Two lower boundedness-preservity auxiliary variable methods for a phase-field model of 3D narrow volume reconstruction

IF 3.4 2区数学 Q1 MATHEMATICS, APPLIED

Communications in Nonlinear Science and Numerical Simulation Pub Date : 2025-02-05 DOI:10.1016/j.cnsns.2025.108649

Xiangjie Kong, Renjun Gao, Boyi Fu, Dongting Cai, Junxiang Yang

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引用次数: 0

Abstract

Three-dimensional (3D) volume reconstruction remains a fundamental technique with wide applications in fields such as 3D printing, medical diagnostics, and industrial design. This paper presents two novel lower boundedness-preserving auxiliary variable methods designed for the phase-field model of 3D narrow volume reconstruction. By employing scattered point data, our approach reconstructs smooth narrow volumes using a phase-field Allen–Cahn model with a control function. The proposed method ensures energy dissipation and smooth surface throughout the reconstruction process. By introducing an auxiliary variable, the nonlinear term in the governing equation is reformulated, allowing for efficient time-marching schemes. The fully discrete scheme is linear, and its unconditional stability is rigorously estimated. Numerical experiments are conducted to demonstrate the energy stability, accuracy, and effectiveness of our proposed methods in various 3D reconstruction tasks, establishing its broad applicability.

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来源期刊

Communications in Nonlinear Science and Numerical Simulation MATHEMATICS, APPLIED-MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

CiteScore

6.80

自引率

7.70%

发文量

378

审稿时长

78 days

期刊介绍： The journal publishes original research findings on experimental observation, mathematical modeling, theoretical analysis and numerical simulation, for more accurate description, better prediction or novel application, of nonlinear phenomena in science and engineering. It offers a venue for researchers to make rapid exchange of ideas and techniques in nonlinear science and complexity. The submission of manuscripts with cross-disciplinary approaches in nonlinear science and complexity is particularly encouraged. Topics of interest: Nonlinear differential or delay equations, Lie group analysis and asymptotic methods, Discontinuous systems, Fractals, Fractional calculus and dynamics, Nonlinear effects in quantum mechanics, Nonlinear stochastic processes, Experimental nonlinear science, Time-series and signal analysis, Computational methods and simulations in nonlinear science and engineering, Control of dynamical systems, Synchronization, Lyapunov analysis, High-dimensional chaos and turbulence, Chaos in Hamiltonian systems, Integrable systems and solitons, Collective behavior in many-body systems, Biological physics and networks, Nonlinear mechanical systems, Complex systems and complexity. No length limitation for contributions is set, but only concisely written manuscripts are published. Brief papers are published on the basis of Rapid Communications. Discussions of previously published papers are welcome.