| 國（境）外文教專家系列講座一百六十四講-Akil Narayan：Structure-preserving numerical methods for the shallow water equations with uncertainty |
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一、主講人介紹：Akil Narayan Akil Narayan副教授于2009年在美國布朗大學應用數學系獲得博士學位，畢業后在普渡大學從事博士后研究，先后在馬薩諸塞大學達特茅斯分校和猶他大學擔任助理教授和副教授等教職，已在SISC、JCP、JSC等國際著名期刊上發表論文60余篇，主持DMS和NSF等基金項目10項，擔任SISC、IJUQ等國際著名期刊的編委。
二、講座信息 講座摘要： In practice, the environment or initial conditions of shallow water equations (SWE) may be imprecisely known due to incomplete information, or uncertain. One effective strategy for propagating this input uncertainty forward through the SWE is the stochastic Galerkin method via polynomial Chaos. An outstanding challenge with numerical methods arising from this approach is that the model may lose important physical structure of the solution. We show that a known elegant connection in the deterministic case between water height positivity and hyperbolicity of the equations can be extended to the stochastic/uncertain case. Our algorithms ensure positivity of the water height, hyperbolicity of the stochastic Galerkin formulation, and obey the well-balanced property, ensuring stable simulation of certain steady-state solutions. We demonstate the effectiveness of the algorithm for simulations in one and two spatial dimensions. 講座時間：6月16日09:00-10:00 騰訊會議號：861 344 413
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