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Davis

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 electronicstructure
(KohnSham equations of DFT) calculations,
virtual element methods,
and physicsinformed neural networks to solve
PDEs.
Other areas of interest include computational geometry, level set methods,
Bayesian probability theory,
maximumentropy 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 MicroprocessorBased 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

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 
PostDoc,
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.


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, 1921)
 Finite Element Procedures in Applied Mechanics (Winter 0110, 1213, 1520)
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 03/05/12/1721, 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, 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

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

 "Exact Imposition of Boundary Condition
in PhysicsInformed Deep Neural Networks to Solve PDEs
(with A. Srivastava),"
USACM Thematic Conference on
Meshfree and Novel Finite Element Methods, Berkeley, CA, September 2022.
 "Virtual Element Method: A Stabilized Galerkin Method on
Polytopes,"
Invited Seminar,
Department of Aerospace Engineering,
IIT Bombay, Mumbai, India, September 2022.
 "Recent Advances in Exact Imposition of Boundary Condition
in PhysicsInformed Deep Neural Networks to Solve PDEs,"
Invited Seminar,
Center for Machine Intelligence and
Data Science,
IIT Bombay, Mumbai, India, September 2022.
 "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.
 "Recent Advances in Exact Imposition of Boundary Condition
in PhysicsInformed Deep Neural Networks to Solve PDEs," Invited Seminar,
Department of Computational and Data Sciences,
Indian Institute of Science, Bengaluru, India, July 2022.
 "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.
 "Recent Advances in Polyhedral Virtual Element Methods and
PhysicsInformed Deep Neural Networks to Solve PDEs," Invited Seminar,
Department of Mechanical Engineering,
Indian Institute of Science, Bengaluru, India, July 2022.
 "Numerical Integration over Polytopes and Curved Regions
and use of VEM to Advance Finite Element Technology," Invited Lecture,
VEM MiniCourse (SDS 2022 Meeting),
Rosa Marina, Italy, June 2022.
 "Recent Advances in Polyhedral Virtual Element Methods and
PhysicsInformed Deep Neural Networks to Solve PDEs," Invited Seminar,
T3 Division, Los Alamos National Laboratory,
Los Alamos, NM, May 2022.
 "Recent Advances in Polyhedral Virtual Element Methods and
PhysicsInformed Deep Neural Networks to Solve PDEs," Invited Seminar,
Engineering Sciences Center,
Sandia National Laboratories,
Albuquerque, NM, May 2022.
 "StabilizationFree Virtual Element Method for Plane
Elasticity (with A. Chen)," Invited Seminar,
T3 Division, Los Alamos National Laboratory,
Los Alamos, NM, March 2022.
 "Exact Imposition of Boundary Conditions with
Distance Functions in PhysicsInformed Deep Neural Networks,"
Invited Seminar,
Mechanics and Computation Seminar,
Stanford University,
Stanford, CA, February 2022.
 "Meshfree Analysis on Complex Geometries Using
PhysicsInformed Deep Neural Networks,"
Invited Seminar,
Instituto Superior Ténico,
University of Lisbon, Portugal, January 2022.
 "Virtual Elements on Agglomerated Finite Elements to Increase the
Critical Time Step in Explicit ThreeDimensional Elastodynamic Simulations,"
US
National Congress on Computational Mechanics, Chicago, IL, July 2021.
 "Meshfree Analysis on Complex Geometries Using
PhysicsInformed Deep Neural Networks,"
Invited Seminar,
Sandia National Laboratories,
Albuquerque, NM, June 2021.
 "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.
 "Exact Imposition of Boundary Conditions with
Distance Functions in PhysicsInformed Deep Neural Networks
(with A. Srivastava),"
CRUNCH Group Seminar,
Brown University,
Providence, RI, May 2021.
 "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.
 "Numerical Integration of Homogeneous Functions on
Curved Geometries," US
National Congress on Computational Mechanics, Austin, TX, July 2019.
 "Modeling Curved Interfaces without ElementPartitioning in
the Extended Finite Element Method (with Eric B. Chin)," Invited Lecture,
XDMS 2019,
Lugano, Switzerland, July 2019.
 "Numerical Integration of Homogeneous Functions on
Curved Geometries," Invited Lecture,
SIAM
Conference on Geometric Design, Vancouver,
British Columbia, Canada, June 2019.
 "Virtual Element Method in Computational
Mechanics," Invited Seminar,
Department of
Mechanical, Materials and Aerospace Engineering,
Illinois
Institute of Technology, Chicago, IL, December 2018.
 "MaximumEntropy Approximation Schemes in
Computational Mechanics," Invited Seminar,
Sandia National Laboratories,
Livermore, CA, September 2018.
 "MaximumEntropy Approximation Schemes in
Computational Mechanics," Plenary Lecture,
USACM Thematic
Workshop on Meshfree and Particle Methods: Application and Theory,
Santa Fe, NM, September 2018.
 "Spectral Finite Elements and Enriched PartitionofUnity
Methods for Bandstructure Calculations in Phononic Crystals
(with Ankit Srivastava)," Keynote Lecture,
World Congress in Computational Mechanics,
New York City, NY, July 2018.
 "Virtual Element Method in Computational
Mechanics," Invited Seminar, CSRI Seminar,
Sandia National Laboratories,
Albuquerque, NM, July 2018.
 "Virtual Element Method in Computational
Mechanics," Invited Seminar, T3 Fluid Dynamics and Solid Mechanics
