CHANGE
New CHallenges for (adaptive) PDE solvers: the interplay of ANalysis and GEometry
ERC-2015-AdG, 2016 - 2022
PI: ECOLE POLYTECHNIQUE FEDERALE DE LAUSANNE (EPFL), Buffa Annalisa
Beneficiaries:
2. CONSIGLIO NAZIONALE DELLE RICERCHE (CNR-IMATI), Roma, Italy,
3. UNIVERSITAT LINZ (JKU-LINZ), Linz, Austria,
4. OESTERREICHISCHE AKADEMIE DER WISSENSCHAFTEN (RICAM), Linz/Wien, Austria
MOTOR
Multi-ObjecTive design Optimization of fluid eneRgy machines
EU H2020-FoF-2015, 2015 - 2018
VORONOI++
I 1836 international projects, Lead Agency Verfahren; DACH: FWF
06/2015 - 05/2018
Projectpartner: TU Graz, Institute for Theoretical Computer Science
EXAMPLE
Exact and Adaptive Modeling and Simulation of the Air Passage of Aircraft Engines
EU FP7-PEOPLE-2012-IAPP, 2013 - 2016
Links: EXAMPLE, EU, Projectpartner: MTU Aero Engines AG
FWF NFN S117 Geometry + Simulation
National Research Network (NFN) funded by FWF, 2012 - 2016, extended until 2020.
Part 1 "Coordination and Service", Part 7 "Geometric Modeling for Numerical Simulation".
Links: FWF, G+S.
Projectpartner: Johannes Kepler University,
Computational Mathematics, Linz, Austria
Austrian Academy of Sciences,
RICAM, Linz, Austria
University of Vienna,
Computational Science Center, Vienna, Austria
Universität Bonn,
Numerical Simulation, Bonn, Germany
ÖAD WTZ Czech Republic CZ 06/2012
Exact and Approximate Description of Shapes for Geometric Modelling
Wissenschaftlich-Technische Zusammenarbeit (WTZ) mit der University of West Bohemia Pilsen (Tschechische Republik) der bilateralen Aktionen des ÖAD, 2012-2013.
INSIST
Integrating Numerical Simulation and Geometric Design Technology
Networks for Initial Training (ITN), 7th Framework programme of the EU, 2012-2015.
Links: INSIST
TERRIFIC
Towards Enhanced Integration of Design and Production in the
Factory of the Future through Isogeometric Technologies
Collaborative project, 7th Framework programme of the EU, 2011-2014.
Medial Axis Computation
Part of the ESF EUROCORES programm VORONOI - Spatial Decompositions and Graphs, 2011 - 2014
PARADISE
Parameterization of computational domains for isogeometric analysis
PEOPLE MARIE CURIE ACTIONS Intra-European Fellowships (IEF) 7th Framework Programme of the EU, 2011-2013.
The institutes serves as host and coordinator of the Marie-Curie-Fellowship of Dr. Carlotta Giannelli.
Links:
EU Marie Curie
AKTION 2009/5
Effective Methods of Algebraic Geometry for Geometric Modelling and Industrial
Applications
Bilaterales Projekt mit der University of West Bohemia Pilsen (Tschechische Republik) der bilateralen Aktionen des ÖAD, 2009-2010.
This cientific programme is devoted both to the theoretical fundamentals
of CAD and to the various computational aspects of applications. We want to
focus on the following relations between Algebraic Geometry and fields from
Applied Geometry: Novel geometric representations and their applications,
Symbolic and numeric techniques for geometric computing, Real algebraic geometry
and for CAD solids.
Links: ÖAD,
University of West Bohemia Pilsen: RNDr. Miroslav LAVICKA
SL 09/2009
Approximation and Geometric Computing mit höherwertigen Beschreibungen geometrischer
Objekte (AGARGO)
Bilateral project with the University of Ljubljana (Slowenien), funded by the WTZ-Programme of the ÖAD, 2009-2010.
The project is devoted to advanced geometric representations, in particular to
Pythagorean hodograph (PH) curves and to surfaces in support function
representation. Compared to standard representations of geometry, the use of
advanced ones provides additional geometric properties, such as the
availability of exact offset curves and surfaces or of exact arc length
functions. The project is to produce new scientific results concerning the
mathematical foundations of these representations.
Links: ÖAD,
University of Ljubljana: Prof. Jernej Kozak
ADOPT
Advanced Simulation-Based Design Methods for Pump Turbines (ADOPT)
Cooperative Research Project, fundet by the FFG, programme FIT-IT Visual Computing (2008-2011).
The project is devoted to improving the design process of blades for hydroelectric
turbines. In particular it deals with the class of pump turbines, which are
used both for generating energy and as pumps. For this important class of
turbines, it is planned to improve the integration of numerical simulation
and the CAD-based design process.
Links: FFG, Projektpartner
VA Tech HYDRO
SAGA
Shapes, Geometry and Algebra
Marie Curie Initial Training Network (ITN), 7th Framework programme of the EU, 2008-2012.
The activities of this network shall be devoted to the mathematical foundations
of Computer-Aided Design. The following four research ares will be addressed:
(1) Change of Representation, (2) Geometric Computing - Algebraic Tools, (3)
Algebraic Geometry for CAD Applications, (4) Practical Industrial Problems.
