We present a general framework for constructing and analyzing finite volume methods applied to the mixed formulation of second-order elliptic problems on quadrilateral grids. The control volumes, or covolumes, in the grids overlap. An overlapping finite volume method of this type was first introduced by Russell in [T. F. Russell, Tech. report 3, Reservoir Simulation Research Corp., Tulsa, OK, 1...

In this paper, we propose a method of applying the Q-Morph to the closed three-dimensional triangular mesh. The Q-Morph is the method in order to transform the triangular mesh to the quadrilateral mesh. The Q-morph begins quadrilateral transformation from the initial front edges which are usually the boundary of the 2D domain. Also, the Q-Morph can be applied to the 3D domain. But, the closed 3...

We present a detailed study of the geometric and algebraic properties of the multidimensional quadrilateral lattice (a lattice whose elementary quadrilaterals are planar; the discrete analogue of a conjugate net) and of its basic reductions. To make this study, we introduce the notions of forward and backward data, which allow us to give a geometric meaning to the τ–function of the lattice, def...

The purpose of this case report is to 1) briefly describe the traditional above-knee (AK) quadrilateral socket, 2) describe the contoured adducted trochanteric-controlled alignment method (CAT-CAM) socket, 3) describe the management of a patient with a temporary CAT-CAM prosthesis, and 4) explain how the CAT-CAM prosthesis approach has resolved a medically complex clinical problem. The 49-year-...

The recently developed consecutive-interpolation procedure (CIP) based 4-node quadrilateral element (CQ4) is used to study free and forced 2-dimensional vibrations of elastic and piezoelectric structures of complex geometries. For some of these problems results have also been computed with the standard quadrilateral element under the constraint that the two approaches have the same number of de...

In this paper, an improved method based on a mixture of Gaussian and quadrilateral functions is presented to process airborne bathymetric LiDAR waveforms. In the presented method, the LiDAR waveform is fitted to a combination of three functions: one Gaussian function for the water surface contribution, another Gaussian function for the water bottom contribution, and a new quadrilateral function...

A quadrilateral is a bordered surface homeomorphic to the closed disc, with 4 marked boundary points called vertices, and equipped with a Riemannian metric of constant curvature K ∈ {0, 1,−1}, such that the sides (the arcs between the vertices) are geodesic. So the metric has the so-called conic singularities at the vertices. Let παj > 0 be the interior angles at the vertices. When K = 0, we kn...

We present a comprehensive assessment of nodal and hybrid modal/nodal discontinuous Galerkin (DG) finite element solutions on a range of unstructured meshes to nonlinear shallow water flow with smooth solutions. The nodal DG methods on triangles and a tensor-product nodal basis on quadrilaterals are considered. The hybrid modal/nodal DG methods utilize two different synergistic polynomial bases...

Thanks to recent improvements, computational methods can now be used to convert triangular meshes into quadrilateral meshes so that the quadrilateral elements capture well the principal curvature directional fields of surfaces and intrinsically have surface parametric values. In this study, a quadrilateral mesh generated using the mixed integer quadrangulation technique of Bommes et al. is used...