We solve acoustic scattering problems by means of the isogeometric boundary integral equation method. In order to avoid spurious modes, we apply the combined field integral equations for either sound-hard scatterers or sound-soft scatterers. These integral equations are discretized by Galerkin's method, which especially enables the mathematically correct regularization of the hypersingular integral operator. In order to circumvent densely populated system matrices, we employ the isogeometric fast multipole method. The result is an algorithm that scales essentially linear in the number of boundary elements. Numerical experiments are performed which show the feasibility and the performance of the approach.

翻译：本文采用等几何边界积分方程方法求解声散射问题。为避免伪模态，我们分别针对硬声散射体和软声散射体应用组合场积分方程。这些积分方程通过伽辽金法进行离散，该方法特别能够实现超奇异积分算子的数学正则化。为克服稠密系统矩阵问题，我们采用等几何快速多极子方法。由此得到的算法在边界元数量上基本呈线性缩放。通过数值实验验证了该方法的可行性与性能。