This paper presents a fast and robust algorithm for contact detection between elliptical and ellipsoidal particles. The algorithm belongs to the class of geometrical potential methods, which consider the solution of two minimization problems in order to determine a contact point between the particles. The efficiency of the algorithm relies on several ingredients, namely, a transformation that maps the pair of ellipses (ellipsoids) into an ellipse (ellipsoid) centered at the origin and a unit circle (sphere), the construction of an effective initial guess to the solution of the minimization problem, the use of Newton's method for the root finding problem, and the introduction of an additional constraint to guarantee convergence to the desired root. The performance of the new algorithm is compared with that of existing contact detection algorithms on large sets of randomly generated pairs of particles. In particular, the results from several numerical examples show that the present algorithm is several times faster than the existing algorithms for comparable accuracy.

中文翻译：

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一种椭球粒子的快速接触检测方法

本文提出了一种用于椭圆和椭球粒子之间接触检测的快速而稳健的算法。该算法属于几何势方法类，它考虑两个最小化问题的解以确定粒子之间的接触点。该算法的效率依赖于几个要素，即，将一对椭圆（椭球）映射为以原点为中心的椭圆（椭球）和单位圆（球体）的变换，构造有效的初始猜测到最小化问题的解决方案，使用牛顿方法解决求根问题，并引入附加约束以保证收敛到所需的根。在大量随机生成的粒子对上，将新算法的性能与现有接触检测算法的性能进行了比较。特别是，几个数值例子的结果表明，在可比精度方面，本算法比现有算法快几倍。