论文标题
在PDE受限优化中，Hessian的代数多移民预处理
Algebraic multigrid preconditioning of the Hessian in PDE-constrained optimization
论文作者
论文摘要
我们为基于代数的多机（AMG）的预处理构建了一个线性季度优化问题，该问题受椭圆形偏微分方程约束的线性优化问题。虽然预处理程序概括了在早期作品中引入的几何多机预处理，但其构造完全依赖于用于求解前向椭圆方程的标准AMG基础架构，从而可以使用各种AMG方法和标准软件包来实现它。我们的分析在预处理的质量与所使用的AMG方法之间建立了明显的联系。提出的策略对非结构性网格，复杂几何形状和变化系数的问题具有广泛而强大的适用性。该方法是使用Hypre软件包实现的，并提供了几个数值示例。
We construct an algebraic multigrid (AMG) based preconditioner for the reduced Hessian of a linear-quadratic optimization problem constrained by an elliptic partial differential equation. While the preconditioner generalizes a geometric multigrid preconditioner introduced in earlier works, its construction relies entirely on a standard AMG infrastructure built for solving the forward elliptic equation, thus allowing for it to be implemented using a variety of AMG methods and standard packages. Our analysis establishes a clear connection between the quality of the preconditioner and the AMG method used. The proposed strategy has a broad and robust applicability to problems with unstructured grids, complex geometry, and varying coefficients. The method is implemented using the Hypre package and several numerical examples are presented.
