Convolution of hp - functions on locally refined grids
نویسنده
چکیده
Usually, the fast evaluation of a convolution integral R R f(y)g(x−y)dy requires that the functions f, g have a simple structure based on an equidistant grid in order to apply the fast Fourier transform. Here we discuss the efficient performance of the convolution of hp-functions in certain locally refined grids. More precisely, the convolution result is projected into some given hp-space (Galerkin approximation). The overall cost is O(p2N logN), where N is the sum of the dimensions of the subspaces containing f , g and the resulting function, while p is the maximal polynomial degree. AMS Subject Classifications: 44A35, 42A55
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