineering, Vol. 112, Number 7, pp. 655–684. [PDF]
  29. S. Banerjee and N. Sukumar (2017), "Exact Integration Scheme for Planewave-Enriched Partition of Unity Finite Element Method to Solve the Helmholtz Problem," Computer Methods in Applied Mechanics and Engineering, Vol. 317, pp. 619–648. [PDF]
  30. J. E. Pask and N. Sukumar (2017), "Partition of Unity Finite Element Method for Quantum Mechanical Materials Calculations," Extreme Mechanics Letters, Vol. 11, pp. 8–17. [PDF] Available at arXiv:1611.00731
  31. E. B. Chin, J. B. Lasserre and N. Sukumar (2017), "Modeling Crack Discontinuities without Element-Partitioning in the Extended Finite Element Method," International Journal for Numerical Methods in Engineering, Vol. 110, Number 11, pp. 1021–1048. [PDF] Erratum
  32. J.-H. Prévost and N. Sukumar (2016), "Faults Simulations for Three-Dimensional Reservoir-Geomechanical Models with the Extended Finite Element Method," Journal of the Mechanics and Physics of Solids, Vol. 86, pp. 1–18. [PDF]
  33. N. Sukumar, J. E. Dolbow and N. Moës (2015), "Extended Finite Element Method in Computational Fracture Mechanics: A Retrospective Examination," International Journal of Fracture, Vol. 196, Number 1–2, pp. 189–206. [PDF]
  34. J.-H. Prévost and N. Sukumar (2015), "Multi-scale X-FEM Faults Simulations for Reservoir-Geomechanical Models," 49th US Rock Mechanics/Geomechanics Symposium, American Rock Mechanics Association. [HTML]
  35. E. B. Chin, J. B. Lasserre and N. Sukumar (2015), "Numerical Integration of Homogeneous Functions on Convex and Nonconvex Polygons and Polyhedra," Computational Mechanics, Vol. 56, Number 6, pp. 967–981. [PDF]
  36. A. Ortiz-Bernardin, M. A. Puso and N. Sukumar (2015), "Improved Robustness for Nearly-Incompressible Large Deformation Meshfree Simulations on Delaunay Tessellations," Computer Methods in Applied Mechanics and Engineering, Vol. 293, pp. 348–374. [PDF]
  37. A. Cangiani, G. Manzini, A. Russo and N. Sukumar (2015), "Hourglass Stabilization and the Virtual Element Method," International Journal for Numerical Methods in Engineering, Vol. 102, Number 3-4, pp. 404–436. [PDF]
  38. D. Millán, N. Sukumar and M. Arroyo (2015), "Cell-Based Maximum-Entropy Approximants," Computer Methods in Applied Mechanics and Engineering, Vol. 284, pp. 712–731. [PDF]
  39. G. Manzini, A. Russo and N. Sukumar (2014), "New Perspectives on Polygonal and Polyhedral Finite Element Methods," Math. Models Methods Appl. Sci., Vol. 24, Number 8, pp. 1665–1699. [PDF]
  40. M. Floater, A. Gillette and N. Sukumar (2014), "Gradient Bounds for Wachspress Coordinates on Polytopes," SIAM Journal on Numerical Analysis, Vol. 52, Number 1, pp. 515–532. [PDF] Available at arXiv:1306.4385
  41. Y. Cai, Z. Bai, J. E. Pask and N. Sukumar (2013), "Hybrid Preconditioning for Iterative Diagonalization of Ill-Conditioned Generalized Eigenvalue Problems in Electronic Structure Calculations," Journal of Computational Physics, Vol. 255, pp. 16–30. [PDF] Available at arXiv:1308.2445
  42. N. Sukumar (2013), "Quadratic Maximum-Entropy Serendipity Shape Functions for Arbitrary Planar Polygons," Computer Methods in Applied Mechanics and Engineering, Vol. 263, pp. 27–41. [PDF]
  43. J. O. Royset, N. Sukumar and R. J-B Wets (2013), "Uncertainty Quantification using Exponential Epi-Splines," Proceedings of the 11th International Conference on Structural Safety and Reliability, New York, NY. [PDF]
