Multiple multiresolution representation of functions and calculus for fast computation
George I. Fann, Robert J. Harrison, Judith C. Hill, Jun Jia, Diego Galindo · 2010
We describe the mathematical representations, data structure and the implementation of the numerical calculus of functions in the software environment multiresolution analysis environment for scientific simulations, MADNESS. In MADNESS, each smooth function is represented using an adaptive pseudo-spectral expansion using the multiwavelet basis to a arbitrary but finite precision. This is an extension of the capabilities of most of the existing net, mesh and spectral based methods where the discretization is based on a single adaptive mesh, or expansions.