Presented in the context of classical molecular mechanics and dynamics are multilevel summation methods for the fast calculation of energies/forces for pairwise interactions, which are based on the hierarchical interpolation of interaction potentials on multiple grids. The concepts and details underlying multigrid interpolation are described. For integration of molecular dynamics the use of dif...

We present a framework using the Quantized Tensor Train (QTT) decomposition to accurately and efficiently solve volume and boundary integral equations in three dimensions. We describe how the QTT decomposition can be used as a hierarchical compression and inversion scheme for matrices arising from the discretization of integral equations. For a broad range of problems, computational and storage...

Simulating wave propagation in 3D configurations is becoming a very active area of research. Themain advantage of the BEM is that only the domain boundaries are discretized. As a result, thismethod is well suited to dealing with unbounded domains. However, the standard BEM leadsto fully-populated matrices, which results in high computational costs in CPU time and mem-ory require...

We investigate the use of the Multipole-accelerated Boundary Element Method (BEM) and of the Singularity Method for studying the interaction of many bubbles rising in a volcanic conduit. Observation shows that the expression of volcanic eruption is extremely variable, from slow release of magma to catastrophic explosive manifestation. We investigate the application of the Fast Multipole Method ...

A novel hybrid boundary element-finite element scheme which is accelerated by an adaptive multi-level fast multipole algorithm is presented to simulate 3D plane wave electromagnetic induction responses in the Earth. The remarkable advantages of this novel scheme are the complete removal of the volume discretization of the air space and the capability of simulating large-scale complicated geoele...

Wave propagation problems play an important role, not only in the scientific community, but also in industry. Think of acoustic scattering, sound radiation and other related problems. A common feature of these problems is the large or even infinite extension of the acoustic domain compared to the rather limited extension of the surface of the embedded scatterer. The appropriateness of solving s...

A parallel high-order Boundary Element Method accelerated by the Fast Multipole Method is presented in this report. The case of potential flow about arbitrary geometries will be investigated using this method. The goal of this application is to provide a ”pushbutton” tool for the design of aircraft, where medium-fidelity solutions can be obtained in seconds and not hours or days required by Nav...

We present a 0.5 Petaflop/s calculation of homogeneous isotropic turbulence in a cube of 2048 particles, using a highly parallel fast multipole method (FMM) using 2048 GPUs on the TSUBAME 2.0 system. We compare this particle-based code with a spectral DNS code under the same calculation condition and the same machine. The results of our particlebased turbulence simulation match quantitatively w...

A method is presented that allows the computation of space charge effects of arbitrary and large distributions of particles in an efficient and accurate way based on a variant of the Fast Multipole Method (FMM). It relies on an automatic multigrid-based decomposition of charges in near and far regions and the use of high-order differential algebra methods to obtain decompositions of far fields ...