In this letter, we propose a new time-domain meshless method without discretization in time based on eigenexpansions of numerical solutions. As a result, numerical time-stepping is not required, and its associated errors are eliminated. Analytical solutions of the radial point interpolation meshless (RPIM) method are derived, and the solutions become always stable. In other words, electric and magnetic field values are available at any time, making late-time electromagnetic field analysis convenient and efficient. Numerical experiments are conducted to verify the effectiveness and accuracy of the proposed method.

中文翻译：

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一种不进行时间离散化的时域无网格方法

在这封信中，我们基于数值解的特征展开提出了一种新的时域无网格方法，无需在时间上进行离散化。因此，不需要数字时间步长，并且消除了其相关错误。导出了径向点插值无网格（RPIM）方法的解析解，并且解变得始终稳定。换句话说，电场和磁场值随时可用，使后期电磁场分析变得方便和高效。数值实验验证了所提出方法的有效性和准确性。