The Explicit Jump Immersed Interface method is a powerful tool to
solve elliptic pde with singular source terms, in complex domains,
or with discontinuous coefficients. Examples include 2d Poisson
problems, 2d and 3d linear elasticity and 2d Stokes to name a few.
The power of the EJIIM lies in the fact that not grid generation is
needed. EJIIM works on a uniform Cartesian grid and uses
additionally some information about the boundary or interface
location such as intersections with grid lines, normals and
curvatures at these points, etc. On the other hand, the
implementation of the EJIIM is rather involved. To make it easier to
overcome the initial hurdle of using it, we provide matlab code and
this documentation that contains detailed explanations of this code
for two dimensional Poisson boundary value problems. We have tried
to keep the notation as close to the sources as possible. For
details of the method see [
4,
5,
1]