A wavelet algorithm for the solution of the double layer potential equation over polygonal boundaries
A piecewise linear collocation method for the solution of the double layer potential equation corresponding to Laplace's equation over polygonal domains is considered. For this collocation, a fast wavelet algorithms is defined which requires no more than \(O(N [\log N]^8)\) arithmetic operations and a storage capacity of \(O(N [\log N])\) numbers. A similar algorithm for piecewise cubic splines is also described. Some numerical results are presented to confirm the effectiveness of the algorithm. The convergence rate \(O (N^{-2} [\log N]^6)\) for the piecewise linear wavelet algorithm is also shown.
scientific article; zbMATH DE number 808208
scientific article