Seminar, Los Alamos National
Laboratory, Los Alamos, NM, July 2018.
 "Finite Element and Enriched PartitionofUnity
Methods for Wave Problems," Invited Lecture,
Department of Civil and
Environmental Engineering,
Duke University,
Durham, NC, April 2018.
 "Polygonal and Polyhedral Finite Element Technology in
Computational Mechanics," Invited Seminar,
Department of Civil and
Environmental Engineering,
Carnegie Mellon University,
Pittsburgh, PA, November 2017.
 "Polygonal and Polyhedral Finite Element Technology in
Computational Mechanics," Invited Seminar,
ANSYS Inc.,
Canonsburg, PA, November 2017.
 "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.
 "OrbitalEnriched 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.
 "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.
 "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.
 "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.
 "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.
 "Modeling Crack Discontinuities and Holes without ElementPartitioning
in the Extended Finite Element Method," Invited Lecture,
POEMS 2017, Milano, Italy, July 2017.
 "MaximumEntropy Approximation Schemes in
Computational Mechanics," Invited Seminar,
Dassault Systemes Simulia
Corporation,
Johnston, RI, April 2017.
 "OrbitalEnriched Partition of Unity Finite Element Method for Ab Initio Density Functional Calculations," Invited Seminar,
PRISM/CEE Seminar,
Princeton University,
Princeton, NJ, April 2017.
 "MaximumEntropy Approximation Schemes in
Computational Mechanics," Invited Seminar,
Pierce
Laboratory Seminar Series,
Department of Civil and
Environmental Engineering,
MIT, Cambridge, MA, April 2017.
 "MaximumEntropy Approximation Schemes in
Computational Mechanics," Invited Seminar,
Joint
Materials/Solid Mechanics Seminar, Brown University, Providence, RI, April 2017.
 "MaximumEntropy Meshfree Methods in
Computational Mechanics," Opening Lecture,
42nd Israeli Symposium on
Computational Mechanics (ISCM42), Technion, Haifa, Israel,
March 2017.
 "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.
 "Partition of Unity Methods,"
GIAN Short
Course,
Department of Mechanical
Engineering, IIT Madras,
Chennai, India, December 2016.
 "Partition of Unity Finite Element Method for Quantum Mechanical Materials Calculations," Invited Seminar,
Department of Mechanical
Engineering, UC Merced,
Merced, CA, October 2016.
 "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.
 "Partition of Unity Finite Element Method for KohnSham 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.
 "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.
 "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.
 "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.
 "Quadrature Methods for Discontinuities and
Singularities," Invited Lectures,
XDMS Short
Course on Extended Discretization Methods, Ferrara, Italy, September 2015.
 "Comparison of Meshfree Galerkin Methods Based on MLS
and MaximumEntropy Approximation Schemes
(with Mathieu Foca and Bo Li),"
ECCOMAS Thematic Conference: XDMS 2015  eXtended Discretization Methods,
Ferrara, Italy, September 2015.
 "Recent Developments in MaximumEntropy Approximation
Schemes,"
Invited Seminar,
Department of Engineering Design,
IIT Madras,
Chennai, India, June 2015.
 "Recent Developments in MaximumEntropy Approximant
Schemes," Invited Seminar,
Department of
Mechanical and Aerospace Engineering,
Case Western Reserve University,
Cleveland, OH, March 2015.
 "CellBased MaximumEntropy Approximants
(with Marino Arroyo
and
Daniel Millan),"
Invited Lecture,
Workshop on Meshfree Methods for LargeScale Computational Science and Engineering Tampa, FL,
October 2014.
 "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.
 "Computations on Polygonal and Polyhedral
Meshes with Entropy Approximants,"
Invited Seminar,
Los Alamos National Laboratory,
Los Alamos, NM, August 2014.
 "Computations on Polygonal and Polyhedral
Meshes with Entropy Approximants,"
Invited Seminar,
Sandia National Laboratories,
Albuquerque, NM, August 2014.
 "Polygonal and Polyhedral Finite Element Methods in
Computational Mechanics,"
Plenary Lecture,
PACAM XIV: Fourteenth PanAmerican Congress
of Applied Mechanics,
Santiago, Chile, March 2014.
 "Polygonal and Polyhedral Finite Element Methods in
Computational Mechanics,"
Invited Seminar,
Department of Civil and Environmental
Engineering,
Stanford University,
CA, February 2014.
 "MaximumEntropy Approximation Schemes:
Theory and Links to BSplines and Isogeometric Analysis
(with
Marino Arroyo),"
Isogeometric Analysis: Integrating
Design and Analysis (IGA 2014),
Austin, TX, January 2014.
 "Polygonal and Polyhedral Finite Element Methods
in Computational Mechanics,"
Keynote Lecture,
23rd International Workshop on Computational
Mechanics of Materials, Singapore, October 2013.
 "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.
 "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.
 "Quadratic MaximumEntropy Serendipity Shape Functions for
Arbitrary Planar Polygons,"
Invited Lecture,
1st Indian Conference on Applied Mechanics, IIT Madras,
Chennai, India, July 2013.
 "MaximumEntropy Approximation Schemes,"
Invited Seminar,
Department of Mechanical Engineering, Indian Institute of Science,
Bangalore, India, June 2013.
 "Meshfree Methods: From the ElementFree Galerkin
Method to MaximumEntropy 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.
 "Quadratic MaximumEntropy 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.
