CG Week 2026: Workshop on Triangulations and More General Meshes for Space-Time Applications

Workshop Objective:

This workshop aims to bring together experts on meshing from the computational geometry and finite element communities. The topic of meshing is of core interest to both communities, but communication between the two communities can be significantly improved. We note that the finite element community has extensive experience building meshes in 3D and lower-dimensional spaces for engineering applications. However, these efforts are often customized to the particular dimension of interest, and are carried out on a ‘case-by-case’ basis. In contrast, the computational geometry community has focused on dimensionally-independent algorithms and theoretical results, but has often neglected to explicitly construct highly optimized implementations of their algorithms for particular applications. This workshop is meant to start building bridges between the two communities, with a specific focus on 4D/space-time applications, because many open questions remain in this area. In particular, the following research topics require further exploration:

• The construction of high-quality, isotropic, non-conforming simplicial meshes
• The enforcement of boundary conformity for simplicial and cuboid meshes
• The discrete reconstruction of manifolds
• The robust morphing of simplicial and cuboid meshes
• The anisotropic refinement of simplicial and cuboid meshes in accordance with Riemannian metric fields
• The construction of methods to circumvent the curse of dimensionality

Although our primary focus is on space-time meshing, we are also open to contributed talks that either focus on arbitrary dimensional meshes and/or lower dimensional results that allow for interesting generalizations into 4 or higher dimensions.

Workshop Schedule:

• Session 1, 4:20 pm-5:20 pm, Wednesday, June 3rd, 2026
  • 4:20 pm: Philip Caplan, Middlebury College: “Tetrahedralizations of moving geometries in four dimensions”
  • 4:50 pm: David Williams: Open Discussion
• Session 2, 4:20 pm-6:20 pm, Thursday, June 4th, 2026
  • 4:20 pm: Tamas Horvath, Oakland University: “Adaptive 2D+t space-time mesh generation”
  • 4:50 pm: Ray Hixon, University of Toledo: “Progress towards a 4D structured multiblock grid generator”
  • 5:20 pm: Raphaël Tinarrage, Institute of Science and Technology, Austria: “Sharp bounds on simplex shrinking under iterated Delaunay refinement”
  • 5:50 pm: John Parks, Pennsylvania State University: “Barycentric refinement techniques for boundary recovery on meshes in R^d”
• Session 3, 4:20 pm-6:20 pm, Friday, June 5th, 2026
  • 4:20 pm: Dominique Attali, French National Centre for Scientific Research: “Triangulating co-dimension 1 submanifolds by collapsing alpha-complexes”
  • 4:50 pm: Hana Dal Poz Kouřimská, University of Potsdam: “On subdividing simplices in spaces of constant curvature while maintaining quality”
  • 5:20 pm: Guillaume Moroz, Inria, and David Williams Pennsylvania State University: “A directed-hyperarea vector identity in R^d with applications to edge-based, node-centered methods”
  • 5:50 pm: Oliver Wege, RWTH Aachen University: “Space-time finite element mesh generation and adaption for fluid dynamics”