報(bào)告人：徐巖 教授
報(bào)告題目：Structure-Preserving Limiters for Time-Implicit Higher Order Accurate Discontinuous Galerkin Discretizations
報(bào)告時(shí)間：2026年4月23日（周四）下午4：30
報(bào)告地點(diǎn)：云龍校區(qū)6號(hào)樓318會(huì)議室
主辦單位：數(shù)學(xué)與統(tǒng)計(jì)學(xué)院、數(shù)學(xué)研究院、科學(xué)技術(shù)研究院
報(bào)告人簡(jiǎn)介：
徐巖，中國(guó)科學(xué)技術(shù)大學(xué)數(shù)學(xué)科學(xué)學(xué)院教授、博導(dǎo)， 教育部國(guó)家重大人才工程項(xiàng)目特聘教授，國(guó)家自然科學(xué)基金優(yōu)秀青年基金獲得者、教育部新世紀(jì)優(yōu)秀人才計(jì)劃。2005年于中國(guó)科學(xué)技術(shù)大學(xué)數(shù)學(xué)系獲計(jì)算數(shù)學(xué)博士學(xué)位；2005-2007年在荷蘭Twente大學(xué)從事博士后研究工作。2009年獲得德國(guó)洪堡基金會(huì)的支持在德國(guó)Freiburg大學(xué)訪問(wèn)工作一年。主要研究領(lǐng)域?yàn)楦呔葦?shù)值計(jì)算方法。2008年度獲全國(guó)優(yōu)秀博士學(xué)位論文獎(jiǎng)，2017年獲中國(guó)數(shù)學(xué)會(huì)計(jì)算數(shù)學(xué)分會(huì)第二屆“青年創(chuàng)新獎(jiǎng)”。主持國(guó)家自然科學(xué)基金面上項(xiàng)目、德國(guó)洪堡基金會(huì)研究組合作計(jì)劃、霍英東青年教師基礎(chǔ)研究課題等科研項(xiàng)目。擔(dān)任中國(guó)數(shù)學(xué)會(huì)計(jì)算數(shù)學(xué)分會(huì)理事，擔(dān)任SIAM Journal on Scientific Computing, Journal of Scientific Computing, Advances in Applied Mathematics and Mechanics, Communication on Applied Mathematics and Computation、計(jì)算物理等雜志的編委。
報(bào)告摘要：
In this talk we use Lagrange multipliers the conditions imposed by the structure preserving limiters are directly coupled to a DG discretization combined with implicit time integration method. The positivity preserving DG discretization is then reformulated as a Karush-Kuhn-Tucker (KKT) problem, which is frequently encountered in constrained optimization. Since the limiter is only active in areas where positivity must be enforced it does not affect the higher order DG discretization elsewhere. The resulting non-smooth nonlinear algebraic equations have, however, a different structure compared to most constrained optimization problems. We therefore develop an efficient active set semi-smooth Newton method that is suitable for the KKT formulation of time-implicit positivity preserving DG discretizations. Convergence of this semi-smooth Newton method is proven using a specially designed quasi-directional derivative of the time-implicit positivity preserving DG discretization. The time-implicit positivity preserving DG discretization is demonstrated for several nonlinear equations.