 "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.
 "Quadratic Polygonal Finite Element Methods,"
Invited Seminar,
Faculty of Informatics,
Universita della Svizzera
italiana, Lugano, Switzerland, September 21, 2012.
 "Polygonal Finite Element Methods,"
Invited Lecture, Workshop on
Discretization
Methods for Polygonal and Polyhedral Meshes,
University of MilanoBicocca, Milan, Italy, September 1719, 2012.
 "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.
 "MaximumEntropy Approximants: Applications in Solid Mechanics
and Structural Engineering,"
Invited Lecture,
Department of Civil and
Environmental Engineering,
University of Pittsburgh,
Pittsburgh, PA, February 2012.
 "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.
 "MaximumEntropy Approximation Schemes,"
Symposium on Meshfree and Extended/Generalized Finite Element Methods,
PACAM XII,
Port of Spain, Trinidad, January 2012.
 "MaximumEntropy Approximations in Computational Mechanics,"
Invited Lecture,
Department of Applied Mechanics,
IIT Madras,
Chennai, India, December 2011.
 "PartitionofUnity Enriched Finite Elements to Solve the HartreeFock 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.
 "Enriched Finite Element Solution for the AllElectron Coulomb
Problem in Solids (with
J. E. Pask and S. E. Mousavi),"
Poster Presentation,
CECAM 
Jülich
Summer School 2011 on Fast Methods for LongRange Interactions in
Complex Systems, Jülich, Germany, September 2011.
 "A New RealSpace Formulation for the AllElectron 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.
 "PartitionofUnity Finite Elements for Large, Accurate QuantumMechanical Materials
Calculations," Plenary Lecture,
ECCOMAS Thematic Conference on the Extended Finite Element Method (XFEM 2011),
Cardiff, UK, July 1, 2011.
 Invited Participant,
MiniWorkshop: Mathematical Models, Analysis, and Numerical Methods for
Dynamic Fracture,
Mathematische Forschungsinstitut Oberwolfach,
Germany, April 2430, 2011.
 "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.
 "MaximumEntropy Meshfree Method in Computational Mechanics,"
Invited Lecture,
Universidad Politecnica de Valencia,
Spain, July 2010.
 "Extended Finite Elements using Harmonic Enrichment Functions for
Crack Modeling,"
Invited Lecture,
Universidad Politecnica de Valencia,
Spain, July 2010.
 "Extended Finite Element Method for Crack Modeling: Formulation
and Recent Developments,"
Invited Seminar,
Dpto. Mecanica de Estructuras,
Universidad de Granada,
Spain, June 2010.
 "Extended Finite Element Method for Crack Modeling: Formulation
and Recent Developments,"
Invited Seminar,
Universidad de Sevilla,
Spain, June 2010.
 "MaximumEntropy Meshfree Method,"
Invited Lecture,
StudentRun Applied & Math Seminar,
Department of Mathematics,
University of California, Davis, CA, April 2010.
 "Partition of Unity Finite Elements for QuantumMechanical
Calculations in Condensed Matter: Have Planewaves Finally Met Their
Match,"
Invited Lecture,
Department of Mechanical Engineering,
Mechanics of Computation Seminar,
Stanford University,
January 2010.
 "MaximumEntropy Approximation in Computational Mechanics,"
Invited Lecture,
Department of Civil and Environmental Engineering,
Structural Engineering Seminar Series,
University of Illinois at UrbanaChampaign, October 2009.
 "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.
 "Linear Scaling Finite Element Solution for the AllElectron
Coulomb Problem in Solids,"
Invited Lecture,
Institute for Numerical Simulation, University of Bonn,
Bonn, Germany, October 1, 2009.
 "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 2830, 2009.
 "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.
 "Partition of Unity Finite Element Method to Solve the KohnSham
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.
 "A New Finite Element Method for ThreeDimensional NonPlanar Crack
Growth Simulations,"
Invited Lecture,
Department of Mechanical and
Aeronautical Engineering,
University of California at
Davis, CA, June 2008.
 "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.
 "Partition of Unity Finite Elements for ElectronicStructure
Calculations in Molecules and Crystalline Solids,"
Invited Lecture,
Department of
Mechanical Engineering and Applied Mechanics,
University of
Pennsylvania, Philadelphia, PA, December 7, 2007.
 "XFEM and FMM: A Paradigm for Planar and NonPlanar Crack
Growth Simulations,"
Invited Presentation,
Global Engineering and Materials, Inc., Baltimore, MD, December 5, 2007.
 "A New RealSpace Finite Element Method to Solve the KohnSham
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.
 "Partition of Unity Finite Elements for ElectronicStructure
Calculations in Molecules and Crystalline Solids,"
Invited Lecture,
Joint Mechanical Engineering/Civil Engineering Seminar,
Columbia
University, New York, NY, November 9, 2007.
 "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.
 "ThreeDimensional NonPlanar 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.
 "MeshIndependent Crack Modeling using the Extended Finite
Element Method,"
Invited Presentation,
Cornell Fracture
Group,
Cornell University,
Ithaca, September 27, 2007.
 "ThreeDimensional NonPlanar 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.
 "Finite Element and Meshfree Methods in Mechanics,"
Invited Lecture,
GGAM MiniConference, Department of Mathematics,
University of California, Davis, CA, March 31, 2007.
 "Linking Geometry and Approximation for Computational Mechanics,"
Invited Lecture,
Mechanics Colloquium,
Technical University of Kaiserslautern,
