标题： 关于各向异性小波坐标中积分算子的可压缩性 显示英文标题

标题： On the Compressibility of Integral Operators in Anisotropic Wavelet Coordinates

摘要： 本文讨论的是各向异性小波坐标系中经典边界积分算子的s*-可压缩性。 具备s*-可压缩性后，可以设计出自适应小波算法，这些算法在渐近意义上是最优的，意味着任何目标精度都可以以计算成本与自由度数量成比例的方式实现（在由底层小波基确定的设置中），这理想情况下是实现该目标精度所必需的自由度数量，如果已知未知解的全部信息的话。 由于我们这里考虑的是各向异性小波坐标系，相比标准的各向同性设置，可以获得更高的收敛速度。 特别是，可以解析各向异性特征的边缘奇异性。 显示英文摘要

摘要： The present article is concerned with the s*-compressibility of classical boundary integral operators in anisotropic wavelet coordinates. Having the s*-compressibility at hand, one can design adaptive wavelet algorithms which are asymptotically optimal, meaning that any target accuracy can be achieved at a computational expense that stays proportional to the number of degrees of freedom (within the setting determined by an underlying wavelet basis) that would ideally be necessary for realising that target accuracy if full knowledge about the unknown solution were given. As we consider here anisotropic wavelet coordinates, we can achieve higher convergence rates compared to the standard, isotropic setting. Especially, edge singularities of anisotropic nature can be resolved.