Boundary Integral Equations: tutorials and resources

Alex Barnett

Boundary integral equations (BIEs) are a wonderfully efficient way to solve PDE boundary value problems (BVPs) or eigenvalue problems (EVPs) with constant (or piecewise-constant) coefficients. This includes elliptic PDE such as the Laplace, Helmholtz, Maxwell, and Stokes equations. Much of my recent research is on better ways to do this. Here are some resources on theory and numerical methods.

Mathematical theory resources

Numerical methods and resources for coding schemes yourself

Established numerical methods:

More advanced numerical methods and research for BVPs:

Methods specific to eigenvalue problems:

Software packages

This list is necessarily incomplete, and skewed to my own interests and community.

This work was enabled in part by NSF grant DMS-1216656.