| Title |
A Data-driven Mesh Refinement Framework for Generating Non-uniform Meshes |
| Authors |
김민성(Minseong Kim) ; 이재승(Jaeseung Lee) ; 김지범(Jibum Kim) |
| DOI |
https://doi.org/10.5573/ieie.2022.59.10.76 |
| Keywords |
Neural network; Supervised learning; Partial differential equation; Mesh generation; Mesh refinement |
| Abstract |
We propose a new mesh refinement framework that performs mesh refinement in a data-driven way for given PDEs, geometric domains, and boundary conditions. The proposed framework is able to produce non-uniform meshes from an initial uniform coarse mesh by reducing the element size at the location where the error is expected to be large. The proposed framework is able to learn and accurately predict the target element size without repeatedly performing the expensive post error estimation process. In the experiment, we test the proposed framework on the Poisson’s equation, which is a representative elliptical PDE. Our experimental results show that the proposed framework successfully produces non-uniform meshes and these non-uniform meshes have better efficiency and accuracy compared with the uniform meshes that have more number of elements. |