论文标题
通用AMG加速嵌入式边界方法，没有小细胞刚度
Universal AMG Accelerated Embedded Boundary Method Without Small Cell Stiffness
论文作者
论文摘要
我们开发了一种普遍适用的嵌入式边界有限差方法，该方法导致对称的正定线性系统，并且不遭受小细胞刚度的困扰。我们的离散化对于具有差点边界条件的波，热和泊松方程是有效的。当需要倒置系统时，我们可以使用共轭梯度方法，该方法通过代数多机技术加速。一系列针对波浪，热量和泊松方程的数值测试以及塑造优化问题的应用，验证了我们方法的准确性，稳定性和效率。我们的快速计算技术可以扩展到移动边界问题（例如Stefan问题），Navier-Stokes方程，以及在具有复杂几何形状和快速模拟的域上提出问题的Grad-Shafranov方程非常重要。
We develop a universally applicable embedded boundary finite difference method, which results in a symmetric positive definite linear system and does not suffer from small cell stiffness. Our discretization is efficient for the wave, heat and Poisson's equation with Dirichlet boundary conditions. When the system needs to be inverted we can use the conjugate gradient method, accelerated by algebraic multigrid techniques. A series of numerical tests for the wave, heat and Poisson's equation and applications to shape optimization problems verify the accuracy, stability, and efficiency of our method. Our fast computational techniques can be extended to moving boundary problems (e.g. Stefan problem), to the Navier-Stokes equations, and to the Grad-Shafranov equations for which problems are posed on domains with complex geometry and fast simulations are very important.
