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We present an algorithm for computing the nonlinear interface dynamics of theMullins-Sekerka model for interfaces that are defined implicitly (e.g. by alevel set function) using integral equations . The computation of the dynamicsinvolves solving Laplace's equation with Dirichlet boundary conditions onmultiply connected and unbounded domains and propagating the interface using anormal velocity obtained from the solution of the PDE at each time step. Ourmethod is based on a simple formulation for implicit interfaces, which rewritesboundary integrals as volume integrals over the entire space. The resultingalgorithm thus inherits the benefits of both level set methods and boundaryintegral methods to simulate the nonlocal front propagation problem withpossible topological changes. We present numerical results in both two andthree dimensions to demonstrate the effectiveness of the algorithm.

An implicit boundary integral method for interfaces evolving by Mullins-Sekerka dynamics