Generation of Curvilinear Coordinates

TL;DR

This paper introduces an algebraic interpolation method for generating curvilinear coordinates in numerical analysis, enabling more flexible mappings between physical and computational domains, with applications to boundary value problems.

Contribution

It presents a novel algebraic least squares interpolation approach for numerically generating curvilinear coordinate mappings, extending beyond analytical solutions.

Findings

The algebraic method effectively generates coordinate mappings.

Application to boundary value problems demonstrates practical utility.

Method improves flexibility over purely analytical approaches.

Abstract

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.