Year: 2025
Type: article
Abstract: In the context of investigating the potential application of quantum computers to the finite element method, we propose a specific approach for solving the two-dimensional parabolic advection-diffusion-reaction boundary value problem by transforming it into a set of corresponding one-dimensional problems. This method employs specialized operator splitting, resulting in a recurrent fractional-step scheme for time integration. While this scheme offers significant parallelization potential, the main goal is to map the original large elliptic 2D problem arising at each time step into a set of smaller 1D problems of the same kind. This transformation, combined with recently proposed quantum-assisted stabilization schemes, allows us to pass smaller linear systems to a quantum linear solver, making them suitable for near-term quantum computers. We combine the proposed algorithm with the finite element method to solve the resulting one-dimensional problems, although these problems can also be addressed using other discretization techniques, such as the finite volume or finite difference methods.
Authors: Roman Drebotiy, Heorhiy Shynkarenko
Institution: Lviv University
Language: English
Subfield: Computational Mechanics
Field: Engineering
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W4414227174
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