@Article{icces.2023.09474,
AUTHOR = {ShiJie Luo, Feng Yang, Yingjun Wang},
TITLE = {Efficient Multigrid Method Based on Adaptive Weighted Jacobi in  Isogeometric Analysis},
JOURNAL = {The International Conference on Computational \& Experimental Engineering and Sciences},
VOLUME = {27},
YEAR = {2023},
NUMBER = {1},
PAGES = {1--1},
URL = {http://www.techscience.com/icces/v27n1/54095},
ISSN = {1933-2815},
ABSTRACT = {The isogeometric analysis Method (IGA) is an efficient and accurate engineering analysis method. However, 
in order to obtain accurate analysis results, the grid must be refined, and the increase of the number of 
refinements will lead to large-scale equations, which will increase the computational cost. Compared with 
the traditional equation solvers such as preconditioned conjugate gradient method (PCG), generalized 
minimal residual (GMRES), the advantage of multigrid method is that the convergence rate is independent 
of grid scale when solving large-scale equations. This paper presents an adaptive weighted Jacobi method 
to improve the convergence of geometric multigrid method to efficiently solve the equations of IGA. 
Geometric multigrid constructs a series of coarse grids by using the refinement of IGA. By coarsening and 
refining the grid, the low-frequency part of the residual can be effectively suppressed. In order to choose the 
best parament of weighted Jacobi to improve the convergence speed, the adaptive weighted Jacobi is 
proposed. The adaptive weighted Jacobi method can effectively reduce the high-frequency part by 
minimizing the residual principle to change the weight. Thus, the convergence condition and convergence 
speed of geometric multigrid can be improved. The numerical examples demonstrate that the proposed 
method has the advantages of fast convergence speed and high efficiency in solving topology optimization 
models, and the weighted Jacobi has superior parallel performance, which has a great application potential 
in solving large-scale problems.},
DOI = {10.32604/icces.2023.09474}
}