We consider the 2D acoustic system with the Gaussian pulse as the initial data. This case was proposed at the first Workshop on benchmark problems in computational aeroacoustics, and it is commonly used for the verification of numerical methods. We construct an efficient algorithm to evaluate the exact solution for a given time t and distance r. For a precision eps, it takes c*ln(1/eps) operations (the evaluation of a Bessel function counts as one operation) where c does not depend on t and r. This becomes possible by using three different integral representations and an asymptotic series depending on t and r.

翻译：我们考虑以高斯脉冲为初始数据的二维声学系统。该算例首次提出于计算气动声学基准问题第一届研讨会，并广泛应用于数值方法的验证。我们构建了一种高效算法以计算给定时间t和距离r下的精确解。对于精度eps，该算法仅需c*ln(1/eps)次运算（其中贝塞尔函数的求值计为一次运算），且常数c不依赖于t和r。这一目标的实现得益于采用三种不同的积分表示形式以及依赖于t和r的渐近级数。