Germany, September 18, 2006.
 "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.
 "Meshfree Methods and Partition of Unity Finite Elements,"
Short Course at
Universidad Politecnica De Valencia, Valencia, Spain, September 511, 2006.
 "Partition of Unity Finite Element Method for LargeScale
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.
 "Continuity of MaximumEntropy Basis Functions via Variational
Analysis (with R. JB Wets)," Seventh World Congress on Computational Mechanics,
Symposium on Computational Geometry and Analysis,
Los Angeles, CA, July 2006.
 "Recent Advances in Polygonal Finite Element Methods," Invited
Lecture, Mathematical Modeling and
Analysis Group, Los Alamos National
Laboratory, Los Alamos, New Mexico, April 2006.
 "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 610, 2006
 "Scattered Data Approximation and Meshfree Methods,"
Invited Lecture,
Applied
Math Seminar,
Department of Mathematics,
University of California, Davis, CA, October 2005
 "Adaptive Computations using Conforming Quadtree
Meshes," (with A. Tabarraei), Invited Lecture,
Mechanics Colloquium,
Technical University of Kaiserslautern,
Germany, September 2005
 "Construction of Meshfree Approximation Schemes:
Use of InformationTheoretic Variational Principles,"
Invited Lecture,
Technical University of Kaiserslautern,
Germany, September 2005
 "Meshfree Methods and Partition of Unity Finite Elements:
Basic Principles and Applications," Invited Lecture,
Technical University of Kaiserslautern,
Germany, September 2005
 "Adaptive Computations using ResidualBased Error Estimators on
Conforming Quadtree Meshes," (with A. Tabarraei),
Third International
Workshop on Meshfree Methods for Partial Differential Equations,
Bonn, Germany, September 2005
 "Maximum Entropy Approximation,"
25th International Workshop on Bayesian Inference
and Maximum Entropy Methods in Science and
Engineering, San Jose State University,
CA, August 2005
 "Maximum Entropy Approximation,"
Symposium on Meshfree and Particle Methods,
Keynote Lecture,
Eight U.S. National
Congress on Computational Mechanics,
Austin, TX, July 2005
 "Scattered Data Approximation using the Maximum Entropy
Principle," Invited Lecture,
Department of Civil and
Environmental Engineering, Cornell
University, Ithaca, NY, May 2005.
 "Scattered Data Approximation using the Maximum Entropy
Principle," Invited Lecture,
Department of Mechanical and Aeronautical Engineering,
University of California, Davis, CA, December 2004.
 "Modeling Arbitrary Crack Discontinuities in Finite Elements,"
Invited Lecture,
Rockwell Scientific Company,
Thousand Oaks, CA, November 2004
 "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.
 "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.
 "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.
 "Polygonal Finite Elements: Construction and Applications to
PDEs,"
Invited Lecture,
Ecole Centrale de Nantes,
Nantes, France, July 2004
 "Partition of Unity and Polygonal Finite Element Methods,"
Invited Lecture,
Universidad Politecnica de Valencia,
Spain, April 2004
 "Numerical Formulation and Application of Polygonal Finite
Elements" (with A. Tabarraei),
7th
International ESAFORM Conference on Material Forming,
Trondheim, Norway, April 2004
 "Conforming Polygonal Finite Elements,"
Invited Lecture,
Laboratoire de Mecanique
des Systemes et des Procedes, ENSAM,
Paris, France, April 2004
 "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
 "Modeling Arbitrary Discontinuities in Finite Elements,"
Invited Lecture, Department of Mechanical Engineering,
Indian Institute of Technology Bombay,
Mumbai, India, March 2004
 "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
 "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
 "Meshless Methods and Partition of Unity Finite Elements"
Keynote Lecture,
6th
International ESAFORM Conference on Material Forming,
Salerno, Italy, April 2830, 2003
 "Finite ElementBased Model for Crack Propagation in
Polycrystalline Materials"
Invited Lecture,
2nd
Symposium on Computational Modeling of MultiScale Phenomena,
Petropolis, Brazil, August 2002
 "Modeling Discontinuities and their Evolution within
Finite Elements: Application to Material Interfaces, 3D Cracks,
and Microstructures,"
Invited Lecture,
Department
of Mechanical and Aerospace Engineering,
Rutgers University,
Piscataway, NJ, September 2001
 "Enriched Natural Neighbor Interpolants for TwoDimensional
Crack Modeling,"
Sixth U.S. National
Congress on Computational Mechanics, Dearborn, MI (August 2001)
 "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
 "Sibson and NonSibsonian Interpolants for Elliptic Partial
Differential Equations,"
First MIT Conference on
Fluid and Solid Mechanics, Cambridge, MA, June 2001
 "Extended Finite Element Method: Introduction and
Applications," MAE
Material Group Seminar, Princeton University,
NJ, December 2000
 "Natural Neighbor Galerkin Methods,"
(with Brian Moran)
ICTAM 2000, Chicago, IL, October 2000
 "Modeling Holes and Inclusions by Level Sets in the Extended Finite
Element Method," Mechanics Club Seminar,
Northwestern University,
Evanston, IL, February 2000
 "The Natural Element Method,"
Number Crunch Seminar,
Engineering Sciences and Applied Mathematics,
Northwestern University, Evanston, IL, October 1999
 "Galerkin Methods for Elliptic Partial Differential Equations,"
Number Crunch Seminar,
Engineering Sciences and Applied Mathematics,
Northwestern University, Evanston, IL, October 1999
 "An ElementFree 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)


