Mesh generation research

The Coreform team's (previously csimsoft) extensive meshing research dates back to the late 1980s with Paving: A New Approach to Automated Quadrilateral Mesh Generation. Here are a few of the papers from those 30 years.

A Comparison of All Hexagonal and All Tetrahedral Finite Element Meshes for Elastic and Elasto-plastic Analysis

Steven E. Benzley, Ernest Perry, Karl Merkley, Brett Clark, Greg Sjaardama, Brigham Young University and Sandia National Laboratories

Published: 1 January 2014

This paper compares the accuracy of elastic and elastio-plastic solid continuum finite element analyses modeled with either all hexagonal or all tetrahedral meshes. Eigenvalues of element stiffness matrices, linear static displacements and stresses, dynamic modal frequencies, and plastic flow values in are computed and compared. Elements with both linear and quadratic displacement functions are evaluated.

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The Verdict Geometric Quality Library

C. J. Stimpson, C. D. Ernst, P. P. Pébay, P. Knupp, D. Thompson, Sandia report SAND2007-1751

Published: 1 March 2007

Verdict is a collection of subroutines for evaluating the geometric qualities of triangles, quadrilaterals, tetrahedra, and hexahedra using a variety of metrics. A metric is a real number assigned to one of these shapes depending on its particular vertex coordinates. These metrics are used to evaluate the input to finite element, finite volume, boundary element, and other types of solvers that approximate the solution to partial differential equations defined over regions of space.

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Methods and Applications of Generalized Sheet Insertion for Hexahedral Meshing

Karl Merkley, Corey Ernst, Jason F. Shepherd, Michael J. Borden, Sandia report.

Published: 2 April 2004

This paper presents methods and applications of sheet insertion in a hexahedral mesh. A hexahedral sheet is dual to a layer of hexahedra in a hexahedral mesh. Because of symmetries within a hexahedral element, every hexahedral mesh can be viewed as a collection of these sheets. It is possible to insert new sheets into an existing mesh, and these new sheets can be used to define new mesh boundaries, refine the mesh, or in some cases can be used to improve quality in an existing mesh.

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An Immersive Topology Environment for Meshing

Steven J. Owen, Brett W. Clark, Darryl J. Melander, Michael Brewer, Jason F. Shepherd, Karl Merkley, Corey Ernst, and Randy Morris, International Meshing Roundtable

Published: 1 April 2004

The Immersive Topology Environment for Meshing (ITEM) is a wizardlike environment, built on top of the CUBIT Geometry and Meshing Toolkit. ITEM is focused on three main objectives: 1) guiding the user through the simulation model preparation workflow; 2) providing the user with intelligent options based upon the current state of the model; and 3) where appropriate, automating as much of the process as possible.

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MOAB: A Mesh — Oriented Database

T. Tautges, R. Meyers, K Merkley, C. Stimpson, C. Ernst, Sandia report SAND2004-1592

Published: 1 April 2004

MOAB is a component for representing and evaluating mesh data. MOAB can store structured and unstructured mesh, consisting of elements in the finite element “zoo”. The functional interface to MOAB is simple yet powerful, allowing the representation of many types of metadata commonly found on the mesh.

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Loop detection in surface patch intersections

Thomas W. Sederberg and Ray J. Meyers, Department of Civil Engineering, Brigham Young University, Provo, UT 84602, U.S.A.

Published: 14 March 2003

A condition is presented for guaranteeing that all branches of the curve of intersection of two parametric surfaces patches contain a point on at least one of the patch boundary curves. This is of value because it eliminates a robustness limitation which arises when computing surface intersections using the marching method, namely, assuring that all branches of the intersection curve have been found.

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The Geode Algorithm: Combining Hex/Tet Plastering, Dicing and Transition Elements for Automatic, All-Hex Mesh Generation

Robert W. Leland, Darryl J. Melander, Ray J. Meyers, Scott A. Mitchell, Timothy J. Tautges, IMR 1998

Published: 1 October 1999

A new all-hexahedral meshing algorithm, referred to as “Geode”, is described. This algorithm is the combination of hex/tet plastering, dicing, and a new 26-hex transition element template.The algorithm is described in detail, and examples are given of problems meshed with this algorithm.

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The Hex-Tet Hex-Dominant Meshing Algorithm as Implemented in CUBIT

Ray J. Meyers., Timothy J. Tautges, Philip M. Tuchinsky, Proceedings, 7th International Meshing Roundtable

Published: 1 October 1998

This is a report of the current status of the Hex-Tet algorithm as implemented in the CUBIT toolset. The Hex-Tet algorithm begins by generating a partial hex mesh using an advancing front “Plastering” algorithm. The boundary of any remaining void is optionally “cleaned-up” to improve its shape and/or other properties. The quad boundary is then converted to a triangular boundary by one of three available methods. Finally, the triangle-bounded void is filled with tetrahedra using the tet-generation capabilities within CUBIT.

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Seams and wedges in plastering: A 3-D hexahedral mesh generation algorithm

Ted D. Blacker and Ray J. Meyers

Published: 1 June 1993

This paper describes mesh correction techniques necessary for meshing an arbitrary volume with a completely hexahedral mesh. Specifically, it describes seams and wedges, mechanisms that overcome major hurdles encountered in the preliminary work on the plastering algorithm. The plastering algorithm iteratively projects layers of elements inward from a quadrilateral discretization of the volume's bounding faces.

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Paving: A New Approach to Automated Quadrilateral Mesh Generation

Ted D. Blacker, and Michael B. Stephenson (1991), International Journal for Numerical Methods in Engineering, Vol 32 pp.811–847

Published: 15 April 1990

This paper presents a new mesh generation technique, paving, which meshes arbitrary 2D geometries with an all-quadrilateral mesh. Paving allows varying element size distributions on the boundary as well as the interior region.

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The Cleave and Fill Tool: An All-Hexahedral Refinement Algorithm for Swept Meshes

Michael J. Borden, Steven E. Benzley, Scott A. Mitchell, David R. White, Ray J. Meyers, IMR 2000

Published: 1 January 0001

Sweeping algorithms provide the ability to generate all hexahedral meshes on a wide variety of three-dimensional bodies. The work presented here provides a method to refine these meshes by first defining a path through either the source or the target mesh and next by locating the sweeping layer to initiate the refinement. A major contribution of this work is the ability to automatically find a minimal distance path through the target or source mesh.

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