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数値解析セミナー
過去の記録 ～05/17｜次回の予定｜今後の予定 05/18～
| 開催情報 | 火曜日 16:30～18:00 数理科学研究科棟(駒場) 002号室 |
|---|---|
| 担当者 | 齊藤宣一、柏原崇人 |
| セミナーURL | https://sites.google.com/g.ecc.u-tokyo.ac.jp/utnas-bulletin-board/ |
今後の予定
2026年05月26日(火)
16:30-18:00 数理科学研究科棟(駒場) 002号室
Qin Sheng 氏 (Baylor University)
Advances in Splitting: Intercardinal Approaches to Nonlinear Hideo Kawarada Equations
(English)
https://sites.google.com/g.ecc.u-tokyo.ac.jp/utnas-bulletin-board/
Qin Sheng 氏 (Baylor University)
Advances in Splitting: Intercardinal Approaches to Nonlinear Hideo Kawarada Equations
(English)
[ 講演概要 ]
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.
[ 参考URL ]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.
https://sites.google.com/g.ecc.u-tokyo.ac.jp/utnas-bulletin-board/
2026年06月02日(火)
16:30-18:00 数理科学研究科棟(駒場) 002号室
Mikhail Lavrentiev 氏 (Novosibirsk State University and Institute of Automation & Electrometry SB RAS)
Fast numerical solution to shallow water system at PC - application to tsunami simulation (English)
https://sites.google.com/g.ecc.u-tokyo.ac.jp/utnas-bulletin-board/
Mikhail Lavrentiev 氏 (Novosibirsk State University and Institute of Automation & Electrometry SB RAS)
Fast numerical solution to shallow water system at PC - application to tsunami simulation (English)
[ 講演概要 ]
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.
[ 参考URL ]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.
https://sites.google.com/g.ecc.u-tokyo.ac.jp/utnas-bulletin-board/
