Exact boundary derivative formulation for numerical conformal mapping method
type: Item
instance of: scholarly article
title: Exact boundary derivative formulation for numerical conformal mapping method
zbMATH Open document ID: 1400.65016
DOI: 10.1155/2016/5072309
author: Wei-Lin Lo
author: Nan-Jing Wu
author: C. S. Chen
author: Ting-Kuei Tsay
published in: Mathematical Problems in Engineering
publication date: 2018-10-12T00:00:00Z
review text: Summary: Conformal mapping is a useful technique for handling irregular geometries when applying the finite difference method to solve partial differential equations. When the mapping is from a hyperrectangular region onto a rectangular region, a specific length-to-width ratio of the rectangular region that fitted the Cauchy-Riemann equations must be satisfied. In this research, a numerical integral method is proposed to find the specific length-to-width ratio. It is conventional to employ the boundary integral method (BIEM) to perform the conformal mapping. However, due to the singularity produced by the BIEM in seeking the derivatives on the boundaries, the transformation Jacobian determinants on the boundaries have to be evaluated at inner points instead of directly on the boundaries. This approximation is a source of numerical error. In this study, the transformed rectangular property and the Cauchy-Riemann equations are successfully applied to derive reduced formulations of the derivatives on the boundaries for the BIEM. With these boundary derivative formulations, the Jacobian determinants can be evaluated directly on the boundaries. Furthermore, the results obtained are more accurate than those of the earlier mapping method.
Mathematics Subject Classification ID: 65E05
Mathematics Subject Classification ID: 30C30
zbMATH DE Number: 6953270
Wikidata QID: Q59131466
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2016/5072309
OpenAlex ID: W2268141395
cites work: Compact finite difference schemes with spectral-like resolution
cites work: Polynomial interpolation methods for viscous flow calculations
cites work: Q3208026
cites work: Boundary-fitted coordinate systems for numerical solution of partial differential equations. A review
cites work: Q3738756
cites work: A numerical technique for two-dimensional grid generation with grid control at all of the boundaries
cites work: Surface grid generation based on elliptic PDE models
cites work: 2D nearly orthogonal mesh generation
cites work: Q3732914
cites work: Numerical modelling of wave propagation using parabolic approximation with a boundary-fitted co-ordinate system
cites work: Q3760216
cites work: Analytical evaluation and application of the singularities in boundary element method
cites work: Numerical Conformal Mapping of a Towel-Shaped Region onto a Rectangle
cites work: Orthogonal grid generation of an irregular region using a local polynomial collocation method
cites work: A generalized Helmholtz equation fundamental solution using a conformal mapping and dependent variable transformation
cites work: Fundamental solutions for variable density two-dimensional elastodynamic problems
description: scientific article; zbMATH DE number 6953270