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Study of radial basis collocation method for wave propagation

机译：径向基配波方法的研究

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摘要

A numerical method based on radial basis functions and collocation method is proposed for wave propagation. Standard collocation and weighted boundary collocation approaches yield significant errors in wave problems. Therefore, a new method based on explicit time integration scheme that can correct the inaccuracy in the solutions and the errors accumulated in time integration is developed. This method can be easily applied for low and high dimensional wave problems. The stability conditions are obtained and the relationships between control parameters and stability are evaluated. Requirement of collocation points in numerical dispersion is studied and nondispersion condition is formulated. Eigenvalue analysis is investigated to evaluate the effectiveness of radial basis collocation method for solving wave problems. Eigenvalue study with and without imposing the boundary conditions are compared. The influences of shape parameters and distribution of collocation points and source points are presented. Numerical examples are simulated to examine and validate the proposed method.
机译：提出了一种基于径向基函数和配点法的波传播数值方法。标准配置和加权边界配置方法会在波动问题中产生重大错误。因此，开发了一种基于显式时间积分方案的新方法，该方法可以纠正解决方案中的误差和时间积分中累积的误差。这种方法可以轻松地应用于低维和高维波问题。获得了稳定性条件，并评估了控制参数与稳定性之间的关系。研究了数值色散中搭配点的要求，并提出了非色散条件。进行了特征值分析，以评估径向基搭配方法在求解波浪问题中的有效性。比较有无条件条件下的特征值研究。给出了形状参数的影响以及并置点和源点的分布。仿真算例验证了该方法的有效性。

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