Three-Dimensional Dynamic Overset Method for Stabilized Finite Elements

Abstract A fully automatic three-dimensional mesh generation method is developed by modifying the well-known ray casting technique. The method is capable of meshing objects modeled using the CSG representation scheme. The input to the method consists of solid geometry information, and mesh attributes such as element size. The method starts by casting rays in 3D space to classify the empty and full parts of the solid. This information is then used to create a cell structure that closely models the solid object. The next step is to further process the cell structure to make it more succinct, so that the cells close to the boundary of the solid object can model the topology with enough fidelity. Moreover, neighborhood relations between cells in the structure are developed and implemented. These relations help produce better conforming meshes. Each cell in the cell structure is identified with respect to a set of pre-defined types of cells. After the identification process, a normalization process is developed and applied to the cell structure in order to ensure that the finite elements generated from each cell conform to each other and to other elements produced from neighboring cells. The last step is to mesh each cell in the structure with valid finite elements.

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Thermal jet drilling of granite rock: a numerical 3D finite-element study

Philosophical Transactions of The Royal Society A Mathematical Physical and Engineering Sciences ◽

10.1098/rsta.2020.0128 ◽

2021 ◽

Vol 379 (2196) ◽

pp. 20200128

Author(s):

Timo Saksala ◽

Reijo Kouhia ◽

Ahmad Mardoukhi ◽

Mikko Hokka

Keyword(s):

Finite Elements ◽

Numerical Study ◽

Thermal Flux ◽

Three Dimensional ◽

Numerical Approach ◽

Mass Scaling ◽

Granite Rock ◽

Fracture Dynamics ◽

Rock Heterogeneity ◽

Thermal Drilling

This paper presents a numerical study on thermal jet drilling of granite rock that is based on a thermal spallation phenomenon. For this end, a numerical method based on finite elements and a damage–viscoplasticity model are developed for solving the underlying coupled thermo-mechanical problem. An explicit time-stepping scheme is applied in solving the global problem, which in the present case is amenable to extreme mass scaling. Rock heterogeneity is accounted for as random clusters of finite elements representing rock constituent minerals. The numerical approach is validated based on experiments on thermal shock weakening effect of granite in a dynamic Brazilian disc test. The validated model is applied in three-dimensional simulations of thermal jet drilling with a short duration (0.2 s) and high intensity (approx. 3 MW m −2 ) thermal flux. The present numerical approach predicts the spalling as highly (tensile) damaged rock. Finally, it was shown that thermal drilling exploiting heating-forced cooling cycles is a viable method when drilling in hot rock mass. This article is part of the theme issue ‘Fracture dynamics of solid materials: from particles to the globe’.

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A structure-exploiting numbering algorithm for finite elements on extruded meshes, and its performance evaluation in Firedrake

Geoscientific Model Development ◽

10.5194/gmd-9-3803-2016 ◽

2016 ◽

Vol 9 (10) ◽

pp. 3803-3815 ◽

Cited By ~ 13

Author(s):

Gheorghe-Teodor Bercea ◽

Andrew T. T. McRae ◽

David A. Ham ◽

Lawrence Mitchell ◽

Florian Rathgeber ◽

...

Keyword(s):

Finite Element ◽

Performance Evaluation ◽

Finite Elements ◽

Aspect Ratio ◽

Three Dimensional ◽

Data Layout ◽

Element System ◽

Continuous Galerkin ◽

Performance Penalty ◽

The Cost

Abstract. We present a generic algorithm for numbering and then efficiently iterating over the data values attached to an extruded mesh. An extruded mesh is formed by replicating an existing mesh, assumed to be unstructured, to form layers of prismatic cells. Applications of extruded meshes include, but are not limited to, the representation of three-dimensional high aspect ratio domains employed by geophysical finite element simulations. These meshes are structured in the extruded direction. The algorithm presented here exploits this structure to avoid the performance penalty traditionally associated with unstructured meshes. We evaluate the implementation of this algorithm in the Firedrake finite element system on a range of low compute intensity operations which constitute worst cases for data layout performance exploration. The experiments show that having structure along the extruded direction enables the cost of the indirect data accesses to be amortized after 10–20 layers as long as the underlying mesh is well ordered. We characterize the resulting spatial and temporal reuse in a representative set of both continuous-Galerkin and discontinuous-Galerkin discretizations. On meshes with realistic numbers of layers the performance achieved is between 70 and 90 % of a theoretical hardware-specific limit.

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On some three-dimensional finite elements for incompressible media

Computer Methods in Applied Mechanics and Engineering ◽

10.1016/0045-7825(87)90072-7 ◽

1987 ◽

Vol 63 (3) ◽

pp. 261-269 ◽

Cited By ~ 26

Author(s):

Rolf Stenberg

Keyword(s):

Finite Elements ◽

Three Dimensional ◽

Incompressible Media

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Truss and Beam Finite Elements Revisited: A Derivation Based on Displacement-Field Decomposition

International Journal of Space Structures ◽

10.1177/026635119601100404 ◽

1996 ◽

Vol 11 (4) ◽

pp. 371-380 ◽

Cited By ~ 19

Author(s):

Alphose Zingoni

Keyword(s):

Finite Element ◽

Finite Elements ◽

Symmetry Group ◽

Displacement Field ◽

Three Dimensional ◽

Beam Elements ◽

Symmetry Properties ◽

Mass Matrices ◽

General Displacement

Where a finite element possesses symmetry properties, derivation of fundamental element matrices can be achieved more efficiently by decomposing the general displacement field into subspaces of the symmetry group describing the configuration of the element. In this paper, the procedure is illustrated by reference to the simple truss and beam elements, whose well-known consistent-mass matrices are obtained via the proposed method. However, the procedure is applicable to all one-, two- and three-dimensional finite elements, as long as the shape and node configuration of the element can be described by a specific symmetry group.

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