A novel method is developed to take into account realistic boundary conditions in intense nonlinear beam dynamics. The algorithm consists of three main ingredients: the boundary element method that provides a solution for the discretized reformulation of the Poisson equation as boundary integrals; a novel fast multipole method developed for accurate and efficient computation of Coulomb potentials and forces; and differential algebraic methods, which form the numerical structures that enable and hold together the different components. The fast multipole method, without any modifications, also accelerates the solution of intertwining linear systems of equations for further efficiency enhancements. The resulting algorithm scales linearly with the number of particles $N$, as $m\log m$ with the number of boundary elements $m$, and, therefore, establishes an accurate and efficient method for intense beam dynamics simulations in arbitrary enclosures. Its performance is illustrated with three different cases and structures of practical interest.

中文翻译：

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任意壳体非线性光束动力学的微分代数快速多极加速边界元方法

开发了一种新颖的方法来考虑强非线性光束动力学中的实际边界条件。该算法包括三个主要成分：边界元法，为离散化的泊松方程重新定义为边界积分提供解决方案；开发了一种新颖的快速多极方法，用于精确有效地计算库仑势和力；以及微分代数方法，它们构成了使不同成分组合在一起的数值结构。快速多极方法，无需做任何修改，也可以加快交织的线性方程组的求解速度，从而进一步提高效率。生成的算法随粒子数量线性缩放$ñ$， 作为 $米\mathrm{日志}米$ 与边界元素的数量 $米$，因此建立了一种精确有效的方法，用于在任意外壳中进行强烈的光束动力学模拟。通过三种不同的案例和具有实际意义的结构来说明其性能。