报告题目：High-order ADER methods for evolutionary partial differential equations.
报告人：Eleuterio F. Toro ，Professor Emeritus, University of Trento, Italy. Academic Visitor, Cavendish Laboratory,Department of Physics, Cambridge University, UK.
Email: eleuterio.toro@unitn.it
Webpage: https://eleuteriotoro.com
报告时间：5月24日 3:00-4:00
报告地点：五教5505
摘要：
ADER is an approach to construct one-step high-order extensions of the Godunov first-order method, in which the conventional Riemann problem is replaced by the generalized Riemann problem (GRPm), a Cauchy problem with piece-wise smooth polynomial data of degree m that may include stiff source terms. The resulting schemes are of arbitrary m+1 order accuracy in both space and time; there is no theoretical accuracy barrier. There are by now several methods for solving the generalized Riemann problem, thus giving rise to several classes of ADER schemes.
ADER is a fully discrete methodology in which the space and time discretizations are intimately linked through the generalized Riemann problem (GRPm). ADER operates in both the finite volume and DG finite elements frameworks. These schemes are orders-of-magnitude cheaper than first-order methods for attaining a prescribed, small error and are therefore mandatory in ambitious scientific and technological applications. Here I review some key aspects of the ADER methodology and discuss its strengths, shortcomings, and issues of current research interest. Sample applications will be shown.
个人简介：
Eleuterio F. Toro is a British/Chilean mathematician, currently a Professor Emeritus at the University of Trento, Italy and academic visitor of the Cavendish Laboratory, University of Cambridge, UK. He holds an Honours BSc in pure mathematics (University of Warwick, UK), an MSc in functional analysis and differential equations (University of Dundee, UK) and a PhD in computational mathematics from Teesside University (UK 1982). Previous academic appointments include the University of Leeds (UK), Cranfield University (UK), Manchester Metropolitan University (UK) and Cambridge University (UK). Professor Toro has received several honours and distinctions, which include the honorary title OBE from Queen Elizabeth II (UK, 2000); Distinguished Citizen of the City of Carahue (Chile, 2001); Life Fellow, Claire Hall, University of Cambridge (UK, 2003); Fellow of the Indian Society for Shock Wave Research (Bangalore, 2005); Doctor Honoris Causa (Universidad de Santiago de Chile, 2008); William Penney Fellow, University of Cambridge (UK, 2010); Doctor Honoris Causa (Universidad de la Frontera, Chile, 2012); Doctor Honoris Causa (Universidad Católica de Temuco, 2024) and Honorary Professor, Moscow Institute of Physics and Technology, Russia. Professor Toro’s research has for many years focused on the construction of computational methods for solving partial differential equations, with particular emphasis on hyperbolic balance laws and applications to industrial, aerospace, environmental and biomedical problems. Contribution highlights include: WAF (1989), HLLC (1992), FORCE (1996), ADER (2001), MUSTA (2004), TV flux splitting (2012). In recent years he has been invited keynote speaker in more than 100 international scientific events. Professor Toro has held many visiting appointments round the world. He is author of more than 300 research works, including books, articles and technical reports.