Refereed Journal and Conference Publications, and Books

A. Chen and N. Sukumar (2022) "StabilizationFree Virtual Element Method for Plane Elasticity,"
arXiv: 2202.10037

N. Sukumar and
M. R. Tupek (2021)
"Virtual Elements on Agglomerated Finite Elements to Increase the Critical Time Step
in Elastodynamic Simulations," arXiv: 2110.00514

N. Sukumar and
A. Srivastava (2022)
"Exact Imposition of Boundary Conditions with Distance Functions in
PhysicsInformed Deep Neural Networks,"
Computer Methods in Applied Mechanics and Engineering,
Vol. 389, Article 114333.
Available at arXiv: 2104.08426

E. Benvenuti,
A. Chiozzi,
G. Manzini
and
N. Sukumar (2022),
"Extended Virtual Element Method for TwoDimensional Linear Elastic Fracture,"
Computer Methods in Applied Mechanics and Engineering,
Vol. 390, Article 114352.
Available at arXiv: 2111.04150

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.

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.

J. Jaśkowiec and
N. Sukumar (2021),
"Addendum to the Paper "HighOrder Symmetric Cubature Rules for
Tetrahedra and Pyramids,"
International Journal for Numerical Methods in Engineering,
Vol. 122, Number 7, pp. 1875–1883.
[Cubature Rules]

J. Jaśkowiec and
N. Sukumar (2021),
"HighOrder Symmetric Cubature Rules for Tetrahedra and Pyramids,"
International Journal for Numerical Methods in Engineering,
Vol. 122, Number 1, pp. 148–171.
[Cubature Rules]

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.
[C++ Code]

J. Jaśkowiec and
N. Sukumar (2020),
"HighOrder Cubature Rules for Tetrahedra,"
International Journal for Numerical Methods in Engineering,
Vol. 121, Number 11, pp. 2418–2436.
[Cubature Rules]

R. SilvaValenzuela,
A. OrtizBernardin,
N. Sukumar,
E. Artioli and N. HitschfeldKahler (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.

J. E. Bishop and
N. Sukumar (2020),
"Polyhedral Finite Elements for Nonlinear Solid Mechanics using
Tetrahedral Subdivisions and DualCell Aggregation,"
Computer Aided Geometric Design,
Vol. 77, Article 101812.

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.

E. B. Chin and
N. Sukumar (2019),
"Modeling Curved Interfaces without ElementPartitioning in the Extended Finite
Element Method,"
International Journal for Numerical Methods in Engineering,
Vol. 120, Number 5, pp. 607–649.

C. Liu,
J. H. Prévost and
N. Sukumar (2019),
"Modeling Branched and Intersecting Faults in ReservoirGeomechanics Models with the
Extended Finite Element Method,"
International Journal for Numerical and Analytical Methods in Geomechanics,
Vol. 43, Number 12, pp. 2075–2089.

C. Liu,
J. H. Prévost and
N. Sukumar (2019),
"Modeling Piecewise Planar Faults without ElementPartitioning in 3D ReservoirGeomechanical Models,"
International Journal for Numerical and Analytical Methods in Geomechanics,
Vol. 43, Number 2, pp. 530–543.

