Deflated Preconditioned Conjugate Gradient Solvers for Linear Elastic Crack Problems

doi:10.19596/j.cnki.1001-246x.8793

Abstract

Abstract:

This paper focuses on some efficient deflated preconditioners for static elastic crack problems modelled by the geometrical extended finite element method. We not only construct the deflation subspace matrix which is suitable for linear elastic crack problems, but also give the principle for selecting the deflated mesh nodes. To further accelerate the convergence, we combine the deflation technique with the "crack tip" domain decomposition preconditioners through multiplicative way, and propose efficient adapted deflated preconditioned conjugate gradient solvers which can eliminate the high-frequency and low-frequency errors simultaneously in the iterations. Numerical experiments demonstrate the effectiveness of our algorithm.

Key words: extended finite element method, deflation technique, domain decomposition preconditioners, static crack problems

CLC Number:

O357.41

Xingkang LIU, Xingding CHEN, Yunlong YU. Deflated Preconditioned Conjugate Gradient Solvers for Linear Elastic Crack Problems[J]. Chinese Journal of Computational Physics, 2024, 41(5): 619-629.

Figures/Tables 13

References 25

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网格剖分	ADCG_H	ADCG_tip	ADCG_Htip
19×19	16	12	28
39×39	32	52	84
59×59	48	112	160
79×79	64	192	256
99×99	80	308	388
119×119	96	448	544
139×139	112	608	720

网格剖分	ADCG_H	ADCG_tip	ADCG_Htip
19×19	16	12	28
39×39	32	52	84
59×59	48	112	160
79×79	64	192	256
99×99	80	308	388
119×119	96	448	544
139×139	112	608	720

网格剖分	Cond_NPre	Cond_Jac	Cond_AS	Cond_RAS
19×19	2.25×10⁶	2.34×10⁵	8.24×10²	6.75×10²
39×39	1.62×10⁹	6.81×10⁷	1.04×10⁵	1.02×10⁵
59×59	3.05×10¹⁰	1.44×10⁹	1.23×10⁶	1.23×10⁶
79×79	1.86×10¹¹	1.08×10¹⁰	7.77×10⁶	7.76×10⁶
99×99	1.43×10¹²	1.35×10¹¹	5.08×10⁷	5.07×10⁷

网格剖分	Cond_NPre	Cond_Jac	Cond_AS	Cond_RAS
19×19	2.25×10⁶	2.34×10⁵	8.24×10²	6.75×10²
39×39	1.62×10⁹	6.81×10⁷	1.04×10⁵	1.02×10⁵
59×59	3.05×10¹⁰	1.44×10⁹	1.23×10⁶	1.23×10⁶
79×79	1.86×10¹¹	1.08×10¹⁰	7.77×10⁶	7.76×10⁶
99×99	1.43×10¹²	1.35×10¹¹	5.08×10⁷	5.07×10⁷