论文标题
有效解决3D弹性问题的解决方案，具有平滑的聚合代数多机和块算术的解决方案
Efficient solution of 3D elasticity problems with smoothed aggregation algebraic multigrid and block arithmetics
论文作者
论文摘要
3D弹性问题的有效解决方案是许多工业和科学应用的重要组成部分。使用刚体模式进行暂定延长操作员构造的平滑聚合代数多机构建是一种有效且可靠的选择，用于解决弹性方程离散化引起的线性系统的解决方案。多机层次结构的每个级别上的系统矩阵都具有块结构，因此使用块表示和块算术应该显着提高求解器效率。但是，暂定延长操作员的构建只能使用标量表示。本文提出了几种实用方法，以实现基于开源AMGCL库的块算术和平滑的聚合代数多机。这是在两个现实世界模型问题的示例中显示的，建议的改进可能会使解决方案加快50％的速度，并将预处理器的内存要求降低30％。实施很简单，仅需要最少的代码。
Efficient solution of 3D elasticity problems is an important part of many industrial and scientific applications. Smoothed aggregation algebraic multigrid using rigid body modes for the tentative prolongation operator construction is an efficient and robust choice for the solution of linear systems arising from the discretization of elasticity equations. The system matrices on every level of the multigrid hierarchy have block structure, so using block representation and block arithmetics should significantly improve the solver efficiency. However, the tentative prolongation operator construction may only be done using scalar representation. The paper proposes a couple of practical approaches for enabling the use of block arithmetics with smoothed aggregation algebraic multigrid based on the open-source AMGCL library. It is shown on the example of two real-world model problems that the suggested improvements may speed up the solution by 50% and reduce the memory requirements for the preconditioner by 30%. The implementation is straightforward and only requires a minimal amount of code.
