2017/11/21 by Hiroshi Isshiki, Isshiki, Hiroshi, Daisuke Kitazawa +1
Engineering · Mathematics · #Advanced Theoretical and Applied Studies in Material Sciences and Geometry #Differential Equations and Numerical Methods #FOS: Mathematics #Iterative Methods for Nonlinear Equations #Numerical Analysis (math.NA)
paper · pdf · doi:10.48550/arxiv.1711.07595
openalex publication_date 2017/11/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The authors have discussed the method and merit of introducing the curvilinear coordinates into numerical analysis and have shown some numerical examples. However, they used analytical functions for the mappings in the examples and didn't mention how to generate a mapping numerically between the physical and mapped coordinates. There is an analytical method using the solution of Dirichlet problem of Poisson equation. The authors present an algebraic method using interpolation of mapping function values at discrete points based on the least square method. Not only the mapping of two coordinates but also the application to the solution of boundary value problem is given.