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In this work we present an algorithm to construct an infinitely differentiable smooth surface from an input consisting of a (rectilinear) triangulation of a surface of arbitrary shape. The original surface can have non-trivial genus and…
We introduce a particle-based simulation method for granular material in interactive frame rates. We divide the simulation into two decoupled steps. In the first step, a relatively small number of particles is accurately simulated with a…
Particle filtering is a numerical Bayesian technique that has great potential for solving sequential estimation problems involving non-linear and non-Gaussian models. Since the estimation accuracy achieved by particle filters improves as…
A non-singular formulation of the boundary integral method (BIM) is presented for the Laplace equation whereby the well-known singularities that arise from the fundamental solution are eliminated analytically. A key advantage of this…
This paper describes the results of our theoretical and numerical studies of hydrodynamic interactions in a suspension of spherical particles confined between two parallel planar walls, under creeping-flow conditions. We propose a novel…
A method of adapting smoothed particle hydrodynamics (SPH) with periodic boundary conditions for use with the special purpose device GRAPE is presented. GRAPE (GRAvity PipE) solves the Poisson and force equations for an N-body system by…
This is a preliminary theoretical discussion on the computational requirements of the state of the art smoothed particle hydrodynamics (SPH) from the optics of pattern recognition and artificial intelligence. It is pointed out in the…
A key challenge when designing particle filters in high-dimensional state spaces is the construction of a proposal distribution that is close to the posterior distribution. Recent advances in particle flow filters provide a promising avenue…
This article describes a new, fully adaptive Particle-Multiple-Mesh numerical simulation code developed primarily for simulations of small regions (such as a group of galaxies) in a cosmological context. It integrates the equations of…
When modeling scientific and industrial problems, geometries are typically modeled by explicit boundary representations obtained from computer-aided design software. Unfitted (also known as embedded or immersed) finite element methods offer…
We present an implementation of smoothed particle hydrodynamics (SPH) with improved accuracy for simulations of galaxies and the large-scale structure. In particular, we combine, implement, modify and test a vast majority of SPH improvement…
We present a novel method for particle splitting in smoothed particle hydrodynamics simulations. Our method utilizes the Voronoi diagram for a given particle set to determine the position of fine daughter particles. We perform several test…
Wet particle separation is widely used in mineral processing and plastic recycling to separate mixtures of particulate materials into further usable fractions due to density differences. This work presents efforts aiming to numerically…
Obtaining high quality particle distribution representing clean geometry in pre-processing is essential for the simulation accuracy of the particle-based methods. In this paper, several level-set based techniques for cleaning up `dirty'…
The typical particle filtering approximation error is exponentially dependent on the dimension of the model. Therefore, to control this error, an enormous number of particles are required, which means a heavy computational burden that is…
Smoothed Particle Hydrodynamics (SPH) is a popular numerical technique developed for simulating complex fluid flows. Among its key ingredients is the use of nonlocal integral relaxations to local differentiations. Mathematical analysis of…
Fluid-Structure Interaction (FSI) is a crucial problem in ocean engineering. The smoothed particle hydrodynamics (SPH) method has been employed recently for FSI problems in light of its Lagrangian nature and its advantage in handling…
Implicit neural representations have emerged as a powerful approach for encoding complex geometries as continuous functions. These implicit models are widely used in computer vision and 3D content creation, but their integration into…
Recent developments in path integral methodology have significantly reduced the computational expense of including quantum mechanical effects in the nuclear motion in ab initio molecular dynamics simulations. However, the implementation of…
We present a novel scheme for modelling quantum plasmas in the warm dense matter (WDM) regime via a hybrid smoothed particle hydrodynamic - molecular dynamic treatment, here referred to as 'Bohm SPH'. This treatment is founded upon Bohm's…