论文标题
按域分解方法基于PML传输条件的域分解方法解决方案解决方案
Solution of time-harmonic Maxwell's equations by a domain decomposition method based on PML transmission conditions
论文作者
论文摘要
大规模麦克斯韦方程式的数值离散化导致了一个不良条件的线性系统，该系统难以解决。该线性系统连续解决方案的关键要求是选择有效的求解器。在这项工作中，我们使用完美匹配的层（PML）来提高此效率。由于提高了溶液的准确性而不是使用吸收边界条件（ABC），因此PML已被广泛用于截断波方程的数值模拟。在这里，我们将通过在我们的域分解方法中的子域之间的接口上提供将PML作为传输条件的替代用途来开发有效的求解器。与选择吸收边界条件作为传输条件相比，我们解决了麦克斯韦方程并评估解决方案的收敛速率。
Numerical discretization of the large-scale Maxwell's equations leads to an ill-conditioned linear system that is challenging to solve. The key requirement for successive solutions of this linear system is to choose an efficient solver. In this work we use Perfectly Matched Layers (PML) to increase this efficiency. PML have been widely used to truncate numerical simulations of wave equations due to improving the accuracy of the solution instead of using absorbing boundary conditions (ABCs). Here, we will develop an efficient solver by providing an alternative use of PML as transmission conditions at the interfaces between subdomains in our domain decomposition method. We solve Maxwell's equations and assess the convergence rate of our solutions compared to the situation where absorbing boundary conditions are chosen as transmission conditions.