  44. F. Greco and N. Sukumar (2013), "Derivatives of Maximum-Entropy Basis Functions on the Boundary: Theory and Computations," International Journal for Numerical Methods in Engineering, Vol. 94, Number 12, pp. 1123–1149. [PDF]
  45. G. Hattori, R. Rojas-Díaz, A. Sáez, N. Sukumar and F. García-Sánchez (2012), "New Anisotropic Crack-Tip Enrichment Functions for the Extended Finite Element Method," Computational Mechanics, Vol. 50, Number 5, pp. 591–601. [PDF]
  46. G. Quaranta, S. K. Kunnath and N. Sukumar (2012), "Maximum-Entropy Meshfree Method for Nonlinear Static Analysis of Planar Reinforced Concrete Structures," Engineering Structures, Vol. 42, pp. 179–189. [PDF]
  47. J. E. Pask, N. Sukumar and S. E. Mousavi (2012), "Linear Scaling Solution of the All-Electron Coulomb Problem in Solids," International Journal for Multiscale Computational Engineering, Vol. 10, Number 1, pp. 83–99. Available at arXiv:1004.1765
  48. S. E. Mousavi, J. E. Pask and N. Sukumar (2011), "Efficient Adaptive Integration of Functions with Sharp Gradients and Cusps in n-Dimensional Parallelepipeds," International Journal for Numerical Methods in Engineering, Vol. 91, Number 4, pp. 343–357. [PDF]
  49. R. Rojas-Díaz, N. Sukumar, A. Sáez and F. García-Sánchez (2011), "Fracture in Magnetoelectroelastic Materials using the Extended Finite Element Method," International Journal for Numerical Methods in Engineering, Vol. 88, Number 12, pp. 1238–1259. [PDF]
  50. G. Hattori, R. Rojas-Díaz, A. Sáez, F. García-Sánchez and N. Sukumar (2011), "El Método de los Elementos Finitos Extendidos (X-FEM) para Medios Bidimensionales Fisurados Totalmente Anisótropos," Anales de Mecánica de la Fractura, Vol. 28, Number 2, pp. 451–455. [PDF]
  51. A. Ortiz, M. A. Puso and N. Sukumar (2011), "Maximum-Entropy Meshfree Method for Incompressible Media Problems," Finite Element in Analysis and Design, Vol. 47, Number 6, pp. 572–585. [PDF]
  52. S. E. Mousavi and N. Sukumar (2011), "Numerical Integration of Polynomials and Discontinuous Functions on Irregular Convex Polygons and Polyhedrons," Computational Mechanics, Vol. 47, Number 5, pp. 535–554. [PDF]
  53. S. E. Mousavi, E. Grinspun and N. Sukumar (2011), "Higher-Order Extended Finite Elements with Harmonic Enrichment Functions for Complex Crack Problems," International Journal for Numerical Methods in Engineering, Vol. 86, Number 4–5, pp. 560–574. [PDF]
  54. S. E. Mousavi, E. Grinspun and N. Sukumar (2011), "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, Vol. 85, Number 10, pp. 1306–1322. [PDF]
  55. J. X. Shi, D. L. Chopp, J. Lua, N. Sukumar and T. Belytschko (2010) "Abaqus Implementation of Extended Finite Element using a Level Set Representation for Three-Dimensional Fatigue Crack Growth and Life Predictions," Engineering Fracture Mechanics, Vol. 77, Number 14, pp. 2840–2863. [Top 25 Hottest article (July 2010-present)] [PDF]
  56. S. E. Mousavi and N. Sukumar (2010), "Generalized Gaussian Quadrature Rules for Discontinuities and Crack Singularities in the Extended Finite Element Method," Computer Methods in Applied Mechanics and Engineering, Vol. 199, Number 49–52, pp. 3237–3249. [PDF]
  57. A. Ortiz, M. A. Puso and N. Sukumar (2010), "Maximum-Entropy Meshfree Method for Compressible and Near-Incompressible Elasticity," Computer Methods in Applied Mechanics and Engineering, Vol. 199, Number 25–28, pp. 1859–1871. [PDF]
  58. S. E. Mousavi and N. Sukumar (2010), "Generalized Duffy Transformation for Integrating Vertex Singularities," Computational Mechanics, 45, Number 2–3, pp. 127–140. [PDF]
