Beijing Institute of Mathematical Sciences and Applications

Jie Du , Computational & Applied Mathematics Group , Hui Yu

Xufeng Xiao

Tuesday, December 14, 2021 2:00 PM - 3:00 PM

清华大学理科楼A404

Tencent 963 275 474 ()

In this talk, a new numerical computational frame is presented for solving moving interface problems modeled by parabolic PDEs on surfaces. The surface PDEs can have Dirac delta source distributions and discontinuous coefficients. One application is for thermally driven moving interfaces on surfaces such as Stefan problems and dendritic solidification phenomena on solid surfaces. One novelty of the new method is the local tangential lifting method to construct discrete delta functions on surfaces. The idea of the local tangential lifting method is to transform a local surface problem to a local two dimensional one on the tangent planes of surfaces at some selected surface nodes. Moreover, a surface version of the front tracking method is developed to track moving interfaces on surfaces. Strategies have been developed for computing geodesic curvatures of interfaces on surfaces. Various numerical examples are presented to demonstrate the effectiveness of the new methods.

In this talk, a new numerical computational frame is presented for solving moving interface problems modeled by parabolic PDEs on surfaces. The surface PDEs can have Dirac delta source distributions and discontinuous coefficients. One application is for thermally driven moving interfaces on surfaces such as Stefan problems and dendritic solidification phenomena on solid surfaces. One novelty of the new method is the local tangential lifting method to construct discrete delta functions on surfaces. The idea of the local tangential lifting method is to transform a local surface problem to a local two dimensional one on the tangent planes of surfaces at some selected surface nodes. Moreover, a surface version of the front tracking method is developed to track moving interfaces on surfaces. Strategies have been developed for computing geodesic curvatures of interfaces on surfaces. Various numerical examples are presented to demonstrate the effectiveness of the new methods.