We present a method for producing quad-dominant subdivided meshes, which supports both adaptive refinement and adaptive coarsening. A hierarchical structure is stored implicitly in a standard half-edge data structure, while allowing us to efficiently navigate through the different level of subdivision. Subdivided meshes contain a majority of quad elements and a moderate amount of triangles and ...

In this paper, a control volume finite element scheme for the capture of spatial patterns for a volume-filling chemotaxis model is proposed and analyzed. The diffusion term, which generally involves an anisotropic and heterogeneous diffusion tensor, is discretized by piecewise linear conforming triangular finite elements (P1-FEM). The other terms are discretized by means of an upstream finite v...

An extended finite element method (XFEM) for the forward model of 3D optical molecular imaging is developed with simplified spherical harmonics approximation (SP(N)). In XFEM scheme of SP(N) equations, the signed distance function is employed to accurately represent the internal tissue boundary, and then it is used to construct the enriched basis function of the finite element scheme. Therefore...

Abstract We propose a least-squares method involving the recovery of gradient and possibly Hessian for elliptic equation in nondivergence form. As our approach is based on Lax–Milgram theorem with curl-free constraint built into target (or cost) functional, discrete spaces require no inf-sup stabilization. show that standard conforming finite elements can be used yielding priori posteriori conv...

The current work focuses on applying an arti cial viscosity approach to the Spectral Di erence (SD) method to enable high-order computation of compressible uid ows with discontinuities. The study modi es the arti cial viscosity approach proposed in the earlier work. Studies show that a dilatation sensor for arti cial viscosity, combined with a dilatation-based switch and lter for smoothing, wor...

Based on the recent work of Yang et al. [2011], we propose several intuitive tools to quickly create new architectural freeform shapes starting from a single input design, while conforming to a set of prescribed constraints and optimizing for specified quality measures. We allow the user to control the final shape by prescribing desirable curves on the final shape, access the desirable regions ...

SUMMARY In this paper an algebraic substructuring preconditioner is considered for non-conforming nite element approximations of second order elliptic problems in 3D domains with a piecewise constant diiusion coeecient. Using a substructuring idea and a block Gauss elimination part of the unknowns is eliminated and the Schur complement obtained is preconditioned by a spectrally equivalent very ...

Let T be a tetrahedral mesh. We present a 3-D local refinement algorithm for T which is mainly based on an 8-subtetrahedron subdivision procedure, and discuss the quality of refined meshes generated by the algorithm. It is proved that any tetrahedron T ∈ T produces a finite number of classes of similar tetrahedra, independent of the number of refinement levels. Furthermore, η(Ti ) ≥ cη(T), wher...

This paper introduces a quasi-interpolation operator for scalarand vector-valued finite element spaces constructed on affine, shape-regular meshes with some continuity across mesh interfaces. This operator gives optimal estimates of the best approximation error in any Lp-norm assuming regularity in the fractional Sobolev spaces W r,p, where p ∈ [1,∞] and the smoothness index r can be arbitraril...

We show how to place a set of seed points such that a given piecewise linear complex is the union of some faces in the resulting Voronoi diagram. The seeds are placed on sufficiently small spheres centered at input vertices and are arranged into little circles around each half-edge where every seed is mirrored across the associated triangle. The Voronoi faces common to the seeds of such arrange...