The 1D Quasicrystal Wave Equation Coefficient Matrix Symmetrization and Its SBP-SAT Simulation

LIU Taiyu; ZHOU Yuee; JIANG Guanxixi; ZHANG Jianwei; SUN Cheng

doi:10.21656/1000-0887.450324

Volume 47 Issue 3

Mar. 2026

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Article Navigation > Applied Mathematics and Mechanics > 2026 > 47(3): 367-380

LIU Taiyu, ZHOU Yuee, JIANG Guanxixi, ZHANG Jianwei, SUN Cheng. The 1D Quasicrystal Wave Equation Coefficient Matrix Symmetrization and Its SBP-SAT Simulation[J]. Applied Mathematics and Mechanics, 2026, 47(3): 367-380. doi: 10.21656/1000-0887.450324

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The 1D Quasicrystal Wave Equation Coefficient Matrix Symmetrization and Its SBP-SAT Simulation

doi: 10.21656/1000-0887.450324

LIU Taiyu^1,2,
ZHOU Yuee^1,2,
JIANG Guanxixi³,
ZHANG Jianwei^4,5,6,
SUN Cheng^{1,2,4,5
,
,}

1. School of Civil Engineering and Architecture, Guangxi Minzu University,Nanning 530006, P.R.China;
2. Engineering Research Center for Intelligent Monitoring and Testing of Engineering Operation and Maintenance, Guangxi Minzu University, Nanning 530006, P.R.China;
3. School of Physical and Mathematical Sciences, Nanjing University of Technology, Nanjing 211816, P.R.China;
4. School of Aerospace and Civil Engineering, Harbin Engineering University, Harbin 150080, P.R.China;
5. Hebei Key Laboratory of Dual Media Power Technology, Handan, Hebei 056000, P.R.China;
6. School of Safety Engineering, Shenyang Aerospace University,Shenyang 110000, P.R.China

Received Date: 2024-12-04
Rev Recd Date: 2025-04-15

Available Online: 2026-04-01

Publish Date: 2026-03-01

Abstract

Abstract

The study of wave propagation in quasicrystals is of significant value for gaining a deeper understanding of the unique physical properties of quasicrystals, however, numerical simulations of such wave behaviors pose considerable challenges. Through symmetrization of the wave equation coefficient matrix, it is possible to effectively integrate different types of wave equations and reduce the complexity of wave propagation simulations. The symmetrized form of the coefficient matrix for the 1D quasicrystal wave equation was derived and the wave equation was discretized with the upwind scheme SBPSAT finite difference method, and the stability was then assessed with the energy method. Numerical simulations demonstrate that the proposed discretization framework exhibits high integration, good stability, and strong scalability. Furthermore, the method can stably simulate wave propagation in curved domains while reducing the implementation cost, indicating the broad application potential of the symmetrization technique and its discretization framework in wave propagation simulations.
- quasicrystal wave equation,
- coefficient matrix symmetrization,
- SBP-SAT,
- finite difference method,
- energy method

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References(35)

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