Integral Operators on Sparse Grids
Integral Operators on Sparse Grids
复制标题
稀疏网格上的积分算子
DOI：
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发表时间：
2001
影响因子：
2.9
通讯作者：
F. Koster
中科院分区：
文献类型：
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作者：
S. Knapek;F. Koster
本文讨论了小波逼近空间的构造和应用，用于快速求积分表达式。该空间基于双正交各向异性张量积小波。我们引入了稀疏网格（双曲交叉）逼近空间，它不仅适应核的平滑性，而且适应测量误差的范数。此外，我们还介绍了相应离散化的压缩方案。对具有Dirichlet边界条件和带光滑核的附加积分项的拉普拉斯方程的数值算例证明了理论结果的有效性。
In this paper we are concerned with the construction and use of wavelet approximation spaces for the fast evaluation of integral expressions. The spaces are based on biorthogonal anisotropic tensor product wavelets. We introduce sparse grid (hyperbolic cross) approximation spaces which are adapted not only to the smoothness of the kernel but also to the norm in which the error is measured. Furthermore, we introduce compression schemes for the corresponding discretizations. Numerical examples for the Laplace equation with Dirichlet boundary conditions and an additional integral term with a smooth kernel demonstrate the validity of our theoretical results.