# Evaluation of convolution integrals involving locally refined hp-Functions

## Prof. Dr. Dr. h.c. Wolfgang Hackbusch

May 15, 2007, 3:30 p.m. HF 136

Let f and g be functions of an hp-element space in R with bounded support. Here, an hp-element space is characterised by local grid sizes h_l=2^{-l}*h (l: refinement level). On each subinterval the functions are polynomials of degree <=p (no continuity between the subintervals required). The convolution f*g is the integral of f(y)g(x-y)dy over R. Its (exact) orthogonal L^2 projection into an hp-element space is to be computed. Wedescribe the algorithm which has the complexity O(p^2*N*log(N)). Here, N is the number of all subintervals involved in the description of the factors f,g and of the result, p is the maximal polynomial degree.