Linear Scaling Solution of the Coulomb problem using wavelets

The Coulomb problem for continuous charge distributions is a central problem in physics. Powerful methods, that scale linearly with system size and that allow us to use different resolutions in different regions of space are therefore highly desirable. Using wavelet based Multi Resolution Analysis we derive for the first time a method which has these properties. The power and accuracy of the method is illustrated by applying it to the calculation of of the electrostatic potential of a full three-dimensional all-electron Uranium dimer.