Tetrahedral Meshes
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Related Articles from SNS
$p$-Robust Trace Liftings for Discrete Harmonic Extensions and Boundary-Preserving $hp$ Interpolation on Tetrahedral Meshes
arXiv:2606.02086v1 Announce Type: new Abstract: We construct p-robust polynomial trace liftings on three-dimensional tetrahedral meshes. The prescribed trace is a continuous piecewise polynomial function on a boundary face patch; the tetrahedra touching this patch have one common degree, while the interior degrees may be arbitrary. The lifting is degree-preserving, supported in the corresponding boundary layer, and satisfies both an H^1 estimate and a scaled boundary-layer L^2 estimate with...
BijectiveRemesh: Maintaining Bijective Mappings for Data Transfer Across Remeshed Manifolds
Announce Type: new Abstract: We introduce BijectiveRemesh, a robust algorithm for maintaining a continuous, bijective mapping across complex remeshing sequences on both 2D triangle surfaces and 3D tetrahedral meshes. Unlike traditional data transfer methods that rely on interpolation or projection, our approach constructs a mathematically rigorous composite map from the input mesh to the output mesh by chaining local bijective atlases defined for each primitive remeshing operation. Our...
Stable Triangle Projections for Variable-Degree Tetrahedral Spaces and Uniform IPDG Preconditioning
Announce Type: new Abstract: The main ingredient of this paper is an edge-local variable-degree projection on a triangle that is uniformly stable in both L2 and H1. We use this two-dimensional operator in two tetrahedral constructions. First, on a reference tetrahedron, we build an H1-stable projection from a high order polynomial space onto a variable-degree space whose degrees are prescribed independently on edges, faces, and in the volume.
Uniform Schwarz Preconditioners for Variable-Degree $hp$ Finite Element Interface Problems
arXiv:2606.03141v1 Announce Type: new Abstract: We construct $h$- and $p$-robust, degree-preserving space decompositions and additive Schwarz preconditioners for variable-degree $hp$ finite element discretizations of reaction-diffusion and fitted-interface problems. On conforming simplicial meshes in arbitrary dimension, the single-domain result allows an arbitrary elementwise degree distribution subject only to $p_K\ge1$. A minimal-average Falk--Winther bubble transform is introduced by...
Compatibility and Accuracy Verification of CADmesh-Based Complex Geometry Modeling in Geant4
arXiv:2606.06508v1 Announce Type: new Abstract: Geant4 Monte Carlo simulation relies on the Constructive Solid Geometry (CSG) method for complex geometric modeling. This method has low efficiency and a high application threshold. Importing triangular facet formats such as STL/OBJ via CADmesh is a promising alternative, but systematic evaluations of format compatibility, geometric accuracy, and physical simulation deviations are lacking.