Geometry, Topology and Numerical Analysis

Reference No.	2023c007
Type/Category	Openings at any time-Workshop (II)
Title of Research Project	Geometry, Topology and Numerical Analysis
Principal Investigator	Shunsaku Nii（FACULTY OF MATHEMATICS , KYUSHU UNIVERSITY.・Associate Professor）
Research Period	December 10,2023. ～ December 10,2023.
Keyword(s) of Research Fields	Finite Element Exterior Calculus, Numerical Analysis, Geometry, Topology
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 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 mesh. 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）