求解Helmholtz方程的非重叠最优Schwarz交替法

Optimized Schwarz Alternating Algorithms Without Overlap for the Helmholtz Equation

讨论求解Helmholtz方程的广义Schwarz交替法,通过调节传输条件中的参数可得到有限步收敛的最优Schwarz交替法。然而,由于这些传输条件是全局相关的,在实际计算中不易实现。对传输条件进行了局部估计,得到近似最优的非重叠Schwarz交替法。

The optimized Schwarz alternating algorithms without overlap for the Helmhohz equation are studied. Optimal transmission conditions are derived which lead to convergence of the algorithms in a finite steps. These conditions are, however, nonlocal and are not applicable in practice. A local approximation is introduced to lead to a class of optimized Schwarz algorithms.