Introduction

The package provides a Matlab implementation of the Spectral Ewald method (SE) for fast Ewald summation related to six different kernels:

  • SE: 3-periodic Laplace (electrostatics)
  • SE2P: 2-periodic Laplace (electrostatics)
  • SE1P: 1-periodic Laplace (electrostatics)
  • SE0P: 0-periodic Laplace-Stokeslet-Stresslet-Rotlet (electrostatics and viscous flow)
  • SE_Stokes: 3-periodic Stokeslet (viscous flow)
  • SE2P_Stokes: 2-periodic Stokeslet (viscous flow)
  • SE_Stresslet: 3-periodic Stresslet (viscous flow)
  • SE_Rotlet: 3-periodic Rotlet (viscous flow)

The aim of this package is to provide fast routines for computing the Fourier space sums for the above kernels. Routines for the real space sums are provided for some kernels.

Most of the computational kernels are written in C, and quite some time has been spent optimizing them using explicit SIMD instructions and OpenMP shared-memory parallelism. The interfacing MEX layer is generally kept thin, so interfacing to another language than Matlab should be quite straightforward.

Building

Most of the C/MEX code is now built with CMake. To build it open a terminal and do

cd build
cmake ..
make

To run the test suite:

make test

Some of the C/MEX code is not yet integrated into CMake, and has to be built using Matlab build script. The build script is then called make.m and is located in the base folder for that kernel.

Getting started

Each directory contains the m-files related to that specific kernel. From any of these directories do

init    % sets up paths

then depending on directory you can do

demo    % Runs demo of spectral convergence + error estimates
        % for both real and Fourier space sums.

or

make             % build C/MEX code for this directory
test_accuracy    % should display plot of spectral convergence

Example (in Matlab):

cd SE_Rotlet
init
demo

Most recent development has focused on 3P Stokes flow, so the directories related to that (SE_Stokes, SE_Rotlet, SE_Stresslet) are more developed.

Code examples for various are kernels can be found by looking at the tests, located in the folder mfile_tests or tests in the folder for the respective kernel.

Testing

Some directories contain a tests folder with unit tests. To run that test suite simply execute

init
run_unit_tests

To run the full suite, go to the root directory and run

run_unit_tests

This is recommended to do after building or before committing changes.

Additional files

The package also contains:

  • util: Common functions
  • SE_fast_gridding: C implementation of fast Gaussian gridding and fast Kaiser gridding
  • SE_direct: C-code for direct Ewald sums for Laplace 2P/3P
  • SE_Stokes_direct: C-code for direct Ewald sums for Stokes 2P/P3
  • SE_leftovers: Spectral Ewald, fast real-space and k=0 codes for Laplace and Stokes. These are unmaintained, but might prove useful.