Solving PDEs on Deconstructed Domains

Sellán, Silvia; Cheng, Herng Yi; Ma, Yuming; Dembowski, Mitchell; Jacobson, Alec

Solving PDEs on Deconstructed Domains

Files

007-008.pdf (13.17 MB)

Date

2018

Authors

Sellán, Silvia
Cheng, Herng Yi
Ma, Yuming
Dembowski, Mitchell
Jacobson, Alec

Publisher

The Eurographics Association

Abstract

When finding analytical solutions to Partial Differential Equations (PDEs) becomes impossible, it is useful to approximate them via a discrete mesh of the domain. Sometimes a robust triangular (2D) or tetrahedral (3D) mesh of the whole domain is a hard thing to accomplish, and in those cases we advocate for breaking up the domain in various different subdomains with nontrivial intersection and to find solutions for the equation in each of them individually. Although this approach solves one issue,it creates another, i.e. what constraints to impose on the separate solutions in a way that they converge to true solution on their union. We present a method that solves this problem for the most common second and fourth order equations in graphics.

        @inproceedings{10.2312:sgp.20181181
,
booktitle = {Symposium on Geometry Processing 2018- Posters
},
editor = {Ju, Tao and Vaxman, Amir
},
title = {{Solving PDEs on Deconstructed Domains
}},
author = {Sellán, Silvia and 
Cheng, Herng Yi and 
Ma, Yuming and 
Dembowski, Mitchell and 
Jacobson, Alec
},
year = {2018
},
publisher = {The Eurographics Association
},
ISSN = {1727-8384
},
ISBN = {978-3-03868-069-7
},
DOI = {10.2312/sgp.20181181
}
}