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.

C. Albrecht, C. Klaar,
J. E. Pask,
M. A. Schweitzer,
N. Sukumar and
A. Ziegenhagel (2018), "Orbitalenriched Flattop
Partition of Unity Method for the Schrödinger Eigenproblem,"
Computer Methods in Applied Mechanic and Engineering,
Vol. 342, pp. 224–239.
Available at
arXiv:1801.09596

Y. Cai,
Z. Bai,
J. E. Pask and
N. Sukumar (2018),
"Convergence Analysis of a Locally Accelerated Preconditioned Steepest
Descent Method for HermitianDefinite Generalized Eigenvalue Problems,"
Journal of Computational Mathematics,
Vol. 36, Number 5, pp. 739–760.

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.

K. Hormann and
N. Sukumar (Eds.)
(2017),
"Generalized Barycentric Coordinates in Computer Graphics and
Computational Mechanics," CRC Press, Boca Raton, FL.
COVER
[Taylor & Francis]
 J.H. Prévost,
A. M. Rubin
and
N. Sukumar (2017),
"Intersecting Fault Simulations for ThreeDimensional ReservoirGeomechanical
Models," Sixth Biot Conference on Poromechanics,
Paris, France, American Society of Civil Engineers.

A. OrtizBernardin,
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.
 S. Banerjee and
N. Sukumar (2017),
"Exact Integration Scheme for PlanewaveEnriched Partition of Unity
Finite Element Method to Solve the Helmholtz Problem,"
Computer Methods in Applied Mechanics and Engineering,
Vol. 317, pp. 619–648.
 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.
Available at
arXiv:1611.00731
 E. B. Chin,
J. B. Lasserre and
N. Sukumar (2017),
"Modeling Crack Discontinuities without ElementPartitioning in the Extended Finite
Element Method,"
International Journal for Numerical Methods in Engineering,
Vol. 110, Number 11, pp. 1021–1048.
Erratum
 J.H. Prévost and
N. Sukumar (2016),
"Faults Simulations for ThreeDimensional ReservoirGeomechanical Models
with the Extended Finite Element Method,"
Journal of the Mechanics and Physics of Solids,
Vol. 86, pp. 1–18.
 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.
 J.H. Prévost and
N. Sukumar (2015),
"Multiscale XFEM Faults Simulations for ReservoirGeomechanical
Models," 49th US Rock Mechanics/Geomechanics Symposium,
American Rock Mechanics Association.
 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.

A. OrtizBernardin,
M. A. Puso and
N. Sukumar
(2015),
"Improved Robustness for NearlyIncompressible Large Deformation
Meshfree Simulations on Delaunay Tessellations,"
Computer Methods in Applied Mechanics and Engineering,
Vol. 293, pp. 348–374.

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 34, pp. 404–436.

D. Millán,
N. Sukumar and
M. Arroyo
(2015),
"CellBased MaximumEntropy Approximants,"
Computer Methods in Applied Mechanics and Engineering,
Vol. 284, pp. 712–731.

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.

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.
Available at
arXiv:1306.4385

Y. Cai,
Z. Bai,
J. E. Pask and
N. Sukumar (2013),
"Hybrid Preconditioning for Iterative Diagonalization of IllConditioned Generalized Eigenvalue Problems in Electronic Structure
Calculations," Journal of Computational Physics,
Vol. 255, pp. 16–30.
Available at
arXiv:1308.2445

N. Sukumar (2013),
"Quadratic MaximumEntropy Serendipity Shape Functions for Arbitrary
Planar Polygons,"
Computer Methods in Applied Mechanics and Engineering,
Vol. 263, pp. 27–41.

J. O. Royset,
N. Sukumar
and R. JB Wets
(2013),
"Uncertainty Quantification using Exponential EpiSplines,"
Proceedings of the 11th International Conference on Structural Safety and
Reliability, New York, NY.
 F. Greco and
N. Sukumar (2013),
"Derivatives of MaximumEntropy Basis Functions on the Boundary: Theory and
Computations,"
International Journal for Numerical Methods in Engineering,
Vol. 94, Number 12, pp. 1123–1149.
 G. Hattori, R. RojasDíaz,
A. Sáez,
N. Sukumar and
F. GarcíaSánchez (2012),
"New Anisotropic CrackTip Enrichment Functions for the Extended
Finite Element Method," Computational Mechanics,
Vol. 50, Number 5, pp. 591–601.

G. Quaranta,
S. K. Kunnath and
N. Sukumar
(2012),
"MaximumEntropy Meshfree Method for Nonlinear Static Analysis of Planar
Reinforced Concrete Structures,"
Engineering Structures,
Vol. 42, pp. 179–189.

