论文标题
非平滑罚款精确罚款二阶方法不可压缩的宾汉流
Nonsmooth Exact Penalization Second-order Methods for incompressible Bingham flows
论文作者
论文摘要
我们认为，根据$ l^1 $ norm的速度场的不可压缩条件$ DIV（U）= 0 $的确切惩罚。这种惩罚过程导致非平滑优化问题，我们使用通用的二阶信息提出了算法。我们的方法通过考虑最陡峭的下降方向和与非平滑术语相关的额外概括的二阶信息来解决所得的非平滑问题。该方法具有一个优点，即通过该方法提出的下降方向强制执行无差异属性，而无需建立无差异近似方案。我们的讨论和比较也考虑了由$ l^2 $ norm给出的不精确惩罚方法。
We consider the exact penalization of the incompressibility condition $div(u)=0$ for the velocity field of a Bingham fluid in terms of the $L^1$-norm. This penalization procedure results in a nonsmooth optimization problem for which we propose an algorithm using generalized second-order information. Our method solves the resulting nonsmooth problem by considering the steepest descent direction and extra generalized second-order information associated to the nonsmooth term. This method has the advantage that the divergence-free property is enforced by the descent direction proposed by the method without the need of build-in divergence-free approximation schemes. The inexact penalization approach, given by the $L^2$-norm, is also considered in our discussion and comparison.
