3 citations · 11 across the 17 of their papers we have counts for
17 papers
A Tensor-Train Discontinuous Galerkin Method for the Vlasov-Maxwell System
Rujeko Chinomona, Dibyendu Adak, William J. Barham +4
We present a tensor-train discontinuous Galerkin (TT-DG) formulation for the Vlasov--Maxwell system that combines a modal DG discretization with low-rank tensor representations of…
Conforming and non-conforming virtual element methods for the biharmonic Steklov eigenvalue problem with minimum regularity
Dibyendu Adak, Daniele Boffi, Francesca Gardini +2
In this work, we analyze the conforming and -non-conforming Virtual Element Method for a fourth-order Steklov eigenvalue problem on a generally shaped, possibly nonconvex, pol…
Nonconforming virtual element methods for fourth-order nonlinear reaction-diffusion systems: a unified framework and analysis
Dibyendu Adak, David Mora, Alberth Silgado
We develop a unified framework for the design and analysis of high-order nonconforming virtual element methods for nonlinear fourth-order reaction--diffusion problems in two dimens…
Space-Time Spectral Collocation Tensor-Network Approach for Maxwell's Equations
Dibyendu Adak, Rujeko Chinomona, Duc P. Truong +3
In this work, we develop a space--time Chebyshev spectral collocation method for three-dimensional Maxwell's equations and combine it with tensor-network techniques in Tensor-Train…
A noncoforming virtual element approximation for the Oseen eigenvalue problem
Dibyendu Adak, Felipe Lepe, Gonzalo Rivera
In this paper we analyze a nonconforming virtual element method to approximate the eigenfunctions and eigenvalues of the two dimensional Oseen eigenvalue problem. The spaces under…
Space-Time Spectral Element Tensor Network Approach for Time Dependent Convection Diffusion Reaction Equation with Variable Coefficients
Dibyendu Adak, Duc P. Truong, Radoslav Vuchkov +5
In this paper, we present a new space-time Petrov-Galerkin-like method. This method utilizes a mixed formulation of Tensor Train (TT) and Quantized Tensor Train (QTT), designed for…
Tensor Network Space-Time Spectral Collocation Method for Solving the Nonlinear Convection Diffusion Equation
Dibyendu Adak, M. Engin Danis, Duc P. Truong +2
Spectral methods provide highly accurate numerical solutions for partial differential equations, exhibiting exponential convergence with the number of spectral nodes. Traditionally…
Tensor Network Space-Time Spectral Collocation Method for Time Dependent Convection-Diffusion-Reaction Equations
Dibyendu Adak, Duc P. Truong, Gianmarco Manzini +2
Emerging tensor network techniques for solutions of Partial Differential Equations (PDEs), known for their ability to break the curse of dimensionality, deliver new mathematical me…
A -conforming arbitrary-order two-dimensional virtual element method for the fourth-order phase-field equation
Dibyendu Adak, Gianmarco Manzini, Hashem M. Mourad +2
We present a two-dimensional conforming virtual element method for the fourth-order phase-field equation. Our proposed numerical approach to the solution of this high-order phase-f…
The Morley-type virtual element method for the Navier-Stokes equations in stream-function form on general meshes
D. Adak, D. Mora, A. Silgado
The nonconforming Morley-type virtual element method for the incompressible Navier-Stokes equations formulated in terms of the stream-function on simply connected polygonal domains…
VEM approximation for the Stokes eigenvalue problem: a priori and a posteriori error analysis
Dibyendu Adak, Felipe Lepe, Gonzalo Rivera
The present paper proposes an inf-sup stable divergence free virtual element method and associated a priori, and a posteriori error analysis to approximate the eigenvalues and eige…
Convergence Analysis of Virtual Element Method for Nonlinear Nonlocal Dynamic Plate Equation
D. Adak, D. Mora, S. Natarajan
In this article, we have considered a nonlinear nonlocal time dependent fourth order equation demonstrating the deformation of a thin and narrow rectangular plate. We propose …
Virtual element approximation of two-dimensional parabolic variational inequalities
Dibyendu Adak, Gianmarco Manzini, Sundararajan Natarajan
We design a virtual element method for the numerical treatment of the two-dimensional parabolic variational inequality problem on unstructured polygonal meshes. Due to the expected…
Virtual element method for semilinear sine-Gordon equation over polygonal mesh using product approximation technique
Dibyendu Adak, Sundararajan Natarajan
In this paper, we employ the linear virtual element spaces to discretize the semilinear sine-Gordon equation in two dimensions. The salient features of the virtual element method (…
A Unified Analysis of Nonconforming Virtual Element Methods for Convection Diffusion Reaction Problem
Dibyendu Adak, E. Natarajan
We discuss nonconforming virtual element method for convection dominated (diffusive coefficient is very small compared to convective coefficient and reac- tion coefficient ) convec…
Analysis of nonconforming virtual element method for the convection diffusion reaction equation with polynomial coefficients
Dibyendu Adak, E. Natarajan
In this paper we discuss the application of nonconforming virtual element methods(VEM) for the second order diffusion dominated convection diffusion reaction equation. Stability of…
Analysis of a combined NC1-C2 method for elliptic problem
Dibyendu Adak, E. Natarajan
It is shown in this paper that non-conforming finite elements on the triangle using -nonconforming polynomials and -conforming polynomials can be easily built and us…