| Abstract: |
| Boundary integral equation methods are highly efficient tools for solving elliptic boundary value problems on domains with complex geometries. Nonetheless, prefractal and self-similar domains with corners, such as the Koch curve, remain challenging because of corner singularities in the solution. In this talk, we show how state-of-the-art numerical methods can overcome these difficulties, yielding a framework for the efficient solution of discretized boundary value problems that lead to dense linear systems with millions of degrees of freedom. This makes it possible to solve the problem on very fine prefractal approximations and to study the convergence of the resulting numerical solutions in the fractal limit. |
|