@Article{icces.2024.010869,
AUTHOR = {Xinyi Guan, Shaoqiang Tang},
TITLE = {Solving Advection-Diffusion Equation by Proper Generalized Decomposition with Coordinate Transformation},
JOURNAL = {The International Conference on Computational \& Experimental Engineering and Sciences},
VOLUME = {29},
YEAR = {2024},
NUMBER = {1},
PAGES = {1--1},
URL = {http://www.techscience.com/icces/v29n1/58231},
ISSN = {1933-2815},
ABSTRACT = {Inheriting a convergence difficulty explained by the Kolmogorov N-width [1], the advection-diffusion equation is not effectively solved by the Proper Generalized Decomposition [2] (PGD) method. In this paper, we propose a new strategy: Proper Generalized Decomposition with Coordinate Transformation (CT-PGD). Converting the mixed hyperbolic-parabolic equation to a parabolic one, it resumes the efficiency of convergence for advection-dominant problems. Combining PGD with CT-PGD, we solve advection-diffusion equation by much fewer degrees of freedom, hence improve the efficiency. The advection-dominant regime and diffusion-dominant regime are quantitatively classified by a threshold, computed numerically. Moreover, we find that appropriate preconditioners may further improve the effectiveness.},
DOI = {10.32604/icces.2024.010869}
}