四面体网格上的Biot-Savart积分评估
Evaluation of Biot-Savart integrals on tetrahedral meshes
AI总结：
提出一种算术简单的方法，通过高斯求积和光线追踪技术评估四面体网格上的Biot-Savart积分，避免了平方根、对数和反正切等复杂运算，实现了二阶收敛和近线性并行加速。
摘要：
开发了一种算术简单的方法，用于评估四面体化涡量分布上的Biot-Savart积分。与通常使用四面体上线性涡量分布诱导速度的解析公式方法不同，该积分采用高斯求积和计算机图形学中的光线追踪技术进行。这完全消除了对平方根、对数和反正切计算的需求，并且几乎完全消除了对三角函数的需求，在主计算循环中不需要比除法更昂贵的操作。给出了算法性能的评估，展示了其准确性、二阶收敛性以及在并行系统上的近线性加速。
英文摘要：
An arithmetically simple method has been developed for the evaluation of Biot--Savart integrals on tetrahedralized distributions of vorticity. In place of the usual approach of analytical formulae for the velocity induced by a linear distribution of vorticity on a tetrahedron, the integration is performed using Gaussian quadrature and a ray tracing technique from computer graphics. This eliminates completely the need for the evaluation of square roots, logarithms and arc tangents, and almost completely eliminates the requirement for trigonometric functions, with no operation more costly than a division required during the main calculation loop. An assessment of the algorithm's performance is presented, demonstrating its accuracy, second order convergence and near-linear speedup on parallel systems.
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