高频问题的混合矩阵压缩
Hybrid matrix compression for high-frequency problems
摘要：
Helmholtz方程的边界元方法导致只有使用有效的压缩技术才能处理的大型稠密矩阵。定向压缩技术即使对于高频问题也可以达到良好的压缩率。目前有两种方法来进行方向压缩：解析方法近似的核函数，而代数方法近似的子矩阵。分析方法是相当快的，并证明是强大的，而代数方法产生显着更好的压缩率。我们提出了一种混合方法，结合了分析方法的速度和可靠性与良好的压缩率的代数方法。
英文摘要：
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.
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