Related papers: The optimal particle-mesh interpolation basis
Theoretical estimates for the cutoff errors in the Ewald summation method for dipolar systems are derived. Absolute errors in the total energy, forces and torques, both for the real and reciprocal space parts, are considered. The…
Typical biomolecular systems such as cellular membranes, DNA, and protein complexes are highly charged. Thus, efficient and accurate treatment of electrostatic interactions is of great importance in computational modelling of such systems.…
A crucial aspect in the simulation of electrochemical interfaces consists in treating the distribution of electronic charge of electrode materials that are put in contact with an electrolyte solution. Recently, it has been shown how a…
To minimise systematic errors in Monte Carlo simulations of charged particles, long range electrostatic interactions have to be calculated accurately and efficiently. Standard approaches, such as Ewald summation or the naive application of…
The evaluation of the electrostatic potential is fundamental to the study of condensed phase systems. We discuss the calculation of the relevant lattice summations by Ewald-type techniques. A model charge density is introduced, that cancels…
In this paper a general theory for interpolation methods on a rectangular grid is introduced. By the use of this theory an efficient B-spline based interpolation method for spectral codes is presented. The theory links the order of the…
Discrete empirical interpolation method (DEIM) is a popular technique for nonlinear model reduction and it has two main ingredients: an interpolating basis that is computed from a collection of snapshots of the solution and a set of indices…
For nonlinear reduced-order models, especially for those with non-polynomial nonlinearities, the computational complexity still depends on the dimension of the original dynamical system. As a result, the reduced-order model loses its…
The smooth particle mesh Ewald (SPME) method is an FFT based method for the fast evaluation of electrostatic interactions under periodic boundary conditions. A highly optimized implementation of this method is available in GROMACS, a widely…
Effective verification and validation techniques for modern scientific machine learning workflows are challenging to devise. Statistical methods are abundant and easily deployed, but often rely on speculative assumptions about the data and…
We develop a computational method for modeling electrostatic interactions of arbitrarily-shaped, polarizable objects on colloidal length scales, including colloids/nanoparticles, polymers, and surfactants, dispersed in explicit ion…
Recent developments in molecular theories and simulation of ions and polar molecules in water are reviewed. The hydration of imidazole and imidazolium solutes is used to exemplify the theoretical issues. The treatment of long-ranged…
The kernel-based multi-scale method has been proven to be a powerful approximation method for scattered data approximation problems which is computationally superior to conventional kernel-based interpolation techniques. The multi-scale…
This paper is devoted to the study of the Bayesian-inference approach in the context of estimating the dipole coupling strength in matter-field interactions. In particular, we consider the simplest model of a two-level system interacting…
We present an efficient scheme for accurate electronic structure interpolations based on the systematically improvable optimized atomic orbitals. The atomic orbitals are generated by minimizing the spillage value between the atomic basis…
A new method for Ewald summation in planar/slablike geometry, i.e. systems where periodicity applies in two dimensions and the last dimension is "free" (2P), is presented. We employ a spectral representation in terms of both Fourier series…
Inverse problem or parameter estimation of ordinary differential equations (ODEs), the iterative process of minimizing the mismatch between model-predicted and experimental states by tuning the parameter values within an optimization…
The three most common methods, Ewald, fast multipole (FMM) and the particle-particle particle-mesh (PPPM), used to compute the interactions in many body Coulombic systems are compared for single and multi-processor machines. The Ewald…
We optimize Hockney and Eastwood's Particle-Particle Particle-Mesh (P3M) algorithm to achieve maximal accuracy in the electrostatic energies (instead of forces) in 3D periodic charged systems. To this end we construct an optimal influence…
We develop an empirical Bayes procedure for estimating the cell means in an unbalanced, two-way additive model with fixed effects. We employ a hierarchical model, which reflects exchangeability of the effects within treatment and within…