A Self-Adaptive Uzawa Block Relaxation Algorithm for Free Boundary Problems

GUO Nanxin; ZHANG Shougui

doi:10.21656/1000-0887.390347

Volume 40 Issue 6

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GUO Nanxin, ZHANG Shougui. A Self-Adaptive Uzawa Block Relaxation Algorithm for Free Boundary Problems[J]. Applied Mathematics and Mechanics, 2019, 40(6): 682-693. doi: 10.21656/1000-0887.390347

Citation:

GUO Nanxin, ZHANG Shougui. A Self-Adaptive Uzawa Block Relaxation Algorithm for Free Boundary Problems[J]. Applied Mathematics and Mechanics, 2019, 40(6): 682-693. doi: 10.21656/1000-0887.390347

Citation:

GUO Nanxin, ZHANG Shougui. A Self-Adaptive Uzawa Block Relaxation Algorithm for Free Boundary Problems[J]. Applied Mathematics and Mechanics, 2019, 40(6): 682-693. doi: 10.21656/1000-0887.390347

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A Self-Adaptive Uzawa Block Relaxation Algorithm for Free Boundary Problems

doi: 10.21656/1000-0887.390347

School of Mathematical Sciences, Chongqing Normal University, Chongqing 401331, P.R.China

Funds: The National Natural Science Foundation of China(General Program)(11471063)

Received Date: 2018-12-10
Rev Recd Date: 2019-03-12
Publish Date: 2019-06-01

Abstract

Abstract

A self-adaptive Uzawa block relaxation algorithm, based on the augmented Lagrangian multiplier method and the self-adaptive rule, was designed and analyzed for free boundary problems with unilateral obstacle. The problem was discretized as a finite-dimensional linear complementary problem which is equivalent to a saddle-point one with an augmented Lagrangian function and an auxiliary unknown. With the Uzawa block relaxation method for the problem, a 2-step iterative method was got with a linear problem as a main subproblem while the auxiliary unknown was computed explicitly. The convergence speed of the method highly depends on the penalty parameter, and it is difficult to choose a proper parameter for an individual problem. To improve the performance of the method, a self-adaptive rule was proposed to adjust the parameter automatically per iteration. Numerical results confirm the theoretical analysis of the proposed method.
- free boundary,
- linear complementarity,
- Uzawa block relaxation algorithm,
- augmented Lagrangian function,
- selfadaptive rule

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References(16)

References

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