  59. S. E. Mousavi, H. Xiao and N. Sukumar (2010), "Generalized Gaussian Quadrature Rules on Arbitrary Polygons," International Journal for Numerical Methods in Engineering, Vol. 82, Number 1, pp. 99–113. [PDF]
  60. R. Rojas-Díaz, N. Sukumar, A. Sáez and F. García-Sánchez (2009), "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, Eds. T.-P. Fries and A. Zilian, Aachen, Germany, pp. 181–186. [PDF]
  61. J. Shi, J. Lua, L. Chen, D. Chopp and N. Sukumar (2009), "X-FEM for Abaqus (XFA) Toolkit for Automated Crack Onset and Growth Simulation: New Development, Validation, and Demonstration," Engineering Fracture Mechanics, 2009 SIMULIA Customer Conference. [PDF]
  62. A. Rajagopal, M. Scherer, P. Steinmann and N. Sukumar (2009), "Smooth Conformal α-NEM for Gradient Elasticity," The International Journal of Structural Changes in Solids – Mechanics and Applications, 1, Number 1, pp. 83–109. [PDF]
  63. W. Aquino, J. C. Brigham, C. J. Earls and N. Sukumar (2009), "Generalized Finite Element Method using Proper Orthogonal Decomposition," International Journal for Numerical Methods in Engineering, Vol. 79, Number 7, pp. 887–906. [PDF]
  64. L. L. Yaw, N. Sukumar and S. K. Kunnath (2009), "Meshfree Co-Rotational Formulation for Two-Dimensional Continua," International Journal for Numerical Methods in Engineering, Vol. 79, Number 8, pp. 979–1003. [PDF]
  65. L. L. Yaw, S. K. Kunnath and N. Sukumar (2009), "Meshfree Method for Inelastic Frame Analysis," ASCE Journal of Structural Engineering, Vol. 135, Number 6, pp. 676–684. [PDF]
  66. N. Sukumar and J. E. Pask (2009), "Classical and Enriched Finite Element Formulations for Bloch-Periodic Boundary Conditions,", International Journal for Numerical Methods in Engineering, Vol. 77, Number 8, pp. 1121–1138. [Erratum: a = 5.7 bohr for the harmonic oscillator problem in Sec. 4.2.1] [PDF]
  67. E. Giner, N. Sukumar, J. E. Tarancón and F. J. Fuenmayor (2009), "An Abaqus Implementation of the Extended Finite Element Method," Engineering Fracture Mechanics, Vol. 76, Number 3, pp. 347–368. [Top 25 Hottest article (January 2009-present)] [PDF]
  68. E. Giner, N. Sukumar, F. J. Fuenmayor and A. Vercher (2008), "Singularity Enrichment for Complete Sliding Contact using the Partition of Unity Finite Element Method," International Journal for Numerical Methods in Engineering, Vol. 76, Number 9, pp. 1402–1418. [PDF]
  69. E. Giner, N. Sukumar, F. D. Denia and F. J. Fuenmayor (2008), "Extended Finite Element Method for Fretting Fatigue Crack Propagation," International Journal of Solids and Structures, Vol. 45, Number 22–23, pp. 5675–5687. [PDF]
  70. K. Hormann and N. Sukumar (2008), "Maximum Entropy Coordinates for Arbitrary Polytopes," Computer Graphics Forum, Vol. 27, Number 5, pp. 1513–1520. Proceedings of SGP 2008. [PDF]
  71. N. Sukumar, D. L. Chopp, E. Béchet and N. Moës (2008), "Three-Dimensional Non-Planar Crack Growth by a Coupled Extended Finite Element and Fast Marching Method," International Journal for Numerical Methods in Engineering, Vol. 76, Number 5, pp. 727–748. [PDF]
  72. N. Sukumar and J. E. Bolander (2009), "Voronoi-based Interpolants for Fracture Modelling," in Tessellations in the Sciences: Virtues, Techniques and Applications of Geometric Tilings, Springer Verlag, pp. xxx–xxx. [PDF]
  73. C. B. Hirschberger, S. Ricker, P. Steinmann and N. Sukumar (2009),"Computational multiscale modelling of heterogeneous material layers," Engineering Fracture Mechanics, Vol. 76, Number 6, pp. 793–812. [PDF]
