Predicting the behavior of a magnetically confined fusion plasma over long time periods requires methods that can bridge the difference between transport and turbulent time scales. The nonlinear transport solver, Tango, enables simulations of very long times, in particular to steady state, by advancing each process independently with different time step sizes and couples them through a relaxed iteration scheme. We examine the use of Anderson Acceleration (AA) to reduce the total number of coupling iterations required by interfacing Tango with the AA implementation, including several extensions to AA, provided by the KINSOL nonlinear solver package in SUNDIALS. The ability to easily enable and adjust algorithmic options through KINSOL allows for rapid experimentation to evaluate different approaches with minimal effort. Additionally, we leverage the GPTune library to automate the optimization of algorithmic parameters within KINSOL. We show that AA can enable faster convergence in stiff and very stiff tests cases without noise present and in all cases, including with noisy fluxes, increases robustness and reduces sensitivity to the choice of relaxation strength.

翻译：预测磁约束聚变等离子体在长时间尺度上的行为，需要能够弥合输运时间尺度与湍流时间尺度差异的方法。非线性输运求解器Tango通过以不同时间步长独立推进每个物理过程，并通过一种松弛迭代方案将它们耦合起来，从而能够模拟极长时间，特别是达到稳态的过程。我们研究了利用安德森加速（AA）来减少所需耦合迭代总次数的方法，具体通过将Tango与SUNDIALS中KINSOL非线性求解器包所提供的AA实现（包括对AA的若干扩展）进行接口来实现。通过KINSOL能够轻松启用和调整算法选项，这允许我们以最小的努力进行快速实验，以评估不同的方法。此外，我们利用GPTune库来自动优化KINSOL内的算法参数。我们证明，在没有噪声存在的刚性和强刚性测试案例中，AA能够实现更快的收敛；并且在所有情况下（包括存在噪声通量的情况），AA都增强了鲁棒性并降低了对松弛强度选择的敏感性。