J. E. Pask,
N. Sukumar and
S. E. Mousavi
(2012), "Linear Scaling Solution of the AllElectron Coulomb Problem
in Solids,"
International Journal for Multiscale Computational Engineering,
Vol. 10, Number 1, pp. 83–99.
Available at
arXiv:1004.1765
 S. E. Mousavi,
J. E. Pask and
N. Sukumar
(2011), "Efficient Adaptive Integration of Functions with Sharp
Gradients and Cusps in nDimensional Parallelepipeds,"
International Journal for Numerical Methods in Engineering,
Vol. 91, Number 4, pp. 343–357.
 R. RojasDíaz,
N. Sukumar,
A. Sáez and F. GarcíaSánchez (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.
 G. Hattori, R. RojasDíaz,
A. Sáez, F. GarcíaSánchez and
N. Sukumar (2011),
"El Método de los Elementos Finitos Extendidos (XFEM) para Medios
Bidimensionales Fisurados Totalmente Anisótropos,"
Anales de Mecánica de la Fractura,
Vol. 28, Number 2, pp. 451–455.

A. Ortiz,
M. A. Puso and
N. Sukumar
(2011),
"MaximumEntropy Meshfree Method for Incompressible Media Problems,"
Finite Element in Analysis and Design,
Vol. 47, Number 6, pp. 572–585.
 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.
 S. E. Mousavi,
E. Grinspun and
N. Sukumar
(2011),
"HigherOrder 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.
 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.
 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 ThreeDimensional Fatigue Crack Growth and Life
Predictions,"
Engineering Fracture Mechanics,
Vol. 77, Number 14, pp. 2840–2863.
[Top 25 Hottest article (July 2010present)]
 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.

A. Ortiz,
M. A. Puso and
N. Sukumar
(2010),
"MaximumEntropy Meshfree Method for Compressible and
NearIncompressible Elasticity,"
Computer Methods in Applied Mechanics and Engineering,
Vol. 199, Number 25–28, pp. 1859–1871.
 S. E. Mousavi and
N. Sukumar
(2010), "Generalized Duffy Transformation for Integrating Vertex
Singularities," Computational Mechanics,
45, Number 2–3, pp. 127–140.
 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.
 R. RojasDíaz,
N. Sukumar,
A. Sáez and F. GarcíaSánchez (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.
 J. Shi, J. Lua, L. Chen, D. Chopp and
N. Sukumar (2009),
"XFEM for Abaqus (XFA) Toolkit for Automated Crack Onset and Growth
Simulation: New Development, Validation, and Demonstration,"
Engineering Fracture Mechanics,
2009 SIMULIA Customer Conference.
 A. Rajagopal, M. Scherer,
P. Steinmann
and N. Sukumar
(2009), "Smooth Conformal αNEM
for Gradient Elasticity," The International Journal of Structural
Changes in Solids – Mechanics and Applications,
1, Number 1, pp. 83–109.

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.

L. L. Yaw,
N. Sukumar and
S. K. Kunnath
(2009),
"Meshfree CoRotational Formulation for TwoDimensional Continua,"
International Journal for Numerical Methods in Engineering,
Vol. 79, Number 8, pp. 979–1003.

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.

N. Sukumar and
J. E. Pask
(2009), "Classical and Enriched Finite Element Formulations for
BlochPeriodic 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]
 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 2009present)]
 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.
 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.

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.

N. Sukumar,
D. L. Chopp,
E. Béchet and
N. Moës (2008),
"ThreeDimensional NonPlanar 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.

N. Sukumar and
J. E. Bolander (2009),
"Voronoibased Interpolants for Fracture Modelling,"
in Tessellations in the Sciences: Virtues, Techniques
and Applications of Geometric Tilings, Springer Verlag, pp. xxx–xxx.
 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.
 J. Shi,
J. Lua,
H. Waisman,
P. Liu,
T. Belytschko,
N. Sukumar
and Y. Liang
(2008), "XFEM Toolkit for Automated Crack Onset and Growth Prediction,"
49th AIAA Conference, Schaumburg, IL, April 2008, pp. 1–22.
 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.
 C. B. Hirschberger,
N. Sukumar and
P. Steinmann
(2008),"Computational homogenization of material layers with micromorphic
mesostructure,"
Philosophical Magazine,
Vol. 88, pp. 3603–3631.
 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.

N. Sukumar
and R. JB Wets
(2007),
"Deriving the Continuity of MaximumEntropy Basis Functions via Variational Analysis,"
SIAM Journal on Optimization,
Vol. 18, Number 3, pp. 914–925.
or Journal
 A. Tabarraei and
N. Sukumar
(2007),
"Adaptive Computations Using Material Forces and ResidualBased Error Estimators on Quadtree Meshes," (2007)
Computer Methods in Applied Mechanics and Engineering,
Vol. 196, Number 25–28, pp. 2657–2680.
 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.
 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.
 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.
(proof)
 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.
 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.
 Z. Huang,
Z. Suo, G. Xu, J. He,
J. H. Prévost and
N. Sukumar,
"Initiation and Arrest of an Interfacial Crack in a FourPoint
Bend Test," Engineering Fracture Mechanics,
72(17), 2005, pp. 2584–2601.
2005.

