This paper presents the design and development of an Anderson Accelerated Preconditioned Modified Hermitian and Skew-Hermitian Splitting (AA-PMHSS) method for solving complex-symmetric linear systems with application to electromagnetics problems, such as wave scattering and eddy currents. While it has been shown that the Anderson Acceleration of real linear systems is essentially equivalent to GMRES, we show here that the formulation using Anderson acceleration leads to a more performant method. We show relatively good robustness compared to existing preconditioned GMRES methods and significantly better performance due to the faster evaluation of the preconditioner. In particular, AA-PMHSS can be applied to solve problems and equations arising from electromagnetics, such as time-harmonic eddy current simulations discretized with the Finite Element Method. We also evaluate three test systems present in previous literature. We show that the method is competitive with two types of preconditioned GMRES. One of the significant advantages of these methods is that the convergence rate is independent of the discretization size.

翻译：本文提出并开发了一种安德森加速预条件修正埃尔米特与斜埃尔米特分裂（AA-PMHSS）方法，用于求解复对称线性系统，并应用于电磁学问题（如波散射和涡流）。虽然已有研究表明，实线性系统的安德森加速本质上等价于GMRES方法，但我们在此证明，基于安德森加速的公式化方法能够带来更优的性能表现。相较于现有预条件GMRES方法，该方法展现出较好的鲁棒性，并因预条件子求值速度更快而显著提升性能。特别地，AA-PMHSS可应用于求解电磁学中的问题与方程，例如采用有限元法离散的时谐涡流模拟。我们还评估了既往文献中的三个测试系统，结果表明该方法与两类预条件GMRES方法具有竞争力。该方法的重要优势之一在于其收敛速度与离散化尺寸无关。