首页> 外文期刊>International Journal of Heat and Mass Transfer >The multiple-scale polynomial Trefftz method for solving inverse heat conduction problems
【24h】

The multiple-scale polynomial Trefftz method for solving inverse heat conduction problems

机译:求解导热反问题的多项式多项式Trefftz方法

获取原文
获取原文并翻译 | 示例
           

摘要

The polynomial Trefftz method consists of the polynomial type solutions as bases, providing a cheap boundary-type meshless method to solve the heat conduction equation, since the bases automatically satisfy the governing equation. In order to stably solve the backward heat conduction problem (BHCP), and the inverse heat source problem (IHSP) together with the boundary condition recovery problem by a polynomial Trefftz method, which are both known to be highly ill-posed, we introduce a multiple-scale post-conditioner in the resultant linear system to reduce the condition number. Then the conjugate gradient method (CGM) is used to solve the post-conditioned linear system to determine the unknown expansion coefficients. In the multiple-scale polynomial Trefftz method (MSPTM) the scales are determined a priori by the collocation points on space-time boundary, which can retrieve the missing initial data, the unknown time-dependent heat source as well as the boundary condition rather well. Several numerical examples of the inverse heat conduction problems demonstrate that the MSPTM is effective and accurate, even for those of severely ill-posed inverse problems under very large noises.
机译:多项式Trefftz方法由多项式类型的解作为基础,提供了一种廉价的边界型无网格方法来求解热传导方程,因为这些基础自动满足控制方程式。为了稳定地解决众所周知的病态严重的多项式Trefftz方法的反向导热问题(BHCP)和逆热源问题(IHSP)以及边界条件恢复问题,我们引入了结果线性系统中的多尺度后置调节器,以减少条件数。然后使用共轭梯度法(CGM)求解后置条件线性系统,以确定未知的膨胀系数。在多尺度多项式Trefftz方法(MSPTM)中,尺度是由时空边界上的搭配点先验确定的,它可以检索丢失的初始数据,未知的时间相关热源以及边界条件。逆热传导问题的几个数值示例表明,即使对于在非常大的噪声下严重不适的逆问题,MSPTM也是有效且准确的。

著录项

相似文献

  • 外文文献
  • 中文文献
  • 专利
获取原文

客服邮箱:kefu@zhangqiaokeyan.com

京公网安备:11010802029741号 ICP备案号:京ICP备15016152号-6 六维联合信息科技 (北京) 有限公司©版权所有
  • 客服微信

  • 服务号