Anderson Acceleration of Nonlinear Solvers for the Stationary Gross-Pitaevskii Equation
Anderson Acceleration of Nonlinear Solvers for the Stationary Gross-Pitaevskii Equation
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DOI：
10.4208/aamm.oa-2020-0270
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发表时间：
2021-06
影响因子：
1.4
通讯作者：
global sci
中科院分区：
文献类型：
--
作者：
global sci
。我们考虑将安德森加速度 (AA) 应用于稳态 Gross-Pitaevskii 方程的两个非线性求解器：Picard 型非线性迭代求解器和归一化梯度流方法。我们将求解器表述为不动点问题，并表明它们都适合最近开发的 AA 分析框架。这使我们能够证明，两种方法的线性收敛速度都比 AA 优化问题在每一步的增益提高了一个因子（小于一）。寻找一维和二维基态解的数值测试表明，AA 显着改善了两个求解器的收敛行为，此外还对两个求解器进行了一些比较。还提供了两种方法的局部收敛分析。
. We consider Anderson acceleration (AA) applied to two nonlinear solvers for the stationary Gross-Pitaevskii equation: a Picard type nonlinear iterative solver and a normalized gradient flow method. We formulate the solvers as fixed point problems and show that they both fit into the recently developed AA analysis framework. This allows us to prove that both methods’ linear convergence rates are improved by a factor (less than one) from the gain of the AA optimization problem at each step. Numerical tests for finding ground state solutions in 1D and 2D show that AA signifi-cantly improves convergence behavior in both solvers, and additionally some comparisons between the solvers are drawn. A local convergence analysis for both methods are also provided.