Výsledky vyhledávání - "Adak, Dibyendu"

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Space-Time Spectral Element Tensor Network Approach for Time Dependent Convection Diffusion Reaction Equation with Variable Coefficients

Autor: Adak, Dibyendu, Truong, Duc P., Vuchkov, Radoslav, De, Saibal, DeSantis, Derek, Roberts, Nathan V., Rasmussen, Kim Ø., Alexandrov, Boian S.

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 the spectral element discretization (Q1-SEM) of the time-dependent co

Externí odkaz: http://arxiv.org/abs/2411.04026

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Tensor Network Space-Time Spectral Collocation Method for Solving the Nonlinear Convection Diffusion Equation

Autor: Adak, Dibyendu, Danis, M. Engin, Truong, Duc P., Rasmussen, Kim Ø., Alexandrov, Boian S.

Spectral methods provide highly accurate numerical solutions for partial differential equations, exhibiting exponential convergence with the number of spectral nodes. Traditionally, in addressing time-dependent nonlinear problems, attention has been

Externí odkaz: http://arxiv.org/abs/2406.02505

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Tensor Network Space-Time Spectral Collocation Method for Time Dependent Convection-Diffusion-Reaction Equations

Autor: Adak, Dibyendu, Truong, Duc P., Manzini, Gianmarco, Rasmussen, Kim Ø., Alexandrov, Boian S.

Emerging tensor network techniques for solutions of Partial Differential Equations (PDEs), known for their ability to break the curse of dimensionality, deliver new mathematical methods for ultrafast numerical solutions of high-dimensional problems.

Externí odkaz: http://arxiv.org/abs/2402.18073

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A $C^1$-conforming arbitrary-order two-dimensional virtual element method for the fourth-order phase-field equation

Autor: Adak, Dibyendu, Manzini, Gianmarco, Mourad, Hashem M., Plohr, JeeYeon N., Svolos, Lampros

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-field (HOPF) equation relies on the design of an arbitrary-order accura

Externí odkaz: http://arxiv.org/abs/2307.16068

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VEM approximation for the Stokes eigenvalue problem: a priori and a posteriori error analysis

Autor: Adak, Dibyendu, Lepe, Felipe, Rivera, Gonzalo

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 eigenfunctions of the Stokes spectral problem in one shot. For the a prior

Externí odkaz: http://arxiv.org/abs/2212.01961

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