  74. J. Shi, J. Lua, H. Waisman, P. Liu, T. Belytschko, N. Sukumar and Y. Liang (2008), "X-FEM Toolkit for Automated Crack Onset and Growth Prediction," 49th AIAA Conference, Schaumburg, IL, April 2008, pp. 1–22. [PDF]
  75. A. Tabarraei and N. Sukumar (2008), "Extended Finite Element Method on Polygonal and Quadtree Meshes," Computer Methods in Applied Mechanics and Engineering, Vol. 197, Number 5, pp. 425–438. [PDF]
  76. C. B. Hirschberger, N. Sukumar and P. Steinmann (2008),"Computational homogenization of material layers with micromorphic mesostructure," Philosophical Magazine, Vol. 88, pp. 3603–3631. [PDF]
  77. C. B. Hirschberger S. Ricker, P. Steinmann and N. Sukumar (2007),"A computational homogenisation approach for cohesive interfaces," in Proceedings of the International Conference on Computational Plasticity, Computational Plasticity IX: Fundamentals and Applications, Eds. D. R. J. Owen and E. Onate, Barcelona, Spain, pp. 442–445.
  78. N. Sukumar and R. J-B Wets (2007), "Deriving the Continuity of Maximum-Entropy Basis Functions via Variational Analysis," SIAM Journal on Optimization, Vol. 18, Number 3, pp. 914–925. [PDF] or Journal
  79. A. Tabarraei and N. Sukumar (2007), "Adaptive Computations Using Material Forces and Residual-Based Error Estimators on Quadtree Meshes," (2007) Computer Methods in Applied Mechanics and Engineering, Vol. 196, Number 25–28, pp. 2657–2680. [PDF]
  80. N. Sukumar and R. W. Wright (2007), "Overview and Construction of Meshfree Basis Functions: From Moving Least Squares to Entropy Approximants," International Journal for Numerical Methods in Engineering, Vol. 70, Number 2, pp. 181–205. [PDF]
  81. A. Tabarraei and N. Sukumar (2006), "Application of Polygonal Finite Elements in Linear Elasticity" International Journal of Computational Methods, Vol. 3, Number 4, pp. 503–520. [PDF]
  82. N. Sukumar and E. A. Malsch (2006), "Recent Advances in the Construction of Polygonal Finite Element Interpolants," Archives of Computational Methods in Engineering, Vol. 13, Number 1, pp. 129–163. [PDF] (proof)
  83. N. Sukumar, "Maximum Entropy Approximation," in Proceedings of the 25th International Workshop on Bayesian Inference and Maximum Entropy Methods in Science and Engineering, Eds. K. H. Knuth, A. E. Abbas, R. D. Morris and J. P. Castle, AIP Conference Proceedings, 803(1), 2005, pp. 337–344. [HTML]
  84. 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), 2005, pp. 409–427. [PDF]
  85. 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(17), 2005, pp. 2584–2601. 2005. [PDF]
  86. J. E. Bolander and N. Sukumar, "Irregular Lattice Model for Quasistatic Crack Propagation," Physical Review B, 71, 2005, 094106 [PDF]
  87. A. Tabarraei and N. Sukumar, "Adaptive Computations on Conforming Quadtree Meshes," Finite Elements in Analysis and Design 41(7–8), 2005, pp. 686–702. [PDF] or UC repository postprints
  88. N. Sukumar, "Construction of Polygonal Interpolants: A Maximum Entropy Approach," International Journal for Numerical Methods in Engineering, 61(12), 2004, pp. 2159–2181. [PDF]
  89. N. Sukumar and A. Tabarraei, "Conforming Polygonal Finite Elements," International Journal for Numerical Methods in Engineering, 61(12), 2004, pp. 2045–2066. [PDF]
  90. N. Sukumar and A. Tabarraei, "Polygonal Interpolants: Construction and Adaptive Computations on Quadtree Meshes," in European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS 2004), Eds. P. Neittaanmäki, T. Rossi, S. Korotov, E. Onate, J. Periaux and D. Knörzer, Jyväskylä, Finland, 2004 [PDF]
