Publications

Dissertation

A. Vijaywargiya, High-Order Computation of Gradient Flows and Barycenters in Generalized Wasserstein Spaces, Dataset, University of Notre Dame. https://doi.org/10.7274/28766591.v1

A. Vijaywargiya, S. McQuarrie, and A. Gruber, Tensor parametric Hamiltonian operator inference, arXiv preprint arXiv:2502.10888, 2025. https://arxiv.org/abs/2502.10888.
A. Vijaywargiya, G. Fu, S. Osher, and W. Li, Efficient computation of mean field control based barycenters from reaction-diffusion systems, J. Comput. Phys., 2025, 113772. https://doi.org/10.1016/j.jcp.2025.113772.
A. Vijaywargiya, S. McQuarrie, and A. Gruber, Tensor Parametric Operator Inference with Hamiltonian Structure, in Computer Science Research Institute Summer Proceedings 2024, M. B. P. Adams, T. A. Casey, and B. W. Reuter, eds., Technical Report SAND2024-16688O, Sandia National Laboratories, 2024, pp. 172–194.
A. Vijaywargiya and G. Fu, Two finite element approaches for the porous medium equation that are positivity preserving and energy stable, J. Sci. Comput., 100 (2024), 86. https://doi.org/10.1007/s10915-024-02642-x.

In High-Order Computation of Gradient Flows and Barycenters in Generalized Wasserstein Spaces:

Section 4.3.3, Paragraph 2, Page 82: Similarly, denote by \(\{\zeta_i\}_{i=1}^{pN_T}\) and \(\{\theta_i\}_{i=1}^{p^d N_T}\) the sets of temporal quadrature nodes and weights, respectively.

In Two finite element approaches for the porous medium equation that are positivity preserving and energy stable:

Theorem 3.1: The physical energy of the PME is \(U(\rho^n) = \frac{(\rho^n)^m}{m-1}\).