2016/04/01 by Chieh Chen, Chen, Chieh, Catherine Kublik +3 · 1 citation
Computer Science · Engineering · Mathematics · Physics and Astronomy · #Advanced Mathematical Modeling in Engineering #Algorithm #Boundary (topology) #Computation #Computer science #Dirichlet boundary condition #Dynamics (music) #Electromagnetic Simulation and Numerical Methods #FOS: Mathematics #Function (biology) #Integral equation #Interface (matter) #Laplace transform #Level set (data structures) #Mathematical analysis #Mathematics #Nonlinear system #Numerical Analysis (math.NA) #Physics #Set (abstract data type) #Simple (philosophy) #Theoretical and Computational Physics
paper · pdf · doi:10.48550/arxiv.1604.00285
openalex publication_date 2016/04/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We present an algorithm for computing the nonlinear interface dynamics of the Mullins-Sekerka model for interfaces that are defined implicitly (e.g. by a level set function) using integral equations . The computation of the dynamics involves solving Laplace's equation with Dirichlet boundary conditions on multiply connected and unbounded domains and propagating the interface using a normal velocity obtained from the solution of the PDE at each time step. Our method is based on a simple formulation for implicit interfaces, which rewrites boundary integrals as volume integrals over the entire space. The resulting algorithm thus inherits the benefits of both level set methods and boundary integral methods to simulate the nonlocal front propagation problem with possible topological changes. We present numerical results in both two and three dimensions to demonstrate the effectiveness of the algorithm.