arXiv subjects

Veronica Montanaro

Publications and source records attributed to Veronica Montanaro.

3 recordsLinked to original sources

arXiv2026

Variance Reduction in the Fokker-Planck Particle Method for Rarefied Gases using Quasi-Random Numbers

The Fokker-Planck (FP) particle method accelerates rarefied-gas simulations by replacing the binary collisions of the commonly used Direct Simulation Monte Carlo (DSMC) method with a drift=diffusion process. Like all particle methods, the FP method is inherently stochastic, which leads to statistical fluctuations in macroscopic quantities and necessitates large particle numbers for accurate results. In this work, we investigate the use of quasi-random numbers, which sample distributions more evenly and thereby reduce the variance. To preserve the low-discrepancy structure across time steps, we employ the Array Randomized Quasi-Monte Carlo (Array-RQMC) technique. We combine the FP method with Array-RQMC and compare it in homogeneous and inhomogeneous problems with other commonly used variance-reduction techniques. The proposed FP-Array-RQMC approach achieves improved convergence rates compared with pseudo-random sampling and yields smaller estimator errors for sufficiently large particle numbers.

math.NA↗

arXiv2025

Fisher entropic Fokker-Planck model of monatomic rarefied gases

Particle-based stochastic approximations of the Boltzmann equation are popular tools for simulations of non-equilibrium gas flows, for which the Navier-Stokes-Fourier equations fail to provide accurate description. However, these numerical methods are computationally demanding, especially in the near-continuum regime, where the collisions become overwhelming. On the other hand, the Fokker-Planck kinetic models offer an efficient alternative, as the binary collisions are described by a diffusive process. Despite the intuitive advantage, rigorous and efficient Fokker-Planck approximations of the Boltzmann equation remain an open problem. On one hand, the moment projection of the Fokker-Planck operator should be consistent with that of the Boltzmann operator. On the other hand, the Fokker-Planck model should be constructed in such a way that the H-theorem is satisfied. The central aim of this study is fulfilling these two categorically different constraints, i.e. moment matching and entropy dissipation, within a flexible and tractable Fokker-Planck framework. To this end, we introduce a Fisher information-based entropic constraint and demonstrate that, with a suitable polynomial expansion of the drift term, it is possible to simultaneously achieve weak moment matching while honouring the H-theorem. We support our theoretical result by numerical experiments on the shock problem, validating our Fisher Entropic Fokker-Planck framework.

math.NA↗

arXiv2025

A Massively Parallel Performance Portable Free-space Spectral Poisson Solver

Vico et al. (2016) suggest a fast algorithm for computing volume potentials, beneficial to fields with problems requiring the solution of the free-space Poisson's equation, such as beam and plasma physics. Currently, the standard is the algorithm of Hockney and Eastwood (1988), with second order in convergence at best. The algorithm proposed by Vico et al. converges spectrally for sufficiently smooth functions i.e. faster than any fixed order in the number of grid points. We implement a performance portable version of the traditional Hockney-Eastwood and the novel Vico-Greengard Poisson solver as part of the IPPL (Independent Parallel Particle Layer) library. For sufficiently smooth source functions, the Vico-Greengard algorithm achieves higher accuracy than the Hockney-Eastwood method with the same grid size, reducing the computational demands of high resolution simulations since one could use coarser grids to achieve them. Additionally, we propose an improvement to the Vico-Greengard method which further reduces its memory footprint. This is important for GPUs, which have limited memory, and should be taken into account when selecting numerical algorithms for performance portable codes. Finally, we showcase performance through GPU and CPU scaling studies on the Perlmutter (NERSC) supercomputer, with efficiencies staying above 50% in the strong scaling case. To showcase portability, we also run the scaling studies on the Alps supercomputer at CSCS, Switzerland and the GPU partition of the Lumi supercomputer at CSC, Finland.

physics.comp-ph↗