Geometry, Topology and Numerical Analysis 2024

Reference No.	2024a013
Type/Category	Grant for General Research-Workshop（Ⅱ）
Title of Research Project	Geometry, Topology and Numerical Analysis 2024
Principal Investigator	Shunsaku Nii（Faculty of Mathematics, Kyushu University・Associate Professor）
Research Period	October 26,2024. - October 27,2024.
Keyword(s) of Research Fields	Finite Element Exterior Calculus, Numerical Analysis, Geometry, Topology, Fluid mechanics on surfaces
Abstract for Research Report	After the advent of electronic computers, theories and methods of numerical analysis has vastly developed along with the development of computers themselves, and they are employed in a wide range of science and engineering. Although numerical analysis has enabled calculations far beyond the capability of human hands, several problems require unexpectedly large computational resources compered with their complexity, and are hard to get sufficient accuracy. One strategy to tackle them is to develop schemes adapted to their geometric or topological structures. One example of this direction is “Finite Element Exterior Calculus” developed by D.Arnold which is a finite element method compatible with topology or geometry of the problems.The effectiveness of this method has been demonstrated by accuracy of calculations in examples in which the usual finite element method often leads to wrong result even for sufficiently fine meshes. Another example is numerical analyses of fluid dynamics on curved surfaces, in which traditional equation of fluid on flat Euclidean space cannot be directly applied. This symposium gathers researchers investigating or being interested in numerical methods adapted to Topology or geometry of the problems, and stimulates discussions and exchange of ideas among them in order to share perspectives, knowledge and techniques for future development.
Organizing Committee Members (Workshop) Participants (Short-term Joint Usage)	Shunsaku Nii（Faculty of Mathematics, Kyushu University・Associate Professor）