報告人: Tao Lin（Department of Mathematics, Virginia Tech）
報告時間：2016年6月23日（星期四）下午4:30-6:30
地點：明理樓B203
報告人簡介：林濤，弗吉尼亞理工大學(xué)教授、博士生導(dǎo)師。林教授1982年獲得四川大學(xué)學(xué)士學(xué)位，1985年在中科院獲得碩士學(xué)位，隨后在美國懷俄明大學(xué)師從Richard Ewing攻讀博士學(xué)位，并于1990年獲得博士學(xué)位。2001年獲得弗吉尼亞理工大學(xué)正教授職位。林教授的研究工作集中在有限元方法進行微分方程、微分積分方程大規(guī)模數(shù)值模擬，是浸入式有限元的提出者和代表人物。浸入式有限元是計算流體領(lǐng)域應(yīng)用廣泛的數(shù)值計算方法。目前，他在該領(lǐng)域出版著作1本，發(fā)表研究性論文100多篇。
Abstract: Interface problems often appear in numerical simulations over domains consisting of multiple materials leading to discontinuous coefficients in the involved partial differential equations whose solutions are inevitably less smooth around the material interfaces. Traditional finite element (FE) methods handle challenges from this deficiency of global regularity by using body-fitting meshes in which each element essentially contains one of the materials; otherwise, their convergence cannot be guaranteed. This presentation will start from a few examples to show that unstructured body-fitting meshes can hinder efficient applications of FE methods in some applications, and this motivates the need for developing FE methods based on structured or Cartesian meshes for interface problems. After surveying related FE methods, the presentation will focus on the recently developed immersed finite element (IFE) methods that can utilize interface-independent, such as structured or Cartesian, meshes even for interfaces with non-trivial geometries. Fundamental mathematical properties of IFE methods and some essential differences between FE and IFE methods will be highlighted. A few application examples will be presented to illustrate features of IFE methods. The presentation will conclude with a few research topics in IFE methods.
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主辦單位：西南石油大學(xué)科研處理學(xué)院
