An implicit boundary integral method for interfaces evolving by Mullins-Sekerka dynamics
An implicit boundary integral method for interfaces evolving by Mullins-Sekerka dynamics
复制标题
Mullins-Sekerka动力学演化界面的隐式边界积分方法
DOI：
10.1007/978-3-319-66764-5_1
复制
发表时间：
2015
期刊：
影响因子：
--
通讯作者：
R. Tsai
中科院分区：
文献类型：
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作者：
Chieh;Catherine Kublik;R. Tsai
我们提出了一种算法，用于计算的非线性界面动力学的Mullins-Sekerka模型的接口隐式定义（例如由水平集函数）使用积分方程。动力学的计算涉及求解拉普拉斯方程的Dirichlet边界条件的多连通和无界域和传播的接口使用的正常速度从解的PDE在每个时间步。我们的方法是基于一个简单的配方隐式接口，重写边界积分的体积积分在整个空间。由此产生的算法，从而继承了水平集方法和边界积分方法来模拟可能的拓扑变化的非局部前传播问题的好处。我们提出了二维和三维的数值结果来证明该算法的有效性。
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.