  91. N. Sukumar and A. Tabarraei, "Numerical Formulation and Application of Polygonal Finite Elements," in Proceedings of the Seventh ESAFORM Conference on Metal Forming, Ed. S. Stören, Trondheim, Norway, pp. 73–76, 2004 [PDF]
  92. 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), 2004, pp. 1075–1102. [Abstract] [PDF] [PS]
  93. N. Sukumar and D. J. Srolovitz, "Finite Element-Based Model for Crack Propagation in Polycrystalline Materials," Computational & Applied Mathematics , 23(2–3), 2004, pp. 363–380 [PDF]
  94. E. Cueto, N. Sukumar, B. Calvo, M. A. Martínez, J. Cegoñino and M. Doblaré (2003), "Overview and Recent Advances in Natural Neighbour Galerkin Methods," Archives of Computational Methods in Engineering, 10(4), 2003, pp. 307–384. [PDF] (proof [M. A. Martínez is missing in the author-list])
  95. N. Sukumar and J. E. Bolander "Numerical Computation of Discrete Differential Operators on Non-Uniform Grids," Computer Modeling in Engineering & Sciences, 4(6), 2003, pp. 691–706. [PDF]
  96. 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), 2003, pp. 7513–7537. [Abstract] [PDF] [PS]
  97. 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), 2003, pp. 7539–7552. [Abstract] [PDF] [PS]
  98. N. Sukumar, "Meshless Methods and Partition of Unity Finite Elements," in Proceedings of the Sixth International ESAFORM Conference on Material Forming, Salerno, Italy, Ed. V. Brucato, April 2003, pp. 603–606. [PDF] [PS]
  99. 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), 2003, pp. 609–635. [PDF]
  100. N. Sukumar, "Voronoi Cell Finite Difference Method for the Diffusion Operator on Arbitrary Unstructured Grids," International Journal for Numerical Methods in Engineering, 57(1), 2003, pp. 1–34. [Abstract] [PDF]
  101. 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), 2003, pp. 845–869. [PDF]
  102. 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), 2003, pp. 29–48. [PDF] [PS]
  103. N. Sukumar, D. J. Srolovitz, T. J. Baker and J.-H. Prévost, "Brittle Fracture in Polycrystalline Materials with the Extended Finite Element Method," International Journal for Numerical Methods in Engineering, 56(14), 2003, pp. 2015–2037. [PDF]
  104. N. Sukumar, "Sibson and Non-Sibsonian Interpolants for Elliptic Partial Differential Equations," in Proceedings of the First MIT Conference on Fluid and Solid Mechanics, Volume 2, Ed. K. J. Bathe, Elsevier Press, 2001, pp. 1665–1667. [PDF]
  105. 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), 2001, pp. 6183–6200. [PDF] [PS]
  106. N. Sukumar, B. Moran, A. Yu Semenov and V. V. Belikov, "Natural Neighbour Galerkin Methods," International Journal for Numerical Methods in Engineering, 50(1), 2001, pp. 1–27. [PDF] [PS]
  107. 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), 2000, pp. 1741–1760. [PDF] [PS]
  108. 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), 2000, pp. 1549–1570. [PDF] [PS]
  109. 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, September 2000. [PDF] [PS]
  110. D. Bueche, N. Sukumar and B. Moran, "Dispersive Properties of the Natural Element Method," Computational Mechanics, 25(2/3), 2000, pp. 209–217. [PDF] [PS]
  111. N. Sukumar and B. Moran "C1 Natural Neighbor Interpolant for Partial Differential Equations," Numerical Methods for Partial Differential Equations, 15(4), 1999, pp. 417–447. [PDF] [PS]
  112. B. Moran, N. Sukumar and T. Belytschko, "Application of the Natural Element Method in Elastostatics," in Modeling and Simulation Based Engineering, Volume 1, Eds. S. Atluri and P. O'Donoghue, Tech. Science Press, 1998.