J. E. Bolander
and
N. Sukumar,
"Irregular Lattice Model for Quasistatic Crack Propagation,"
Physical Review B,
71, 2005, 094106
 A. Tabarraei and
N. Sukumar,
"Adaptive Computations on Conforming Quadtree Meshes,"
Finite Elements in Analysis and Design
41(7–8), 2005, pp. 686–702.
or
UC repository postprints

N. Sukumar,
"Construction of Polygonal Interpolants: A Maximum Entropy Approach,"
International Journal for Numerical Methods in Engineering,
61(12), 2004, pp. 2159–2181.

N. Sukumar
and A. Tabarraei,
"Conforming Polygonal Finite Elements,"
International Journal for Numerical Methods in Engineering,
61(12), 2004, pp. 2045–2066.

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

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
 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]
 N. Sukumar
and D. J.
Srolovitz, "Finite ElementBased Model for Crack Propagation in
Polycrystalline Materials," Computational & Applied Mathematics
, 23(2–3), 2004, pp. 363–380

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.
(proof [M. A. Martínez is missing in the authorlist])
 N. Sukumar
and
J. E. Bolander
"Numerical Computation of Discrete Differential Operators on
NonUniform Grids,"
Computer Modeling in Engineering & Sciences,
4(6), 2003, pp. 691–706.
 N. Sukumar
and
J.H. Prévost
"Modeling QuasiStatic 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]
 R. Huang,
N. Sukumar
and
J.H. Prévost
"Modeling QuasiStatic 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]
 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.
 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.
 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]
 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.
 N. Sukumar,
D. L. Chopp and
B. Moran,
"Extended Finite Element Method and Fast Marching Method for
ThreeDimensional Fatigue Crack Propagation,"
Engineering Fracture Mechanics,
70(1), 2003, pp. 29–48.
 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.
 N. Sukumar,
"Sibson and NonSibsonian 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.
 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.
 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.
 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.
 N. Sukumar,
N. Moës,
B. Moran and
T. Belytschko,
"Extended Finite Element Method for ThreeDimensional Crack Modelling,"
International Journal for Numerical Methods in Engineering,
48(11), 2000, pp. 1549–1570.
 N. Moës,
N. Sukumar,
B. Moran and
T. Belytschko,
"An Extended Finite Element Method (XFEM) for Two and ThreeDimensional
Crack Modeling," in
Proceedings of the European Congress on Computational Methods in Applied Sciences and
Engineering, ECCOMAS 2000, Barcelona, Spain, September 2000.
 D. Bueche,
N. Sukumar and
B. Moran,
"Dispersive Properties of the Natural Element Method,"
Computational Mechanics,
25(2/3), 2000, pp. 209–217.
 N. Sukumar and
B. Moran
"C^{1} Natural Neighbor Interpolant for Partial
Differential Equations,"
Numerical Methods for Partial Differential Equations,
15(4), 1999, pp. 417–447.
 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.
 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.
 N. Sukumar,
B. Moran,
T. Belytschko and
T. Black, "An ElementFree Galerkin Method for ThreeDimensional Fracture
Mechanics," Computational Mechanics,
20, 1997, pp. 170–175.
 N. Sukumar and
M.
Kumosa,
"Finite Element Analysis of Axial Splits in Iosipescu Specimens,"
International Journal of Fracture,
62, 1993, pp. 55–85.
 N. Sukumar and
M.
Kumosa, "Stress Singularities at Sharp Notches: Interpolation
Formulas," International Journal of Fracture,
58, 1992, pp. R45–R49.
 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
 B. Moran,
T. Belytschko and
N. Sukumar,
" On the Element Free Galerkin Method for 3D Fracture Mechanics"
FAA Technical Report, 1998.
 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
 B. Moran,
T. Belytschko and
N. Sukumar,
" NUFORM, Program Documentation and Listing"
FAA Technical Report, July 1994.
Unpublished/Web Documents
 N. Sukumar,
"Where Do We Stand on Meshfree Approximation Schemes?"
in Online Blog on Meshfree Methods, September 2006
or
 N. Sukumar,
" A C^{1} NEM Interpolant for FourthOrder
PDEs," Internal Report,
Theoretical and Applied Mechanics, Northwestern University, December 1997
[LaTeX2HTML document]
 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]
 N. Sukumar,
" Patch test in 1D using FEEFG coupling," Theoretical and
Applied Mechanics, Northwestern University, 1996
 N. Sukumar,
" Application of the coupled FEEFG method to material
discontinuities in 1D and 2D,"
Theoretical and Applied Mechanics, Northwestern University, 1996
 N. Sukumar,
" SIF computations for 2D cracks using enriched basis functions,"
Theoretical and Applied Mechanics, Northwestern University, 1996
 N. Sukumar,
" PUFEM in onedimension,"
Theoretical and Applied Mechanics, Northwestern University, 1996
 N. Sukumar,
" PUFEMrevisited,"
Theoretical and Applied Mechanics, Northwestern University, 1996

Last update: February 26, 2022
N. Sukumar [Email]

