MPSpack is a user-friendly and fully object-oriented MATLAB toolbox that implements the method of particular solutions, nonpolynomial FEM, and related boundary methods (e.g. fundamental solutions, layer potentials) for efficient and highly accurate solution of Laplace eigenvalue problems, interior/exterior Helmholtz boundary-value problems (e.g. wave scattering), and related PDE problems, on piecewise-homogeneous 2D domains.

We released Version 1.0 in September 2009. As of June 2010, the current Version 1.1 beta includes new methods for quasi-periodic (grating) scattering.

Please see the Downloads page for a gzipped tar archive of the package, the manual which has installation instructions, and the all-important tutorial. See the Source page for how to download via svn (subversion); this gives access to the current development version, including e.g. a Dirichlet eigenmode solver.

This material is based upon work supported by the National Science Foundation under grant DMS-0811005, and Engineering and Physical Sciences Research Council Grant EP/H00409/1.

First is an example showing scattering from a square, accurate to 10 digits, computed in a few seconds on a laptop. Spectral convergence is achieved using the following ingredients: decomposition into subdomains (nonpolynomial FEM), fractional-order Fourier-Bessel expansions around corner singularities, and an exterior fundamental solutions representation. With MPSpack this needs no more than 20 lines of code.

Next is an example showing the first 45 Dirichlet eigenmodes of a smooth planar domain, computed to 12 digit accuracy and evaluated on a grid of 3600 points, in around 1 second per mode. Convergence is again spectral, using layer potential representations, and analytic root-finding on a Fredholm determinant. With MPSpack the code is 9 lines long.