论文标题
$ \ MATHCAL {H}^2 $ -MATRICES用于翻译不变的内核函数
$\mathcal{H}^2$-matrices for translation-invariant kernel functions
论文作者
论文摘要
椭圆形部分微分方程的边界元素方法通常会导致边界积分运算符具有翻译不变的内核函数。对于粒子方法，例如NyStrom型离散化，利用此属性非常简单，但是如果必须考虑基础函数的支持，则更具挑战性。 在本文中，我们提出了用于$ \ MATHCAL {H}^2 $ -MATRICES的修改构造，该建筑使用翻译不变性大大降低了存储要求。由于用于构造的框的均匀性，我们只需要几个简单的假设即可证明所得的存储复杂性的估计。
Boundary element methods for elliptic partial differential equations typically lead to boundary integral operators with translation-invariant kernel functions. Taking advantage of this property is fairly simple for particle methods, e.g., Nystrom-type discretizations, but more challenging if the supports of basis functions have to be taken into account. In this article, we present a modified construction for $\mathcal{H}^2$-matrices that uses translation-invariance to significantly reduce the storage requirements. Due to the uniformity of the boxes used for the construction, we need only a few uncomplicated assumptions to prove estimates for the resulting storage complexity.
