講演者（所属）: Franz Chouly (Universidad de la República)
題目：Finite Element Methods for the Elasto-Plastic Torsion Problem
日時：2026年2月10日（火）16:30-18:00
場所：東京大学大学院数理科学研究科 122 室及びオンライン (アクセス)
概要：We will describe finite element methods for the elasto-plastic torsion problem, as a prototype of variational inequality with constraints on the gradient of the solution. This problem has been an object of study from the theoretical viewpoint since the 1970s. From the numerical analysis viewpoint, it remains difficult to obtain optimal a priori error estimates. We will present the numerical analysis and numerical results for three methods based on standard Lagrange finite elements of orden 1 or 2: a direct discretization and a Nitsche discretization of a modified variational inequality, when the source term is constant, and a penalty technique for a non constant source term. Particularly the Nitsche technique yields fully optimal a priori error bounds. This is a joint work with Patrick Hild (Université Paul Sabatier, Toulouse, France) and Tom Gustafsson (Aalto University, Finland).
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題目：Advances in Splitting: Intercardinal Approaches to Nonlinear Hideo Kawarada Equations
日時：2026年5月26日（火）16:30-18:00
場所：東京大学大学院数理科学研究科 002 室及びオンライン (アクセス)
概要：This presentation addresses two main issues. First, we shall discuss recent advancements in both exponential and non-exponential splitting methods, with particular emphasis on their stability, accuracy and global error estimates. Second, we shall introduce a new splitting configuration for solving nonlinear Hideo Kawarada equations with mixed derivative terms. This approach leads to intercardinal splitting finite-difference schemes that provide efficient and accurate numerical approximations of the underlying solutions. We shall further demonstrate that the resulting implicit methods are numerically stable, convergent, and efficient, while preserving key physical properties such as the positivity and monotonicity. The dynamic orders of accuracy of the proposed algorithms will be illustrated using generalized Milne devices. Simulation examples of the solution procedure will be presented and investigated, and several open problems will also be outlined.
備考：Students at all levels are warmly encouraged to attend and participate in the discussion.
講演者（所属）: Mikhail Lavrentiev (Novosibirsk State University and Institute of Automation & Electrometry SB RAS)
題目：Fast numerical solution to shallow water system at PC - application to tsunami simulation
日時：2026年6月2日（火）16:30-18:00
場所：東京大学大学院数理科学研究科 002 室及びオンライン (アクセス)
概要：To calculate the distribution of maximal tsunami wave heights along the shoreline immediately after the earthquake a number of algorithms have been developed. Due to the hardware acceleration (the use of FPGA - Field Programmable Gates Array - microchip) numerical solution to the shallow water system takes 1 minute with Personal Computer within 1000x600 km water area, grid step compared to 250 m. It takes 25 min to compute wave propagation over the entire Pacific Ocean at 1 min grid. Using the advantages of FPGA architecture, values of wave parameters are calculated at 7 time layers at one computer clock. The propores technology could be applied for more problems in computational hydrodynamics.
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