  113. N. Sukumar, B. Moran and T. Belytschko, "The Natural Element Method in Solid Mechanics," International Journal for Numerical Methods in Engineering, 43(5), 1998, pp. 839–887. [PDF] [PS]
  114. N. Sukumar, B. Moran, T. Belytschko and T. Black, "An Element-Free Galerkin Method for Three-Dimensional Fracture Mechanics," Computational Mechanics, 20, 1997, pp. 170–175. [PDF] [PS]
  115. N. Sukumar and M. Kumosa, "Finite Element Analysis of Axial Splits in Iosipescu Specimens," International Journal of Fracture, 62, 1993, pp. 55–85.

  116. N. Sukumar and M. Kumosa, "Stress Singularities at Sharp Notches: Interpolation Formulas," International Journal of Fracture, 58, 1992, pp. R45–R49.

  117. 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, 1992, pp. 177–192.

Technical Reports

  1. B. Moran, T. Belytschko and N. Sukumar, " On the Element Free Galerkin Method for 3D Fracture Mechanics" FAA Technical Report, 1998.
  2. B. Moran, A. Zulfiqar and N. Sukumar, " On the Direct Integration Method for Fatigue Reliability Calculations" Technical Report to Center for Integrated Diagnostics, Georgia Tech., July 1996
  3. B. Moran, T. Belytschko and N. Sukumar, " NU-FORM, Program Documentation and Listing" FAA Technical Report, July 1994.

Unpublished/Web Documents

  1. N. Sukumar, "Where Do We Stand on Meshfree Approximation Schemes?" in Online Blog on Meshfree Methods, September 2006 [HTML] or [HTML]
  2. N. Sukumar, " A C1 NEM Interpolant for Fourth-Order PDEs," Internal Report, Theoretical and Applied Mechanics, Northwestern University, December 1997 [LaTeX2HTML document]
  3. N. Sukumar, " A Note on Natural Neighbor Interpolation and the Natural Element Method," Internal Report, Theoretical and Applied Mechanics, Northwestern University, May 1997 [LaTeX2HTML document]
  4. N. Sukumar, " Patch test in 1D using FE-EFG coupling," Theoretical and Applied Mechanics, Northwestern University, 1996 [PDF] [PS]
  5. N. Sukumar, " Application of the coupled FE-EFG method to material discontinuities in 1D and 2D," Theoretical and Applied Mechanics, Northwestern University, 1996 [PDF] [PS]
  6. N. Sukumar, " SIF computations for 2D cracks using enriched basis functions," Theoretical and Applied Mechanics, Northwestern University, 1996 [PDF] [PS]
  7. N. Sukumar, " PUFEM in one-dimension," Theoretical and Applied Mechanics, Northwestern University, 1996 [PDF] [PS]
  8. N. Sukumar, " PUFEM--revisited," Theoretical and Applied Mechanics, Northwestern University, 1996 [PDF] [PS]

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Last update: December 15, 2022
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