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ORCIDVarun Shankar
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2020 – today
- 2024
[j17]Urban Duh, Varun Shankar, Gregor Kosec
:
Discretization of Non-uniform Rational B-Spline (NURBS) Models for Meshless Isogeometric Analysis. J. Sci. Comput. 100(2): 51 (2024)- [i29]Ramansh Sharma, Varun Shankar:
Ensemble and Mixture-of-Experts DeepONets For Operator Learning. CoRR abs/2405.11907 (2024) - [i28]Madison Cooley, Shandian Zhe, Robert M. Kirby, Varun Shankar:
Polynomial-Augmented Neural Networks (PANNs) with Weak Orthogonality Constraints for Enhanced Function and PDE Approximation. CoRR abs/2406.02336 (2024) - [i27]Matthew Lowery, John Turnage, Zachary Morrow, John D. Jakeman, Akil Narayan, Shandian Zhe, Varun Shankar:
Kernel Neural Operators (KNOs) for Scalable, Memory-efficient, Geometrically-flexible Operator Learning. CoRR abs/2407.00809 (2024) - 2023
- [j16]Shivam Barwey, Varun Shankar, Venkatasubramanian Viswanathan, Romit Maulik:
Multiscale graph neural network autoencoders for interpretable scientific machine learning. J. Comput. Phys. 495: 112537 (2023) - [j15]Varun Shankar, Vedant Puri, Ramesh Balakrishnan, Romit Maulik, Venkatasubramanian Viswanathan:
Differentiable physics-enabled closure modeling for Burgers' turbulence. Mach. Learn. Sci. Technol. 4(1): 15017 (2023) - [j14]Grady B. Wright, Andrew M. Jones, Varun Shankar:
MGM: A Meshfree Geometric Multilevel Method for Systems Arising from Elliptic Equations on Point Cloud Surfaces. SIAM J. Sci. Comput. 45(2): 312- (2023) - [i26]Shivam Barwey, Varun Shankar, Venkatasubramanian Viswanathan, Romit Maulik:
Multiscale Graph Neural Network Autoencoders for Interpretable Scientific Machine Learning. CoRR abs/2302.06186 (2023) - [i25]Urban Duh, Varun Shankar, Gregor Kosec:
Discretization of non-uniform rational B-spline (NURBS) models for meshless isogeometric analysis. CoRR abs/2303.02638 (2023) - [i24]Varun Shankar, Romit Maulik, Venkatasubramanian Viswanathan:
Differentiable Turbulence. CoRR abs/2307.03683 (2023) - [i23]Varun Shankar, Shivam Barwey, Zico Kolter, Romit Maulik, Venkatasubramanian Viswanathan:
Importance of equivariant and invariant symmetries for fluid flow modeling. CoRR abs/2307.05486 (2023) - [i22]Varun Shankar, Romit Maulik, Venkatasubramanian Viswanathan:
Differentiable Turbulence II. CoRR abs/2307.13533 (2023) - [i21]Mingxuan Han, Varun Shankar, Jeff M. Phillips, Chenglong Ye:
Locally Adaptive and Differentiable Regression. CoRR abs/2308.07418 (2023) - 2022
- [j13]Andrew T. Kassen, Varun Shankar, Aaron L. Fogelson:
A fine-grained parallelization of the immersed boundary method. Int. J. High Perform. Comput. Appl. 36(4): 443-458 (2022) - [j12]Andrew T. Kassen, Aaron Barrett, Varun Shankar, Aaron L. Fogelson:
Immersed boundary simulations of cell-cell interactions in whole blood. J. Comput. Phys. 469: 111499 (2022) - [c1]Ramansh Sharma, Varun Shankar:
Accelerated Training of Physics-Informed Neural Networks (PINNs) using Meshless Discretizations. NeurIPS 2022 - [i20]Grady B. Wright, Andrew M. Jones, Varun Shankar:
