N. Sukumar
· Professor of MathematicsUniversity of California, Davis · Biomedical Engineering
Active 1992–2025
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About
N. Sukumar is a professor in the Department of Civil & Environmental Engineering at UC Davis, where he is a member of the Structural Engineering and Structural Mechanics (SESM) faculty and the Graduate Group in Applied Mathematics. He holds a Ph.D. in Theoretical & Applied Mechanics from Northwestern University, an M.S. from OGI, and a B.Tech. from IIT Bombay. His research interests encompass computational solid mechanics and applied mathematics, with recent focus on developing new methods for modeling fracture in materials, ab initio electronic-structure calculations based on the Kohn-Sham equations of DFT, virtual element methods, and physics-informed neural networks. Other areas of interest include generalized barycentric coordinates, cubature rules on polytopes and curved geometries, maximum-entropy methods in mechanics, convex optimization, semidefinite programming, and deep learning. Sukumar is actively involved in editorial roles as a Regional Editor of the International Journal of Fracture and as a member of the editorial boards for Computer Methods in Applied Mechanics and Engineering and Finite Elements in Analysis and Design. Prior to his tenure at UC Davis, he was a research associate at Princeton University. He also supports the osteosarcoma alliance through MIB.
Research topics
- Mathematics
- Computer Science
- Applied mathematics
- Structural engineering
- Mathematical analysis
- Geometry
- Engineering
- Mathematical optimization
- Physics
Selected publications
Computer Methods in Applied Mechanics and Engineering · 2021 · 342 citations
1st authorCorrespondingIn this paper, we introduce a new approach based on distance fields to exactly impose boundary conditions in physics-informed deep neural networks. The challenges in satisfying Dirichlet boundary conditions in meshfree and particle methods are well-known. This issue is also pertinent in the development of physics informed neural networks (PINN) for the solution of partial differential equations. We introduce geometry-aware trial functions in artifical neural networks to improve the training in d…
Stabilization-free serendipity virtual element method for plane elasticity
Computer Methods in Applied Mechanics and Engineering · 2022 · 49 citations
Senior authorCorrespondingExtended virtual element method for two-dimensional linear elastic fracture
Computer Methods in Applied Mechanics and Engineering · 2022 · 40 citations
Senior authorCorrespondingIn this paper, we propose an eXtended Virtual Element Method (X-VEM) for two-dimensional linear elastic fracture. This approach, which is an extension of the standard Virtual Element Method (VEM), facilitates mesh-independent modeling of crack discontinuities and elastic crack-tip singularities on general polygonal meshes. For elastic fracture in the X-VEM, the standard virtual element space is augmented by additional basis functions that are constructed by multiplying standard virtual basis fun…
Stabilization-free virtual element method for plane elasticity
Computers & Mathematics with Applications · 2023-03-16 · 34 citations
articleSenior authorCorrespondingComputer Methods in Applied Mechanics and Engineering · 2021-04-08 · 33 citations
articleOpen accessSenior author
Recent grants
Robust Polyhedral Finite Element Methods for Pervasive Fracture Simulations
NSF · $364k · 2013–2017
Information-Theoretic Meshfree Approximation Schemes in Solid Mechanics
NSF · $229k · 2006–2010
A New Real-Space Finite Element Method to Solve the Kohn-Sham Equations of Density Functional Theory
NSF · $48k · 2008–2011
Frequent coauthors
- 133 shared
Gianmarco Manzini
Los Alamos National Laboratory
- 132 shared
John E. Pask
- 124 shared
Isuru Fernando
University of Illinois Urbana-Champaign
- 123 shared
Jiří Vackář
- 123 shared
Rohit Goswami
- 122 shared
L. A. Collins
Los Alamos National Laboratory
- 13 shared
Ondřej Čertı́k
Los Alamos National Laboratory
- 12 shared
Ted Belytschko
Education
- 1998
Ph.D.
Northwestern University
M.S.
OGI
Other
IIT Bombay
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