Speaker
Martin Legeland
Description
The finite element method is a cornerstone of computational science and engineering, providing approximate solutions to boundary value problems. The solution quality is highly dependent on the underlying mesh, traditionally optimized through iterative adaptive refinement. We present a novel deep learning architecture that limits training data requirements by leveraging invariance and equivariance properties. Our approach directly generates high-quality h-adaptive meshes for specified boundary value problems and a target approximation error without iterative steps. Applied to 2D linear-elastic problems, our method achieves a median error reduction of 22.6% compared to uniform meshes with equivalent computational cost.
