论文标题
平行不推行的牛顿 - 克里洛夫和准牛顿求解器，用于非线性弹性
Parallel inexact Newton-Krylov and quasi-Newton solvers for nonlinear elasticity
论文作者
论文摘要
在这项工作中，我们介绍了不精确的牛顿 - 克莱洛夫和准牛顿算法的实现和性能，更具体地说是BFGS方法，用于解决非线性弹性方程的解决方案，并将它们与标准的牛顿 - 凯里洛夫方法进行比较。这是通过对求解器的性能相对于问题大小，数据的大小以及几乎不可压缩和不可压缩力学的处理器数量进行的系统分析来完成的。我们考虑三个测试用例：库克的膜（静态，几乎不可压缩），扭曲测试（静态，不可压缩）和心脏模型（复杂的材料，相关，几乎不可压缩）。我们的结果表明，对于可压缩的力学，应优选准牛顿的方法，而对于不可压缩的问题，应首选牛顿 - 克里洛夫的不切实方法。我们表明，这些主张也得到了方法的收敛分析。无论如何，所有方法都表现出足够的性能，并对标准的牛顿 - 克里洛夫方法提供了显着的加速性，在最佳情况下，CPU时间的缩短超过50％。
In this work, we address the implementation and performance of inexact Newton-Krylov and quasi-Newton algorithms, more specifically the BFGS method, for the solution of the nonlinear elasticity equations, and compare them to a standard Newton-Krylov method. This is done through a systematic analysis of the performance of the solvers with respect to the problem size, the magnitude of the data and the number of processors in both almost incompressible and incompressible mechanics. We consider three test cases: Cook's membrane (static, almost incompressible), a twist test (static, incompressible) and a cardiac model (complex material, time dependent, almost incompressible). Our results suggest that quasi-Newton methods should be preferred for compressible mechanics, whereas inexact Newton-Krylov methods should be preferred for incompressible problems. We show that these claims are also backed up by the convergence analysis of the methods. In any case, all methods present adequate performance, and provide a significant speed-up over the standard Newton-Krylov method, with a CPU time reduction exceeding 50% in the best cases.
