报告题目

后验误差分析在电磁场数值计算中新的应用

New application of a posteriori error estimates in computational electromagnetics

报告摘要

The description of the laws of physics phenomena are usually expressed in system of partial differential equations (PDEs). Unfortunately the exact solutions of these equations can almost never be found. Thus, numerical approaches are developed to find their approximate solutions. During the numerical resolution of these PDEs, major computational challenge in nowadays is how to make an efficient use of computational resources (GPU, CPU...) with a reliable outcome. Although this has been an important subject of numerical analysis and scientific computing for decades, still, surprisingly, often more than 90% of the CPU time in numerical simulations is literally wasted and the accuracy of the final outcome is not guaranteed. As an example, in the finite element computation, the total numerical error is the sum of discretization error and algebraic error. When the mesh is constructed, the discretization error cannot be improved, so it is interesting to avoid a large number of iterations in algebraic solver which leads a too small algebraic error. Recently, a stopping criteria based on a posteriori estimate is developed for nonlinear diffusion PDEs in a general framework [1]. With a posteriori estimate, we can distinguish different error components in the numerical resolution, namely the discretization error, algebraic error, and possibly linearization error. This result is extended to the linear Stokes problems, and applied to any iterative solver [2]. In this work, we develop this strategy to the potential formulations in the magnetostatic problems. Implementation into the FreeFem++ programming language is invoked. An academic example is provided to illustrate the performance of our adaptive stopping criteria.

[1] A. Ern, M. Vohralk, “Adaptive inexact Newton methods with a posteriori stopping criteria for nonlinear diffusion PDEs”, SIAM J. Sci. Comput. Vol. 35, no. 4, pp. A1761A1791, 2013.

[2] M. Cermak, F. Hecht, Z. Tang and M. Vohralik, “Adaptive inexact iterative algorithms based on polynomial-degree-robust a posteriori estimates for the Stokes problem”, <hal-01097662v1>, 2014.

报告时间、地点

2017年4月18日上午10:00~11:30 电气学院院北会议室

报告人简历

唐祖祁(Zuqi Tang), 1984年生，博士，法国国家科学研究中心（CNRS）助理研究员。

2003年9月至2007年6月就读于武汉大学数学基地班专业，同年留学法国，于2009年获得法国里尔科技大学(L'Université de Lille, Sciences et Technologies)应用数学专业硕士，于2012年取得法国里尔科技大学电气工程/应用数学方向的博士学位，同年获得国家留学基金委员会（CSC）颁发的国家优秀留学生奖学金。随后先后于2012-2013年在法国电力（EDF）以及2013-2015年在法国国家信息与自动化研究所（INRIA Paris--Rocquencourt）从事博士后研究，从2015年开始加入CNRS，在中央理工-高等电力学院(centrale-supélec)下的GeePs(Group of electrical engineering, Paris)实验室工作。

主要从事电磁场的计算，误差分析，以及多物理耦合相关问题的建模仿真。从事开发法国电力（EDF）自主研发的3D有限元软件CARMEL3D以及建模平台SALOME.目前已经发表论文30多篇，其中SCI收录的论文15篇,会议特邀报告论文2篇。