MGM: A meshfree geometric multilevel method for systems arising from elliptic equations on point cloud surfaces. CoRR abs/2204.06154 (2022) - [i19]Ramansh Sharma, Varun Shankar:
Accelerated Training of Physics Informed Neural Networks (PINNs) using Meshless Discretizations. CoRR abs/2205.09332 (2022) - [i18]Varun Shankar, Vedant Puri, Ramesh Balakrishnan, Romit Maulik, Venkatasubramanian Viswanathan:
Differentiable physics-enabled closure modeling for Burgers' turbulence. CoRR abs/2209.11614 (2022) - 2021
- [j11]Varun Shankar, Grady B. Wright, Aaron L. Fogelson:
An efficient high-order meshless method for advection-diffusion equations on time-varying irregular domains. J. Comput. Phys. 445: 110633 (2021) - [i17]M. Keith Ballard, Roman Amici, Varun Shankar, Lauren A. Ferguson, Michael Braginsky, Robert M. Kirby:
Towards an Extrinsic, CG-XFEM Approach Based on Hierarchical Enrichments for Modeling Progressive Fracture. CoRR abs/2104.14704 (2021) - [i16]Andrew T. Kassen, Aaron Barrett, Varun Shankar, Aaron L. Fogelson:
Immersed boundary simulations of cell-cell interactions in whole blood. CoRR abs/2108.09396 (2021) - 2020
- [j10]Sean D. Lawley, Varun Shankar:
Asymptotic and Numerical Analysis of a Stochastic PDE Model of Volume Transmission. Multiscale Model. Simul. 18(2): 887-915 (2020) - [j9]Varun Shankar, Grady B. Wright, Akil Narayan:
A Robust Hyperviscosity Formulation for Stable RBF-FD Discretizations of Advection-Diffusion-Reaction Equations on Manifolds. SIAM J. Sci. Comput. 42(4): A2371-A2401 (2020) - [i15]Varun Shankar, Grady B. Wright, Aaron L. Fogelson:
An Efficient High-Order Meshless Method for Advection-Diffusion Equations on Time-Varying Irregular Domains. CoRR abs/2011.06715 (2020) - [i14]Andrew T. Kassen, Varun Shankar, Aaron L. Fogelson:
A fine-grained parallelization of the immersed boundary method. CoRR abs/2012.06646 (2020)
2010 – 2019
- 2019
- [i13]Varun Shankar, Grady B. Wright, Akil Narayan:
A Robust Hyperviscosity Formulation for Stable RBF-FD Discretizations of Advection-Diffusion-Reaction Equations on Manifolds. CoRR abs/1910.07059 (2019) - 2018
- [j8]Varun Shankar, Grady B. Wright:
Mesh-free semi-Lagrangian methods for transport on a sphere using radial basis functions. J. Comput. Phys. 366: 170-190 (2018) - [j7]Varun Shankar, Aaron L. Fogelson:
Hyperviscosity-based stabilization for radial basis function-finite difference (RBF-FD) discretizations of advection-diffusion equations. J. Comput. Phys. 372: 616-639 (2018) - [j6]Varun Shankar, Akil Narayan, Robert M. Kirby:
RBF-LOI: Augmenting Radial Basis Functions (RBFs) with Least Orthogonal Interpolation (LOI) for solving PDEs on surfaces. J. Comput. Phys. 373: 722-735 (2018) - [j5]Vidhi Zala, Varun Shankar, Shankar P. Sastry, Robert M. Kirby:
Curvilinear Mesh Adaptation Using Radial Basis Function Interpolation and Smoothing. J. Sci. Comput. 77(1): 397-418 (2018) - [j4]Varun Shankar, Robert M. Kirby, Aaron L. Fogelson:
Robust Node Generation for Mesh-free Discretizations on Irregular Domains and Surfaces. SIAM J. Sci. Comput. 40(4): A2584-A2608 (2018) - [i12]Varun Shankar, Grady B. Wright:
