We investigate high-order Convolution Quadratures methods for the solution of the wave equation in unbounded domains in two dimensions that rely on Nystr\"om discretizations for the solution of the ensemble of associated Laplace domain modified Helmholtz problems. We consider two classes of CQ discretizations, one based on linear multistep methods and the other based on Runge-Kutta methods, in conjunction with Nystr\"om discretizations based on Alpert and QBX quadratures of Boundary Integral Equation (BIE) formulations of the Laplace domain Helmholtz problems with complex wavenumbers. We present a variety of accuracy tests that showcase the high-order in time convergence (up to and including fifth order) that the Nystr\"om CQ discretizations are capable of delivering for a variety of two dimensional scatterers and types of boundary conditions.

翻译：我们研究了用于求解二维无界区域中波动方程的高阶卷积求积法，该方法基于Nyström离散化来解决相关联的Laplace域修正Helmholtz问题的集合。我们考虑两类CQ离散化方法：其一基于线性多步法，另一基于Runge-Kutta法，并结合使用基于Alpert和QBX求积的边界积分方程（BIE）公式来离散化具有复波数的Laplace域Helmholtz问题。我们展示了多种精度测试，表明Nyström CQ离散化能够针对各类二维散射体及边界条件类型实现时间方向的高阶收敛（最高可达五阶）。