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We present a parallel and linear scaling implementation of the calculation of the electrostatic potential arising from an arbitrary charge distribution. Our approach is making use of the multi-resolution basis of multiwavelets. The potential is obtained as the direct solution of the Poisson equation in its Green's function integral form. In the multiwavelet basis, the formally non local integral operator decays rapidly to negligible values away from the main diagonal, yielding an effectively banded structure where the bandwidth is only dictated by the requested accuracy. This sparse operator structure has been exploited to achieve linear scaling and parallel algorithms. Parallelization has been achieved both through the shared memory (OpenMP) and the message passing interface (MPI) paradigm. Our implementation has been tested by computing the electrostatic potential of the electronic density of long-chain alkanes and diamond fragments showing (sub)linear scaling with the system size and efficent parallelization. [ABSTRACT FROM AUTHOR]

We have developed a new strategy to reduce the storage requirements of a multivariate function in a multiwavelet framework. We propose that alongside the commonly used adaptivity in the grid refinement one can also vary the order of the representation k as a function of the scale n . In particular the order is decreased with increasing refinement scale. The consequences of this choice, in particular with respect to the nesting of scaling spaces, are discussed and the error of the approximation introduced is analyzed. The application of this method to some examples of mono- and multivariate functions shows that our algorithm is able to yield a storage reduction up to almost 60%. In general, values between 30 and 40% can be expected for multivariate functions. Monovariate functions are less affected but are also much less critical in view of the so called “curse of dimensionality”. [ABSTRACT FROM AUTHOR]