In this paper we present and analyse a high accuracy method for computing wave directions defined in the geometrical optics ansatz of Helmholtz equation with variable wave number. Then we define an "adaptive" plane wave space with small dimensions, in which each plane wave basis function is determined by such an approximate wave direction. We establish a best $L^2$ approximation of the plane wave space for the analytic solutions of homogeneous Helmholtz equations with large wave numbers and report some numerical results to illustrate the efficiency of the proposed method.
翻译：在本文中,我们提出并分析一种高精度的方法,用于计算Helmholtz等方程式中带有可变波数的几何光学 ansatz 所定义的波形方向。然后,我们定义了一个小尺寸的“适应性”平面波空间,其中每个平面波基函数由这样一个近似波形方向决定。我们为具有大波数的同质海尔mholtz等方程式的分析解决方案,确定了最佳的平面波位近似值2美元,并报告了一些数字结果,以说明拟议方法的效率。
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