chunkIE: a MATLAB integral equation toolbox

A MATLAB package for prototyping integral equation methods in two dimensions. While chunkie is primarily intended as a proto-typing or pedagogical tool, it is designed to be reasonably efficient and has been used to produce research-grade results.

At-a-glance:

given a parametrization of a curve, chunkIE will return a "chunker" object which stores the description of the curve into a panel-based format (the curve is discretized into chunks such that on each chunk a Legendre interpolant in parameter space is accurate to some prescribed accuracy).
chunkIE has routines for setting up system matrices corresponding to logarithmically singular and principal value type integral equation kernels defined on a chunker
chunkIE is designed to inter-operate with Ken Ho's fast linear algebra in MATLAB package (FLAM)
chunkIE includes various routines for evaluating layer potentials and functions defined on chunkers
chunkIE applies a version of Johan Helsing's recursively compressed inverse preconditioning (RCIP) scheme for effectively treating problems with corners and multiple junctions.

Detailed documentation is being built here

Installing chunkIE

For other install options, see the documentation.

To compile from git, clone the repository with the submodules

git clone --recurse-submodules https://github.com/fastalgorithms/chunkie.git

and run startup.m in the install directory. This will download the FLAM and fmm2d submodules, include FLAM in the matlab path, and generate the fmm2d mex file if a fortran compiler exists.

For troubleshooting suggestions, see the documentation

Using chunkIE

Check out the chunkie/demo folder or the guide (under construction)

License

chunkIE proper (the contents of the chunkie folder) is available under the terms of the BSD 3-clause license, which should have been included in the distribution (see chunkie/LICENSE.md)

chunkIE team

chunkIE has benefitted from the contributions of several developers: Travis Askham, Manas Rachh, Michael O'Neil, Jeremy Hoskins, Dan Fortunato, Shidong Jiang, Fredrik Fryklund, Hai Yang Wang, Hai Zhu, and Tristan Goodwill.

James Bremer and Zydrunas Gimbutas provided generalized Gaussian quadrature rules (chunkie/+chnk/+quadggq)

Many routines were modelled after parts of the legeexps.f library (Copyright Vladimir Rokhlin, Free BSD 3-clause), FMMLIB2D (Copyright Leslie Greengard and Zydrunas Gimbutas, Free BSD 3-clause), and Johan Helsing's RCIP tutorial

Citing this software

If you found this software useful, we ask that you please cite the following works

{This software} see CITATIONS.cff for details
{The fast multipole method library} https://github.com/flatironinstitute/fmm2d
{The fast direct solver library} Ho, Kenneth L. "FLAM: Fast linear algebra in MATLAB-Algorithms for hierarchical matrices." Journal of Open Source Software 5.51 (2020): 1906.
{Quadrature generation routines} Bremer, James, Zydrunas Gimbutas, and Vladimir Rokhlin. "A nonlinear optimization procedure for generalized Gaussian quadratures." SIAM Journal on Scientific Computing 32.4 (2010): 1761-1788.
{Corner and multiple junction handling} Helsing, Johan. "Solving integral equations on piecewise smooth boundaries using the RCIP method: a tutorial." Abstract and applied analysis. Vol. 2013. Hindawi, 2013.
{Fast multipole method paper} Greengard, Leslie, and Vladimir Rokhlin. "A fast algorithm for particle simulations." Journal of computational physics 73.2 (1987): 325-348.

Contributing

Contributions are welcome. See the issues tab or create a new issue if there is something you're interested in bringing to chunkIE. See the wiki for more on the developer process.

fastalgorithms / chunkie