Mesh-free Semi-Lagrangian Methods for Transport on a Sphere Using Radial Basis Functions. CoRR abs/1804.01609 (2018) - [i11]Vidhi Zala, Varun Shankar, Shankar P. Sastry, Robert M. Kirby:
Curvilinear Mesh Adaptation using Radial Basis Function Interpolation and Smoothing. CoRR abs/1804.03358 (2018) - [i10]Varun Shankar, Robert M. Kirby, Aaron L. Fogelson:
Robust Node Generation for Meshfree Discretizations on Irregular Domains and Surfaces. CoRR abs/1806.02972 (2018) - [i9]Varun Shankar, Aaron L. Fogelson:
Hyperviscosity-Based Stabilization for Radial Basis Function-Finite Difference (RBF-FD) Discretizations of Advection-Diffusion Equations. CoRR abs/1806.03798 (2018) - [i8]Varun Shankar, Akil Narayan, Robert M. Kirby:
RBF-LOI: Augmenting Radial Basis Functions (RBFs) with Least Orthogonal Interpolation (LOI) for Solving PDEs on Surfaces. CoRR abs/1807.02775 (2018) - 2017
- [j3]Varun Shankar:
The overlapped radial basis function-finite difference (RBF-FD) method: A generalization of RBF-FD. J. Comput. Phys. 342: 211-228 (2017) - [j2]Erik Lehto, Varun Shankar, Grady B. Wright:
A Radial Basis Function (RBF) Compact Finite Difference (FD) Scheme for Reaction-Diffusion Equations on Surfaces. SIAM J. Sci. Comput. 39(5) (2017) - 2016
- [i7]Varun Shankar:
The Overlapped Radial Basis Function-Finite Difference (RBF-FD) Method for the Numerical Solution of PDEs. CoRR abs/1606.03135 (2016) - 2015
- [j1]Varun Shankar, Grady B. Wright, Robert M. Kirby, Aaron L. Fogelson:
A Radial Basis Function (RBF)-Finite Difference (FD) Method for Diffusion and Reaction-Diffusion Equations on Surfaces. J. Sci. Comput. 63(3): 745-768 (2015) - [i6]Varun Shankar, Sarah D. Olson:
Radial Basis Function (RBF)-based Parametric Models for Closed and Open Curves within the Method of Regularized Stokeslets. CoRR abs/1503.00034 (2015) - [i5]Edward J. Fuselier, Varun Shankar, Grady B. Wright:
A High-Order Radial Basis Function (RBF) Leray Projection Method for the Solution of the Incompressible Unsteady Stokes Equations. CoRR abs/1509.05669 (2015) - 2014
- [b1]Varun Shankar:
Radial Basis Function-Based Numerical Methods for the Simulation of Platelet Aggregation. University of Utah, USA, 2014 - [i4]Varun Shankar, Grady B. Wright, Robert M. Kirby, Aaron L. Fogelson:
A Radial Basis Function (RBF)-Finite Difference (FD) Method for Diffusion and Reaction-Diffusion Equations on Surfaces. CoRR abs/1404.0812 (2014) - 2013
- [i3]Varun Shankar, Grady B. Wright, Robert M. Kirby, Aaron L. Fogelson:
Augmenting the Immersed Boundary Method with Radial Basis Functions (RBFs) for the Modeling of Platelets in Hemodynamic Flows. CoRR abs/1304.7479 (2013) - [i2]Varun Shankar, Grady B. Wright, Aaron L. Fogelson, Robert M. Kirby:
A Radial Basis Function (RBF)-Finite Difference Method for the Simulation of Reaction-Diffusion Equations on Stationary Platelets within the Augmented Forcing Method. CoRR abs/1310.5207 (2013) - 2012
- [i1]Varun Shankar, Grady B. Wright, Aaron L. Fogelson, Robert M. Kirby:
A Study of Different Modeling Choices For Simulating Platelets Within the Immersed Boundary Method. CoRR abs/1210.1885 (2012)
Coauthor Index
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