most citedA pressure-correction and bound-preserving discretization of the phase-field method for variable density two-phase flows

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math.NA2020★ 1 cited

A pressure-correction and bound-preserving discretization of the phase-field method for variable density two-phase flows

Chen Liu, Deep Ray, Christopher Thiele +2

In this paper, we present an efficient numerical algorithm for solving the time-dependent Cahn--Hilliard--Navier--Stokes equations that model the flow of two phases with different…

math.NA2020

Multi-level Monte Carlo Finite Difference Methods for Fractional Conservation Laws with Random Data

Ujjwal Koley, Deep Ray, Tanmay Sarkar

We establish a notion of random entropy solution for degenerate fractional conservation laws incorporating randomness in the initial data, convective flux and diffusive flux. In or…

math.NA2019

On the approximation of rough functions with deep neural networks

Tim De Ryck, Siddhartha Mishra, Deep Ray

Deep neural networks and the ENO procedure are both efficient frameworks for approximating rough functions. We prove that at any order, the ENO interpolation procedure can be cast…