Diagonal Material Matrices for Arbitrary Simplicial Meshes for Solving Poisson Problems With One Unknown Per Element

We present a technique to construct diagonal material matrices for arbitrary triangular and tetrahedral meshes and arbitrary scalar material parameters. The recipe is based on a novel dual complex called folded Voronoï diagram. The proposed matrices are tailored to enable the use of a complementary-dual formulation for Poisson problems featuring one unknown per element.