Related papers: The optimal particle-mesh interpolation basis
The structure and function of biological molecules are strongly influenced by the water and dissolved ions that surround them. This aqueous solution (solvent) exerts significant electrostatic forces in response to the biomolecule's…
We propose a very simple but realistic enough model which allows to include a large number of molecules in molecular dynamics MD simulations of these bilayers, but nevertheless taking into account molecular charge distributions, flexible…
Engineering problems often involve data sources of variable fidelity with different costs of obtaining an observation. In particular, one can use both a cheap low fidelity function (e.g. a computational experiment with a CFD code) and an…
Complex phenomena can be better understood when broken down into a limited number of simpler "components". Linear statistical methods such as the principal component analysis and its variants are widely used across various fields of applied…
When methods of moments are used for identification of power spectral densities, a model is matched to estimated second order statistics such as, e.g., covariance estimates. If the estimates are good there is an infinite family of power…
Chebyshev interpolation is a highly effective, intensively studied method and enjoys excellent numerical properties. The interpolation nodes are known beforehand, implementation is straightforward and the method is numerically stable. For…
In the era of big data, we first need to manage the data, which requires us to find missing data or predict the trend, so we need operations including interpolation and data fitting. Interpolation is a process to discover deducing new data…
We present a rigorous Ewald summation formula to evaluate the electrostatic interactions in two-dimensionally periodic planar interfaces of three-dimensional systems. By rewriting the Fourier part of the summation formula of the original…
An extrapolation method in shell model calculations with deformed basis is presented, which uses a scaling property of energy and energy variance for a series of systematically approximated wave functions to the true one. Such approximated…
Simulating charged many-body systems has been a computational demanding task due to the long-range nature of electrostatic interaction. For the multi-scale model of electrolytes which combines the strengths of atomistic/continuum…
This work investigates theoretically the interplay between interpolation and aggregation in regression. We establish that the $\gamma$-graph dimension characterizes learnability for a broad class of natural aggregation procedures.…
Infrared spectroscopy is key to elucidate molecular structures, monitor reactions and observe conformational changes, while providing information on both structural and dynamical properties. This makes the accurate prediction of infrared…
Meshfree methods, including the reproducing kernel particle method (RKPM), have been widely used within the computational mechanics community to model physical phenomena in materials undergoing large deformations or extreme topology…
The Performance Estimation Problem (PEP) approach consists in computing worst-case performance bounds on optimization algorithms by solving an optimization problem: one maximizes an error criterion over all initial conditions allowed and…
A multilevel kernel-based interpolation method, suitable for moderately high-dimensional function interpolation problems, is proposed. The method, termed multilevel sparse kernel-based interpolation (MLSKI, for short), uses both level-wise…
A modified 3D-Ewald summation is presented for accurately simulating the ion-dipole mixture under dielectric confinement. The method is based on the combination of image charges and image dipoles with the conventional Ewald summation and…
Ewald summation and physically equivalent methods such as particle-mesh Ewald, kubic-harmonic expansions, or Lekner sums are commonly used to calculate long-range electrostatic interactions in computer simulations of polar and charged…
The Particle-Particle-Particle-Mesh algorithm elegantly extends the standard Particle-In-Cell scheme by direct summation of interaction that happens over distances below or around mesh size. Generally, this allows for a more accurate…
We present a technique to efficiently compute long-range interactions in systems with periodic boundary conditions. We extend the well-known Ewald method by using a linear combination of screening Gaussian charge distributions instead of…
Radiative transfer effects need to be taken into account when analysing spectral line observations. When the data are not sufficient for detailed modelling, simpler methods are needed. The escape probability formalism (EPF) is one such…