演講者：清華大學數學系朱家杰教授

時間：2022年4月12日 下午1點10分

地點：校本部第二綜合大樓8樓 A813 教室

標題：
A numerical method for solving partial differential equations on surfaces

摘要：
Partial differential equations on surfaces have wild applications in
many areas, such as material science, surfactant problems, image
processing and biology. These PDEs usually originate from minimizing
energy functions defined on surfaces.  This work targets applications
that use implicit or non-parametric representations of closed surfaces
or curves and require numerical solution for minimization problems
defined on the surfaces.

In this talk, I will show that the energy function defined on surfaces
can be extended to the energy function defined on the nearby tubular
neighborhood that gives the same energy when input the
constant-along-normal extension. Furthermore, the extended energy
function gives the same minimizer as which the original energy function
gives in the sense of restriction on the surface. This new approach
connects the original energy function to an extended energy function and
provides a good framework to solve PEDs numerically on Cartesian grids.
We demonstrate that our method can be applied successfully on the
TV-denoising and obstacle problems defined on surfaces. Recently a small
progress for mean curvature flow will be introduced as well.