Theoretical approach of numerical differentiation with high accuracy and speed based on hyper-dual numbers
| Reference No. | 2022a013 |
|---|---|
| Type/Category | Grant for Young Researchers and Students-Short-term Joint Research |
| Title of Research Project | Theoretical approach of numerical differentiation with high accuracy and speed based on hyper-dual numbers |
| Principal Investigator | Yusuke Imoto（Kyoto University・Assistant professor） |
| Research Period |
August 8,2022. ～
August 10,2022. |
| Keyword(s) of Research Fields | Hyper-dual number, Matrix representation, Composite material, Numerical analysis |
| Abstract for Research Report |
This joint research will apply algebraic theory to develop higher-order numerical differentiation, the core of composite material simulations used to create next-generation materials such as passenger rockets and flying cars, to achieve high accuracy and high speed. Recent advances in computers and computational theory have made it possible to simulate composite materials with next-generation properties such as superelasticity. However, it is necessary to calculate the nine-variable fourth-order partial derivatives of the constitutive equation of materials with high accuracy. Unfortunately, because the conventional methods such as automatic differentiation are not accurate enough, applications to meet the industry's requirements are limited. Therefore, it is necessary to construct a new theory of differential computation that can perform differential computation with high accuracy and speed. In this joint research, we invite researchers from industry (Toyota Motor North America), engineering, and informatics to develop the computational theory using algebraic objects called hyper-dual numbers, which the applicants have been studying, into a method that meets the demands of the industry. In particular, we aim to develop a theory to solve the current problem of the exponential increase in the computational cost of computational methods based on matrix representations of hyper-dual numbers for the differential order. This will enable faster calculation of higher-order partial derivatives, which will promote the development of next-generation composite materials and contribute to the practical application of next-generation air mobility, such as passenger rockets and flying cars. |
| Organizing Committee Members (Workshop) Participants (Short-term Joint Usage) |
Takeo Uramoto（Kyushu University・Assistant professor） Masaki Fujikawa（University of the Ryukyus・Associate professor） Masato Tanaka（Toyota Central R&D Laboratories, INC.・Researcher） Naoya Yamanaka（Meisei University・Associate professor） Naoto Mitsume（University of Tsukuba・Assistant professor） Naoki Morita（University of Tsukuba・Assistant professor） |
| Adviser | Akira Ohata (MathWorks.Inc.) |