2,799 research outputs found
Solid/FEM integration at SNLA
The effort at Sandia National Labs. on the methodologies and techniques being used to generate strict hexahedral finite element meshes from a solid model is described. The functionality of the modeler is used to decompose the solid into a set of nonintersecting meshable finite element primitives. The description of the decomposition is exported, via a Boundary Representative format, to the meshing program which uses the information for complete finite element model specification. Particular features of the program are discussed in some detail along with future plans for development which includes automation of the decomposition using artificial intelligence techniques
Linear Complexity Hexahedral Mesh Generation
We show that any polyhedron forming a topological ball with an even number of
quadrilateral sides can be partitioned into O(n) topological cubes, meeting
face to face. The result generalizes to non-simply-connected polyhedra
satisfying an additional bipartiteness condition. The same techniques can also
be used to reduce the geometric version of the hexahedral mesh generation
problem to a finite case analysis amenable to machine solution.Comment: 12 pages, 17 figures. A preliminary version of this paper appeared at
the 12th ACM Symp. on Computational Geometry. This is the final version, and
will appear in a special issue of Computational Geometry: Theory and
Applications for papers from SCG '9
On a general implementation of - and -adaptive curl-conforming finite elements
Edge (or N\'ed\'elec) finite elements are theoretically sound and widely used
by the computational electromagnetics community. However, its implementation,
specially for high order methods, is not trivial, since it involves many
technicalities that are not properly described in the literature. To fill this
gap, we provide a comprehensive description of a general implementation of edge
elements of first kind within the scientific software project FEMPAR. We cover
into detail how to implement arbitrary order (i.e., -adaptive) elements on
hexahedral and tetrahedral meshes. First, we set the three classical
ingredients of the finite element definition by Ciarlet, both in the reference
and the physical space: cell topologies, polynomial spaces and moments. With
these ingredients, shape functions are automatically implemented by defining a
judiciously chosen polynomial pre-basis that spans the local finite element
space combined with a change of basis to automatically obtain a canonical basis
with respect to the moments at hand. Next, we discuss global finite element
spaces putting emphasis on the construction of global shape functions through
oriented meshes, appropriate geometrical mappings, and equivalence classes of
moments, in order to preserve the inter-element continuity of tangential
components of the magnetic field. Finally, we extend the proposed methodology
to generate global curl-conforming spaces on non-conforming hierarchically
refined (i.e., -adaptive) meshes with arbitrary order finite elements.
Numerical results include experimental convergence rates to test the proposed
implementation
Low-order continuous finite element spaces on hybrid non-conforming hexahedral-tetrahedral meshes
This article deals with solving partial differential equations with the
finite element method on hybrid non-conforming hexahedral-tetrahedral meshes.
By non-conforming, we mean that a quadrangular face of a hexahedron can be
connected to two triangular faces of tetrahedra. We introduce a set of
low-order continuous (C0) finite element spaces defined on these meshes. They
are built from standard tri-linear and quadratic Lagrange finite elements with
an extra set of constraints at non-conforming hexahedra-tetrahedra junctions to
recover continuity. We consider both the continuity of the geometry and the
continuity of the function basis as follows: the continuity of the geometry is
achieved by using quadratic mappings for tetrahedra connected to tri-affine
hexahedra and the continuity of interpolating functions is enforced in a
similar manner by using quadratic Lagrange basis on tetrahedra with constraints
at non-conforming junctions to match tri-linear hexahedra. The so-defined
function spaces are validated numerically on simple Poisson and linear
elasticity problems for which an analytical solution is known. We observe that
using a hybrid mesh with the proposed function spaces results in an accuracy
significantly better than when using linear tetrahedra and slightly worse than
when solely using tri-linear hexahedra. As a consequence, the proposed function
spaces may be a promising alternative for complex geometries that are out of
reach of existing full hexahedral meshing methods
Orbital and Maxillofacial Computer Aided Surgery: Patient-Specific Finite Element Models To Predict Surgical Outcomes
This paper addresses an important issue raised for the clinical relevance of
Computer-Assisted Surgical applications, namely the methodology used to
automatically build patient-specific Finite Element (FE) models of anatomical
structures. From this perspective, a method is proposed, based on a technique
called the Mesh-Matching method, followed by a process that corrects mesh
irregularities. The Mesh-Matching algorithm generates patient-specific volume
meshes from an existing generic model. The mesh regularization process is based
on the Jacobian matrix transform related to the FE reference element and the
current element. This method for generating patient-specific FE models is first
applied to Computer-Assisted maxillofacial surgery, and more precisely to the
FE elastic modelling of patient facial soft tissues. For each patient, the
planned bone osteotomies (mandible, maxilla, chin) are used as boundary
conditions to deform the FE face model, in order to predict the aesthetic
outcome of the surgery. Seven FE patient-specific models were successfully
generated by our method. For one patient, the prediction of the FE model is
qualitatively compared with the patient's post-operative appearance, measured
from a Computer Tomography scan. Then, our methodology is applied to
Computer-Assisted orbital surgery. It is, therefore, evaluated for the
generation of eleven patient-specific FE poroelastic models of the orbital soft
tissues. These models are used to predict the consequences of the surgical
decompression of the orbit. More precisely, an average law is extrapolated from
the simulations carried out for each patient model. This law links the size of
the osteotomy (i.e. the surgical gesture) and the backward displacement of the
eyeball (the consequence of the surgical gesture)
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