论文标题
非线性求解器加速自然对流问题
Acceleration of nonlinear solvers for natural convection problems
论文作者
论文摘要
本文使用应用于PICARD迭代的Anderson加速度的非等温流量的稳定的非等热流动模型开发了一种有效且可靠的解决方案技术。在分析了与非线性迭代相关的固定点算子以证明某些稳定性和规则性属性的成立之后，我们应用了作者最近构建的安德森加速度理论，这为Anderson加速的PICARD迭代而言，BousSinesQ系统会产生收敛的结果。结果表明，优化问题的增益可以提高残差中的前学期，但以额外的高阶项为代价，当残留物较大时可能很重要。我们执行说明理论的数值测试，并表明安德森深度的2阶段选择可能是有利的。我们还考虑将安德森的加速器应用于牛顿迭代的布斯辛克方程，并观察到加速度使牛顿迭代能够收敛，即使有标准的线路搜索，也可以在没有加速度的情况下明显更高的雷利数字。
This paper develops an efficient and robust solution technique for the steady Boussinesq model of non-isothermal flow using Anderson acceleration applied to a Picard iteration. After analyzing the fixed point operator associated with the nonlinear iteration to prove that certain stability and regularity properties hold, we apply the authors' recently constructed theory for Anderson acceleration, which yields a convergence result for the Anderson accelerated Picard iteration for the Boussinesq system. The result shows that the leading term in the residual is improved by the gain in the optimization problem, but at the cost of additional higher order terms that can be significant when the residual is large. We perform numerical tests that illustrate the theory, and show that a 2-stage choice of Anderson depth can be advantageous. We also consider Anderson acceleration applied to the Newton iteration for the Boussinesq equations, and observe that the acceleration allows the Newton iteration to converge for significantly higher Rayleigh numbers that it could without acceleration, even with a standard line search.
