S. Knapek and F. Koster.
Integral operators on sparse grids.
SIAM J. Num. Anal., 39(5):1794-1809, 2002.
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This paper is concerned with the construction and use of wavelet approximation spaces for the fast evaluation of integral expressions. Based on the framework of tensor-product biorthogonal wavelet bases we introduce sparse grid (hyperbolic cross) type approximation spaces and discuss additional compression schemes on top of these discretizations. We introduce blending schemes for the efficient evaluation of such integral expressions and for the solution of integro-differential equations. Numerical examples for the Laplace equation with Dirichlet boundary conditions and an additional integral term with smooth kernel validate our theoretical findings.