1,457 research outputs found
Flipping Cubical Meshes
We define and examine flip operations for quadrilateral and hexahedral
meshes, similar to the flipping transformations previously used in triangular
and tetrahedral mesh generation.Comment: 20 pages, 24 figures. Expanded journal version of paper from 10th
International Meshing Roundtable. This version removes some unwanted
paragraph breaks from the previous version; the text is unchange
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
Surface cubications mod flips
Let be a compact surface. We prove that the set of surface
cubications modulo flips, up to isotopy, is in one-to-one correspondence with
.Comment: revised version, 18
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)
Computational Geometry Column 42
A compendium of thirty previously published open problems in computational
geometry is presented.Comment: 7 pages; 72 reference
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