Opening for a Post-Doc position: Adaptive anisotropic mesh for automated geometric reconstruction

A postdoctoral researcher is required to work on adaptive
anisotropic mesh refinement algorithms for the CEMEF, Center for Material
Forming at MINES ParisTech in Sophia Antipolis, French Riviera, France.

The proposed
work is part of an advanced program involving several industrial and academic
partners. The objective of this project referred as TOCATA (FUI French program)
is to design an optical system able to automatically detect material defects in
existing structures. Consequently, it is necessary to build a 3D numerical model
from the set of geometrical points obtained by the optical devices. The
developed model must be able to drive accurately the camera to the regions of
interest in order to do a finer analysis. As a result, the provided 3D model
will be able to render all the geometrical details by the simplest constructed
coarse mesh.

The research aspects of the project will involve developing
and exploring three important routes. Note that a set of meshing tools developed
in the lab and included in a parallel Finite Element library, CIMLIB, are
available and can be used by the applicant. This also includes a highly parallel
protocol wrapping the anisotropic adaptive MTC mesher.

The first route
describes general mesh decimation methods which operate on triangle meshes. The
goal of the mesh decimation is the reduction of triangles in a mesh while
preserving the shape and topology as good as possible. All the output and data
of the optical device measurement are given under the form of an initial mesh
(STL format) containing possibly a huge number of elements which can be used as
the first guess of the decimation procedure. The existing version of the mesher
can deal easily with such meshes as well as the metric map which preserves the
geometrical details is well defined. The main drawback of this approach is that
the current mesh technology requires that the initial mesh is a true mesh with
connected elements.

The second route consists on the use of the
Level Set method combined to an anisotropic adaptive meshing. At this stage, we
assume that the surface is still defined by a possibly huge number of triangles
not anymore strictly connected. The idea is to use an immersed surface technique
by means of the Level Set framework and then to adapt the background mesh until
the aimed domain is a part of it. To perform that we need to combine the PDE
level set solver, the interpolation error analysis with metric construction and
the adaptive remeshing procedure under the lower number of elements. This will
result the geometry reconstruction by mesh adaptation.

The last point is
described by the trajectory calculation from LS definition. Here, the objective
is to explore the possibility to use the adapted level set volume description to
calculate directly the required trajectories inside the volume of the background
mesh. More generally, it will open the door towards the required actual
objectives into the adaptive procedure.

The applicant will work closely
with researchers and computer scientists in the developing of the needed
algorithms as well as with external academic and industrial partners.

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Key-words: adaptive anisotropic mesh, finite element, Level Set method

Duration: 18 months (starting date : as soon as possible)

Skills
and abilities requested:

A working knowledge of both the theoretical aspect
of anisotropic framework and the practical difficulties of meshing is an
important asset. C++ programming skills are desirable. Proficiency of French,
although not compulsory, will be a selection criterion.

Gross salary:
about 34 000 € / year

Location: MINES ParisTech - CEMEF, Sophia
Antipolis (French Riviera), France

Team CIM : Advanced Computing (CEMEF)

Contact: Pr. Thierry Coupez

e-mail :
Thierry.Coupez@mines-paristech.fr