Computation of singular integral operators in wavelet coordinates
With respect to a wavelet basis, singular integral operators can be well approximated by sparse matrices, and in Found. Comput. Math. 2: 203-245 (2002) and SIAM J. Math. Anal. 35: 1110-1132 (2004), this property was used to prove certain optimal complexity results in the context of adaptive wavelet methods. These results, however, were based upon the assumption that, on average, each entry of the approximating sparse matrices can be computed at unit cost. In this paper, we confirm this assumption by carefully distributing computational costs over the matrix entries in combination with choosing efficient quadrature schemes.
singular integrals wavelets adaptivity boundary integral operators matrix compression numerical integration nearly singular integrals optimal computational complexity