论文标题
糖果包装器问题 - PDE/PDE系统的时间多尺度方法
The candy wrapper problem -- a temporal multiscale approach for pde/pde systems
论文作者
论文摘要
我们描述了一种时间多尺度方法，用于模拟具有涉及部分微分方程的短期影响的长期过程。所考虑的具体问题是血管中的生长过程。 \ emph {糖果包装工艺}描述了血管中的再狭窄，以前通过插入支架可以扩大。新狭窄的发展是在长期（几个月）的长时间内发生的，而表演力主要是由脉动血流给出的。我们描述了一个耦合的PDE模型和有限元仿真，该模拟被用作我们的多尺度方法的基础，该模型基于平均长度方程并通过局部周期性及时问题来近似快速尺度影响。原型3D配置中的数值测试用例证明了该方法的功能。
We describe a temporal multiscale approach for the simulation of long-term processes with short-term influences involving partial differential equations. The specific problem under consideration is a growth process in blood vessels. The \emph{Candy Wrapper Process} describes a restenosis in a vessel that has previously be widened by inserting a stent. The development of a new stenosis takes place on a long time horizon (months) while the acting forces are mainly given by the pulsating blood flow. We describe a coupled pde model and a finite element simulation that is used as basis for our multiscale approach, which is based on averaging the long scale equation and approximating the fast scale impact by localized periodic-in-time problems. Numerical test cases in prototypical 3d configurations demonstrate the power of the approach.
