应用数学和力学2026，Vol.47Issue(3)：367-380,14.DOI:10.21656/1000-0887.450324
一维准晶波动方程系数矩阵对称化及其SBP-SAT模拟
The 1D Quasicrystal Wave Equation Coefficient Matrix Symmetrization and Its SBP-SAT Simulation
摘要
Abstract
The study of wave propagation in quasicrystals is of significant value for gaining a deeper under-standing of the unique physical properties of quasicrystals,however,numerical simulations of such wave be-haviors pose considerable challenges.Through symmetrization of the wave equation coefficient matrix,it is pos-sible 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 sta-bility was then assessed with the energy method.Numerical simulations demonstrate that the proposed discreti-zation 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 propaga-tion simulations.关键词
准晶波动方程/系数矩阵对称式/SBP-SAT/有限差分方法/能量法Key words
quasicrystal wave equation/coefficient matrix symmetrization/SBP-SAT/finite difference method/energy method分类
数理科学引用本文复制引用
刘泰玉,周月娥,蒋关希曦,张剑伟,孙铖..一维准晶波动方程系数矩阵对称化及其SBP-SAT模拟[J].应用数学和力学,2026,47(3):367-380,14.基金项目
国家自然科学基金青年科学基金(12002182) （12002182）
广西高校中青年教师科研基础能力提升项目(2022KY0155) （2022KY0155）
广西民族大学科研基金资助项目(2021KJQD24) （2021KJQD24）
