An Enhanced and Highly Efficient Semi-Implicit Combined Lagrange Multiplier Approach Preserving Original Energy Law for Dissipative Systems

IF 2.7 3区 工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY
Zhengguang Liu, Nan Zheng, Xiaoli Li
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引用次数: 0

Abstract

Recently, a new Lagrange multiplier approach was introduced by Cheng, Liu, and Shen, which has been broadly used to solve various challenging phase field problems. To design original energy-stable schemes, they have to solve a nonlinear algebraic equation to determine the introduced Lagrange multiplier, which can be computationally expensive, especially for large-scale and long-time simulations involving complex nonlinear terms. In this article, we propose an essential improved technique to modify this issue, which can be seen as a semi-implicit combined Lagrange multiplier approach. In general, the newly constructed schemes keep all the advantages of the Lagrange multiplier method and significantly reduce the computation costs. Besides, the new proposed second-order backward difference formula (BDF2) scheme dissipates the original energy, as opposed to a modified energy for the classic Lagrange multiplier approach. In addition, we establish a general framework for extending our constructed method to dissipative systems. Finally, several examples have been presented to demonstrate the effectiveness of the proposed approach.

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来源期刊
CiteScore
5.70
自引率
6.90%
发文量
276
审稿时长
5.3 months
期刊介绍: The International Journal for Numerical Methods in Engineering publishes original papers describing significant, novel developments in numerical methods that are applicable to engineering problems. The Journal is known for welcoming contributions in a wide range of areas in computational engineering, including computational issues in model reduction, uncertainty quantification, verification and validation, inverse analysis and stochastic methods, optimisation, element technology, solution techniques and parallel computing, damage and fracture, mechanics at micro and nano-scales, low-speed fluid dynamics, fluid-structure interaction, electromagnetics, coupled diffusion phenomena, and error estimation and mesh generation. It is emphasized that this is by no means an exhaustive list, and particularly papers on multi-scale, multi-physics or multi-disciplinary problems, and on new, emerging topics are welcome.
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