GMP-X 2026

Quad meshes play a key role in discrete differential geometry and various applications, including geometry processing, computational design and architecture.

Vibrations of musical strings are well understood by Fourier analysis while the vibrations of geometric shapes exhibit surprising properties triggered by careful choices of differential geometric energies. We will review solved problems and introduce novel approaches with applications in biology, computer graphics and crystallography, and in topology.

Let (M,∇,⟨ , ⟩) be a manifold endowed with a flat torsionless connection ∇ and a Riemannian metric ⟨ , ⟩ and (TkM)k≥1 the sequence of tangent bundles given by TkM = T(Tk−1M) and T1M = TM.

This talk presents a high-order Bernstein-Bézier finite element (FE) discretisation for the efficient solution of time harmonic elastic and electromagnetic wave problems on unstructured triangular mesh grids.