A
short course
January
24 and 25, 2019
Aula
Dal Passo
Dipartimento di MatematicaUniversità
di Roma "Tor Vergata"
Schedule:
Abstract
Over the
last fifty years, computer simulations have
dramatically increased their impact on research,
design and production, and are now an
indispensable tool for development and innovation
in science and technology. Partial Differential
Equations (PDEs) offer a broad and flexible
framework for modelling and analysing a number of
phenomena arising in fields as diverse as physics,
engineering, biology, and medicine. Not
surprisingly, research on methods to simulate PDEs
have a central role in modern science. In
reality, the simulation of PDEs is a brick within
a workflow where, at the beginning, the
geometrical entities are created, described and
manipulated with a geometry processor, often
through Computer-Aided Design systems (CAD), and
then used as input in Computer-Aided Engineering
systems (CAE) where they are handled and processed
for the simulation. The representation of
geometric entities has its roots in geometric
modelling, and often the requirements of shape
design are different from those of simulation,
which is based on numerical methods for PDEs. The
simulation of PDEs on CAD geometries (which are
mainly represented through their boundaries) calls
then for (re-)meshing and re-interpolation
techniques that are computationally expensive and
result in non-exact geometries as well as
inaccurate solutions.
In this
course, A. Buffa will give an introduction to the
recent scientific efforts devoted to tackle this
bottleneck both from the perspective of geometric
modelling and of the numerical analysis of PDEs.
From volumetric modelling to the framework of
isogeometric analysis, within a mathematical
perspective, she will provide an overview of the
state of the art and of the many questions that
are still open.
Annalisa
Buffa is professor of Numerical Modelling and
Simulation at the Mathematical
Institute
of Computational Science and Engineering of the École
Polythechnique Fédé- rale de Lausanne; she is the
PI of the ERC Advanced Grant 2016-2021 CHANGE "New CHallenges for (adaptive)
PDE solvers: the interplay of ANalysis and
GEometry".
Among the many
invitations and awards, we recall the invitation to the ICM 2014
as speaker in the Numerical Analysis and Scientific
Computing section, the ICIAM Collatz Prize 2015, and the
election as a corresponding member of the Accademia dei
LIncei in 2018.
She is the
Jacques-Louis Lions Lecturer 2018.
Wikipedia
entry
This course is part of the MIUR Excellence Department Project awarded to the Department of Mathematics, University of Rome Tor Vergata, CUP E83C18000100006 |
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