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 have now released Version 1.0.

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 material is based upon work supported by the National Science Foundation under grant DMS-0811005 and Engineering and Physical Sciences Research Council Grant EP/F06795X/1.

Below is an example image showing scattering from a square, accurate to 10 digits, computed in a few seconds. 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.