# A smooth particle mesh Ewald method

@article{Essmann1995ASP, title={A smooth particle mesh Ewald method}, author={Ulrich Essmann and Lalith E. Perera and Max L. Berkowitz and Thomas A. Darden and Hsing-Chou Lee and Lee G. Pedersen}, journal={Journal of Chemical Physics}, year={1995}, volume={103}, pages={8577-8593} }

The previously developed particle mesh Ewald method is reformulated in terms of efficient B‐spline interpolation of the structure factors. This reformulation allows a natural extension of the method to potentials of the form 1/rp with p≥1. Furthermore, efficient calculation of the virial tensor follows. Use of B‐splines in place of Lagrange interpolation leads to analytic gradients as well as a significant improvement in the accuracy. We demonstrate that arbitrary accuracy can be achieved…

## 15,261 Citations

### On mesh-based Ewald methods: optimal parameters for two differentiation schemes.

- PhysicsThe Journal of chemical physics
- 2008

The particle-particle particle-mesh Ewald method for the treatment of long-range electrostatics under periodic boundary conditions is reviewed. The optimal Green's function for exact (real-space…

### Optimizing working parameters of the smooth particle mesh Ewald algorithm in terms of accuracy and efficiency.

- Computer ScienceThe Journal of chemical physics
- 2010

It is demonstrated that it is possible to straightforwardly and precisely determine the SPME parameters via the error estimates prior to the simulation for a predetermined accuracy, which can save precious computer and user time and allows an easy choice of a suitable parameter set for nearly optimal speed.

### Multiple Staggered Mesh Ewald: Boosting the Accuracy of the Smooth Particle Mesh Ewald Method.

- Computer ScienceJournal of chemical theory and computation
- 2016

This work develops the multiple staggered mesh Ewald (MSME) method, which averages the SPME forces computed on, for example, M, staggered meshes, and proves, from a theoretical perspective, that the MSME is as accurate as the S PME, but uses M2 times less mesh points in a certain parameter range.

### On the Numerical Accuracy of Ewald, Smooth Particle Mesh Ewald, and Staggered Mesh Ewald Methods for Correlated Molecular Systems.

- Computer ScienceJournal of chemical theory and computation
- 2012

In this work, we develop the accurate error estimates for three state-of-art algorithms of long-range electrostatic interaction in inhomogeneous and correlated molecular systems. They are the Ewald…

### Kaiser-Bessel basis for particle-mesh interpolation.

- PhysicsPhysical review. E
- 2017

A reliable a priori error estimate is developed to measure the accuracy of the force computation in correlated charge systems, and is shown to be effective in optimizing the shape parameter of the Kaiser-Bessel basis in terms of accuracy.

### HOW TO MESH UP EWALD SUMS. II. AN ACCURATE ERROR ESTIMATE FOR THE PARTICLE-PARTICLE-PARTICLE-MESH ALGORITHM

- Computer Science
- 1998

An accurate estimate for the root mean square force error of the P3M algorithm is constructed by extending a single particle pair error measure which has been given by Hockney and Eastwood and an easy to use analytic approximation to the error formula is derived.

### A Finite Element Based P3M Method for N-Body Problems

- Computer ScienceSIAM J. Sci. Comput.
- 2016

A fast mesh-based method for computing N-body interactions that is both scalable and accurate and employs specially designed polynomial bases to construct the screened potentials.

### The optimal particle-mesh interpolation basis.

- Computer ScienceThe Journal of chemical physics
- 2017

It is demonstrated that the general optimal basis is always more accurate than the B-spline basis in the investigated parameter range, while the computational cost is at most 5% more expensive.

### The optimal P3M algorithm for computing electrostatic energies in periodic systems.

- PhysicsThe Journal of chemical physics
- 2008

An optimal influence function is constructed that minimizes the root-mean-square errors of the energies of the particle-particle particle-mesh algorithm and allows an easy and precise determination of the optimal values of the various parameters in the algorithm.

### Staggered Mesh Ewald: An extension of the Smooth Particle-Mesh Ewald method adding great versatility.

- PhysicsJournal of chemical theory and computation
- 2009

An old technique for improving the accuracy of mesh-based field calculations is drawn on to extend the popular Smooth Particle Mesh Ewald algorithm as the StaggeredMesh Ewald (StME) algorithm, which improves the accuracies of computed forces and reduces the drift in system momentum inherent in the SPME method by averaging the results of two separate reciprocal space calculations.

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