In this paper, we present a method for performing isotropic and anisotropic adaptive computations. The discontinuous Galerkin method that is used for solving transient flow problem is briefly introduced. We show then a general scheme to compute high-order derivatives of discontinuous fields. The Hessian of the density is used for computing a correction indicator. We present three sample problem...

An algorithm is introduced for converting a non-conforming hexahedral mesh that is topologically equivalent and geometrically similar to a given geometry into a conforming mesh for the geometry. The procedure involves embedding geometric topology information into the given non-conforming base mesh and then converting the mesh to a fundamental hexahedral mesh. The procedure is extensible to mult...

Many physical phenomena can be modeled by partial differential equations which may be solved by numerical methods such as finite element and finite volume methods. In this context, a given domain must first be subdivided into many simple cells. Both the shape and size of the cells will affect the accuracy and convergence of the method. A boundary conforming Delaunay mesh is a partition of a pol...

This paper presents a new method for handling nonconforming hexahedral-to-hexahedral interfaces. One or both of the adjacent hexahedral meshes are locally modified to create a one-to-one mapping between between the mesh nodes and quadrilaterals at the interface allowing a conforming mesh to be created. In the finite element method, nonconforming interfaces are currently handled using constraint...

In this paper we define the new alignment energy for non-conforming triangle meshes, and describes its use to compute unstable conforming discrete minimal surfaces. Our algorithm makes use of the duality between conforming and non-conforming discrete minimal surfaces which was observed earlier. In first experiments the new algorithm allows us the computation of unstable periodic discrete minima...

Three dimensional realistic simulation are often unsteady and include moving domains. One of major challenges associated with such simulations is the robust mesh generation for the moving domain. There has been significant research and development in this specific field[1, 2, 3, 4]. We describe a method for generating conforming tetrahedral mesh to the given C continuous surfaces in R immersed ...

Given a two dimensional oriented surface equipped with a simplicial mesh, the standard lowest order finite element spaces provide a complex X• centered on Raviart-Thomas divergence conforming vector fields. It can be seen as a realization of the simplicial cochain complex. We construct a new complex Y • of finite element spaces on the barycentric refinement of the mesh which can be seen as a re...

We describe a method for discretizing C continuous surface(s) in R immersed in a non-conforming tetrahedralization. The method consists of constructing a homeomorphic mapping from the tetrahedrons in a background mesh to ones conforming to the immersed geometry. Such a map relies on the way we parametrize the surface(s) of the immersed geometry over a collection of a nearby triangular faces wit...

This paper gives a method of quantifying (small) visual differences between 3D mesh models with conforming topology, based on the theory of strain fields. Our experiments show that our difference estimates are well correlated with human perception of differences. This work has applications in the evaluation of 3D mesh watermarking, 3D mesh compression reconstruction, and 3D mesh filtering.