41 citations · 383 across the 48 of their papers we have counts for
6 papers · 1 filter
Material degradation due to moisture and temperature. Part 1: Mathematical model, analysis, and analytical solutions
C. Xu, M. K. Mudunuru, K. B. Nakshatrala
The mechanical response, serviceability, and load bearing capacity of materials and structural components can be adversely affected due to external stimuli, which include exposure…
Large-scale Optimization-based Non-negative Computational Framework for Diffusion Equations: Parallel Implementation and Performance Studies
J. Chang, S. Karra, K. B. Nakshatrala
It is well-known that the standard Galerkin formulation, which is often the formulation of choice under the finite element method for solving self-adjoint diffusion equations, does…
On enforcing maximum principles and achieving element-wise species balance for advection-diffusion-reaction equations under the finite element method
M. K. Mudunuru, K. B. Nakshatrala
We present a robust computational framework for advective-diffusive-reactive systems that satisfies maximum principles, the non-negative constraint, and element-wise species balanc…
Do current lattice Boltzmann methods for diffusion and diffusion-type equations respect maximum principles and the non-negative constraint?
S. Karimi, K. B. Nakshatrala
The lattice Boltzmann method (LBM) has established itself as a valid numerical method in computational fluid dynamics. Recently, multiple-relaxation-time LBM has been proposed to s…
On mesh restrictions to satisfy comparison principles, maximum principles, and the non-negative constraint: Recent developments and new results
M. K. Mudunuru, K. B. Nakshatrala
This paper concerns with mesh restrictions that are needed to satisfy several important mathematical properties -- maximum principles, comparison principles, and the non-negative c…
Mechanics-based solution verification for porous media models
M. Shabouei, K. B. Nakshatrala
This paper presents a new approach to verify accuracy of computational simulations. We develop mathematical theorems which can serve as robust a posteriori error estimation techniq…