SUMMARYQ-Morph is a new algorithm for generating all-quadrilateral meshes on bounded three-dimensional surfaces. After first triangulating the surface, the triangles are systematically transformed to create an all-quadrilateral mesh. An advancing front algorithm determines the sequence of triangle transformations. Quadrilaterals are formed by using existing edges in the triangulation, by inserting additional nodes, or by performing local transformations to the triangles. A method typically used for recovering the boundary of a Delaunay mesh is used on interior triangles to recover quadrilateral edges. Any number of triangles may be merged to form a single quadrilateral. Topological clean-up and smoothing are used to improve final element quality. Q-Morph generates well-aligned rows of quadrilaterals parallel to the boundary of the domain while maintaining a limited number of irregular internal nodes. The proposed method also offers the advantage of avoiding expensive intersection calculations commonly associated with advancing front procedures. A series of examples of Q-Morph meshes are also presented to demonstrate the versatility of the proposed method.

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SUMMARYThe generation of all-hexahedral finite element meshes has been an area of ongoing research for the past two decades and remains an open problem. Unconstrained plastering is a new method for generating all-hexahedral finite element meshes on arbitrary volumetric geometries. Starting from an unmeshed volume boundary, unconstrained plastering generates the interior mesh topology without the constraints of a pre-defined boundary mesh. Using advancing fronts, unconstrained plastering forms partially defined hexahedral dual sheets by decomposing the geometry into simple shapes, each of which can be meshed with simple meshing primitives. By breaking from the tradition of previous advancing-front algorithms, which start from pre-meshed boundary surfaces, unconstrained plastering demonstrates that for the tested geometries, high quality, boundary aligned, orientation insensitive, all-hexahedral meshes can be generated automatically without pre-meshing the boundary. Examples are given for meshes from both solid mechanics and geotechnical applications.

Summary:Unconstrained Paving and Plastering [1] were introduced as new methods of generating all-quadrilateral and all-hexahedral finite element meshes. Their introduction was after preliminary conceptual studies. This paper presents an update on Unconstrained Paving and Plastering after significant implementation and conceptual development.

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A template-based generic programming approach was presented in a previous paper [19] that separates the development effort of programming a physical model from that of computing additional quantities, such as derivatives, needed for embedded analysis algorithms. In this paper, we describe the implementation details for using the template-based generic programming approach for simulation and analysis of partial differential equations (PDEs). We detail several of the hurdles that we have encountered, and some of the software infrastructure developed to overcome them. We end with a demonstration where we present shape optimization and uncertainty quantification results for a 3D PDE application.