Related papers: Yet another fast multipole method without multipol…
The objective of this paper is to investigate a new numerical method for the approximation of the self-diffusion matrix of a tagged particle process defined on a grid. While standard numerical methods make use of long-time averages of…
This article introduces a new fast direct solver for linear systems arising out of wide range of applications, integral equations, multivariate statistics, radial basis interpolation, etc., to name a few. \emph{The highlight of this new…
This paper has two purposes. First we present a new definition of the multivariate Pad\'e approximation, a new fast numerical method. Then numerical solution of the one-dimensional (1D) time-dependent nonlinear Sine-Gordon equation (SGE) is…
Let $P\subset\mathbb{R}^{2}$ be a set of $n$ points. In this paper we show two new algorithms, one to compute the number of triangulations of $P$, and one to compute the number of pseudo-triangulations of $P$. We show that our algorithms…
To simulate the dynamics of fluid with polydisperse particles on macroscale level, one has to solve hydrodynamic equations with several relaxation terms, representing momentum transfer from fluid to particles and vice versa. For small…
Many fundamental statistical methods have become critical tools for scientific data analysis yet do not scale tractably to modern large datasets. This paper will describe very recent algorithms based on computational geometry which have…
Hybrid particle-field molecular dynamics combines standard molecular potentials with density-field models into a computationally efficient methodology that is well-adapted for the study of mesoscale soft matter systems. Here, we introduce a…
We present a method for reconstructing two-dimensional velocity fields at specified length scales using observational data from tracer particles in a flow, without the need for interpolation or smoothing. The algorithm, adapted from…
The Fast Multipole Method (FMM) is well known to possess a bottleneck arising from decreasing workload on higher levels of the FMM tree [Greengard and Gropp, Comp. Math. Appl., 20(7), 1990]. We show that this potential bottleneck can be…
We provide a first-principle, materials-specific theory of multipolar order and superexchange in NpO$_2$ by means of a non-collinear local-density approximation +$U$ (LDA+$U$) method. Our calculations offer a precise microscopic description…
In this paper, we design an algorithm to accelerate the diffusion process on the $SO(3)$ manifold. The inherently sequential nature of diffusion models necessitates substantial time for denoising perturbed data. To overcome this limitation,…
The discrete-dipole approximation (DDA) is a flexible technique for computing scattering and absorption by targets of arbitrary geometry. In this paper we perform systematic study of various non-stationary iterative (conjugate gradient)…
We proposed a method based on microwave magnetic dipole transitions to prepare samples of atoms with well defined position and velocity. Each microwave pulse corresponds to a position measurement for the atoms and two pulses separated by a…
We address binary classification using neural ordinary differential equations from the perspective of simultaneous control of $N$ data points. We consider a single-neuron architecture with parameters fixed as piecewise constant functions of…
In this paper we consider the problem of finding $\epsilon$-approximate stationary points of convex functions that are $p$-times differentiable with $\nu$-H\"{o}lder continuous $p$th derivatives. We present tensor methods with and without…
Using the auxiliary field method, we give an analytical expression for the eigenenergies of a system composed of two non-relativistic particles interacting via a potential of type $\sqrt{a^2 r^2 + b}$. This situation is usual in the case of…
We introduce a nonmonotone extension of the Front Descent framework for multiobjective optimization. The method uses novel nonmonotone line searches that allow temporary increases in some objective functions. To our knowledge, this is the…
Dynamic programming is a powerful technique that is, unfortunately, often inherently sequential. That is, there exists no unified method to parallelize algorithms that use dynamic programming. In this paper, we attempt to address this issue…
An implementation of the fast multiple method (FMM) is performed for magnetic systems with long-ranged dipolar interactions. Expansion in spherical harmonics of the original FMM is replaced by expansion of polynomials in Cartesian…
A novel approach for non-intrusive uncertainty propagation is proposed. Our approach overcomes the limitation of many traditional methods, such as generalised polynomial chaos methods, which may lack sufficient accuracy when the quantity of…