Boundary element methods for the Helmholtz equation lead to large dense matrices that can only be handled if efficient compression techniques are used. Directional compression techniques can reach good compression rates even for high-frequency problems. Currently there are two approaches to directional compression: analytic methods approximate the kernel function, while algebraic methods approximate submatrices. Analytic methods are quite fast and proven to be robust, while algebraic methods yield significantly better compression rates. We present a hybrid method that combines the speed and reliability of analytic methods with the good compression rates of algebraic methods.

中文翻译：

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高频问题的混合矩阵压缩

Helmholtz 方程的边界元方法会导致大的密集矩阵，只有使用有效的压缩技术才能处理这些矩阵。即使对于高频问题，定向压缩技术也可以达到良好的压缩率。目前有两种方向压缩方法：解析方法近似核函数，而代数方法近似子矩阵。分析方法非常快并且被证明是稳健的，而代数方法产生明显更好的压缩率。我们提出了一种混合方法，它将分析方法的速度和可靠性与代​​数方法的良好压缩率相结合。