基于时间依赖基本解的奇异边界法模拟二维狄利克雷边界标量波方程

发布时间：2018-04-14 01:22

本文选题：奇异边界法 + 时间依赖基本解　；参考：《计算力学学报》2017年02期

【摘要】：奇异边界法是一个半解析边界配点强格式方法,具有无数值积分和无网格、编程容易以及数学简单等优点。本文首次将时间依赖基本解运用于奇异边界法,计算模拟二维标量波方程;结合确定源点强度因子的反插值技术,提出了二维狄利克雷边界标量波方程源点强度因子的一个经验公式;引进了解决波方程基本解G奇异性的一种无奇异积分处理方法。数值实验证明,基于时间依赖基本解的奇异边界法可精确高效地模拟二维狄利克雷边界标量波方程,在计算效率、精度、稳定性和适应性等方面有明显优势。
[Abstract]:Singular boundary method is a semi-analytic boundary collocation strong scheme method, which has the advantages of no numerical integration and meshless, easy programming and simple mathematics.In this paper, the time dependent fundamental solution is applied to the singular boundary method for the first time to simulate the two-dimensional scalar wave equation, and the inverse interpolation technique is used to determine the intensity factor of the source point.An empirical formula for the intensity factor of the source point of the two-dimensional Dilikley boundary scalar wave equation is presented, and a non-singular integral processing method for solving the G singularity of the fundamental solution of the wave equation is introduced.Numerical experiments show that the singular boundary method based on the time-dependent fundamental solution can accurately and efficiently simulate the two-dimensional Delikley boundary scalar wave equation, and has obvious advantages in computational efficiency, accuracy, stability and adaptability.
【作者单位】：河海大学工程与科学数值模拟软件中心
【基金】：国家自然科学基金(11372097,11302069) 111计划(B12032) 国家杰出青年科学基金(11125208) 声场声信息国家重点实验室开放基金(SKLA201509)资助项目
【分类号】：O241.8

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