Related papers: Yet another fast multipole method without multipol…
In this paper we recreate, and improve, the binary classification method for particles proposed in Roe et al. (2005) paper "Boosted decision trees as an alternative to artificial neural networks for particle identification". Such particles…
Fast Multipole Methods (FMM) are a fundamental operation for the simulation of many physical problems. The high performance design of such methods usually requires to carefully tune the algorithm for both the targeted physics and the…
We present a new Monte Carlo algorithm for the interpolation of a straight-line program as a sparse polynomial $f$ over an arbitrary finite field of size $q$. We assume a priori bounds $D$ and $T$ are given on the degree and number of terms…
A numerical method using implicit surface representations is proposed to solve the linearized Poisson-Boltzmann equations that arise in mathematical models for the electrostatics of molecules in solvent. The proposed method used an implicit…
The Fast Multipole Method (FMM) reduces the computation of pairwise two-body interactions among $N$-particles to order $N$, whose computation cost should be of order $N^2$ by brute force. However, its implementation is somewhat complicated…
We present a method that gives highly accurate electrostatic potentials for systems where we have periodic boundary conditions in two spatial directions but free boundary conditions in the third direction. These boundary conditions are…
We propose a new class of semi-implicit methods for solving nonlinear fractional differential equations and study their stability. Several versions of our new schemes are proved to be unconditionally stable by choosing suitable parameters.…
The kd-tree is a fundamental tool in computer science. Among others, an application of the kd-tree search (oct-tree method) to fast evaluation of particle interactions and neighbor search is highly important since computational complexity…
We present a detailed comparison between ONETEP, our linear-scaling density functional method, and the conventional pseudopotential plane wave approach in order to demonstrate its high accuracy. Further comparison with all-electron…
In the presence of a strong magnetic field, the effective action of a composite scalar field in an scalar O(N) model is derived using two different methods. First, in the framework of worldline formalism, the 1PI n-point vertex function for…
In this work we present a variant of the fast multipole method (FMM) for efficiently evaluating standard layer potentials on geometries with complex coordinates in two and three dimensions. The complex scaled boundary integral method for…
Tree codes that approximate groups of distant particles with multipole expansions are the standard way to accelerate the computation of self-gravity on particles. While momentum-conserving fast multipole methods exist, parallelisation is…
The multipole-expansion (MPE) model is an implicit solvation model used to efficiently incorporate solvent effects in quantum chemistry. Even within the recent direct approach, the multipole basis used in MPE to express the dielectric…
The multipole expansions for massive vector and symmetric tensor fields in the region outside spatially compact stationary sources are obtained by using the symmetric and trace-free formalism in terms of the irreducible Cartesian tensors,…
In this paper, we present an efficient Particle-In-Cell algorithm for the simulation of the three dimensional Vlasov-Poisson system in the presence of a strong external magnetic field. When the intensity of the magnetic field is…
In this paper, we describe a multiscale model based on magneto-static traps of neutral atoms or ion traps. The idea is to levitate a magnetic spinning top in the air repelled by a base magnet. For such a problem, we have to deal with…
This paper introduces a generalised 3rd-order Spectral Representation Method for the simulation of multi-dimensional stochastic fields with asymmetric non-linearities. The simulated random fields satisfy a prescribed Power Spectrum and…
We present an extension of the tensor grid method for stray field computation on rectangular domains that incorporates higher-order basis functions. Both the magnetization and the resulting magnetic field are represented using higher-order…
Sequential Monte Carlo techniques are useful for state estimation in non-linear, non-Gaussian dynamic models. These methods allow us to approximate the joint posterior distribution using sequential importance sampling. In this framework,…
In order to avoid the evaluation of the Jacobian matrix and its inverse, the present author recently introduced the pseudo-Jacobian matrix with a general applicability of any nonlinear systems of equations. By using this concept, this paper…