Generation of Curvilinear Coordinates
For researchers in numerical analysis and computational physics, this provides a practical algebraic alternative to analytical or PDE-based mapping methods, though the novelty is incremental.
The authors propose an algebraic method using least squares interpolation to generate curvilinear coordinate mappings, addressing a gap in numerical mapping generation, and demonstrate its application to boundary value problems.
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.