We contribute a novel algorithm for aligning and stitching non-overlapping 3D meshes. Mesh aligning and stitching are often combined to construct a complete 3D model of an object. There are standard algorithms that address this task for the case of overlapping meshes, i.e., meshes that share common parts of a given object. The overlap allows the registration and alignment of different meshes. T...

The objective of the study is to develop an algorithm for automatic directional coarsening of anisotropic meshes based on the finest level mesh to provide coarser meshes for geometric multigrid. Characteristic parameters of the meshes are high aspect ratio (of order 10 near the profile). The meshes are assumed to have a layer structure in boundary-layer zones. The aim of the study is to design ...

Unfitted (also known as embedded or immersed) finite element approximations of partial differential equations are very attractive because they have much lower geometrical requirements than standard body-fitted formulations. These schemes do not require unstructured mesh generation. In turn, the numerical integration becomes more involved, one has to compute integrals on portions cells (only int...

We propose an a posteriori approach for generating curved meshes for viscous flow simulations composed by high-order tetrahedra. The proposed approach is performed in the following three steps: (1) generate a linear tetrahedral mesh for inviscid flow; (2) insert a boundary layer mesh, composed by linear tetrahedra, on the viscous part; and (3) convert the linear tetrahedral mesh to a curved and...

Electrostatics interactions play amajor role in the stabilization of biomolecules : as such, they remain a major focus of theoretical and computational studies in biophysics. Electrostatics in solution is strongly dependent on the nature of the solvent and on the ions it contains. While methods that treat the solvent and ions explicitly provide an accurate estimate of these interactions, they a...

We develop a theory of one-forms on meshes. The theory culminates in a discrete analog of the Poincare-Hopf index theorem for meshes. We apply this theorem to obtain some old and new results concerning the parameterization of 3D mesh data. Our first result is an easy proof of Tutte's celebrated "spring-embedding" theorem for planar graphs, which is widely used for parameterizing meshes with the...

The present study is concerned with optimal shape determination of inhomogeneous and temperature dependent domains under steady state heat conduction. Such situations are important in many thermal design problems, especially in shape design of electronic components and chips. In the present paper, we formulate the shape optimization problem based on volume minimization of heat conductive materi...

We generate Voronoi meshes over three dimensional domains with prescribed boundaries. Voronoi cells are clipped at one-sided domain boundaries. The seeds of Voronoi cells are generated by maximal Poisson-disk sampling. In contrast to centroidal Voronoi tessellations, our seed locations are unbiased. The exception is some bias near concave features of the boundary to ensure well-shaped cells. Th...