Links: SAGA,
Open positions,
CATT success story
EXCITING
Exact Geometry Simulation for Optimized Design of Vehicles and Vessels
Collaborative Project, 7th framework programme of the EU, 2008-2011.
The project is devoted to the numerical simulation and the design optomization
for the class of functional free-form surfaces. In particular it will focus
on applications from the field of surface transportation. Based on the novel
paradigm of Isogeometric Analysis (T. Hughes 2004), which allows to use an
exact geometry representation for numerical simulation, it is planned to create
a new class of tools for numerical simulation. The institute acts as coordinator
of the EXCITING consortium.
Links: EXCITING,
CATT
success story
DK W1214
Doktoratskolleg: Computational Mathematics: Numerical Analysis and Symbolic
Computation
Doktoratskolleg W1214, 2008-2011, funded by the FWF.
The doctoral school aims at providing research training for PhD students
in two fundamental areas of computational mathematics: Numerical Analsyis
and Symbolic Computation. The institute participates with a project on "Geometric
Solvers for Polynomial Systems".
Links: FWF, DK
NFN S92
Industrial Geometry / Dynamic Spline Surfaces
National Research Network (NFN) S92 "Industrial Geometry",
Subprojects 1 "Coordination and Service, Knowledge Transfer and Sustainability"
2005-2008,
and 2 "Dynamic Spline Surfaces", 2005-2011, funded by the FWF Nationales
Forschungsnetzwerk (NFN).
The activities of the research network aims at supporting the cooperation and ineraction between the different fields of application-oriented geometric research. These include Computer Aided Geometric design, Computational geometry, Image Processing, Kinematics and Robotics. During the first funding period, our institute has coordinated the activities of the research network.
Subproject 2 is devoted to dynamic spline surfaces. Among other topics, it
deals with the reconstruction of geometric objects from measurement data.
Another topic is the use of nonlinear geometric primitives for geometric computations.
Links: FWF,
IG
(Industrial Geometry);
Projektpartner: Universitäten
TU Wien, Graz,
Universität Wien
ES 111/2007
Advancing the Geometric Fundamentals of Computer-Aided Design
Bilateral project with the University of Cantabria (Spanien), funded by the WTZ-Programme of the ÖAD, 2007-2008.
The cooperation focuses on various questions which are related to the use
of new methaical methods in Computer Aided Design. This involves results from
different areas of mathematics and computer science,
ranging from numerical analysis to symbolic computation.
Links: ÖAD, University
of Cantabria: Prof. Laureano Gonzalez-Vega
SFB F013
Computational techniques for algebraic spline surfaces
Special research programme (SFB) F013 "Numerical and Symbolic Scientific Computing", subproject 15 "Computational techniques for algebraic spline surfaces" (2001-2008), funded by the FWF.
The project is devoted to numerical and symbolic methods for free--form curves
and surfaces. It is dealt with in cooperation with Dr. Josef Schicho (RICAM).
In particular, computational techniques for approximate implicitization and
approx8imate parameterization of surfaces have been studied.
Links: FWF, SFB,
RICAM
ISIS
Intelligent 3D Geometry reconstruction using dynamic and evolution-based techniques
Marie Curie Incoming International Fellowship, 6th Framework Programme of the EU, 2006-2008
The institutes served as host and coordinator of the
Marie-Curie-Fellowship of Dr. Huaiping Yang. The research programme
focused mainly on intelligent techniques for 3D geometry
reconstruction.
Links: EU
P17387-N12
Pythagorean hodograph curves and surfaces
Stand-alone Project P17387-N12, 2004-2007, supported by the FWF
This project was devoted to the class of Pythagorean hodograph curves
and surfaces. As an important advantage, these curves and surfaces
have rational offsets. In addition, the arc length can be evaluated
exactly, which is helpful for applications in numerically controlled
machining.
Links: FWF
GAIA II
Intersection algorithms for geometry based IT-applications using
approximate algebraic methods
Collaborative Project, 5th Framework programme of the EU, contract no. IST 2001-35512, 2002-2005
The institute took partner in the GAIA II project. The aim of the
project was to derive a new class of robust algorithms for detecting
and computing intersection curves (in particular self-intersections)
in Computer Aided Design.
Links: GAIA 2
COMPASS
Workshop on Computational Methods for Algebraic Spline Surfaces
ESF Exploratory workshop, funded by the European Science Foundation
The first such workshop was held in September 2003.
It has brought together experts from the two fields of algebraic geometry
and applied geometry, thereby supporting the scientific exchange between both
fields. Further workshops were held in 2005 and 2007.
Links: Springer
Proceedings 2003, Proceedings
2005
Research activities, Main Topics
The research activities of the department are devoted to applications of geometry in various branches of mathematics and engineering; in particular focusing on scientific computing. Among others, the following topics are studied / have been studied:
-
Computer Aided Geometric Design (CAGD),
"reverse engineering",
shape-preserving methods for generating
curves and surfaces,
-
Applications of (classical) algebraic geometry,
approximate implicitisation and parameterization
parameterization of special algebraic surfaces (SFB F013),
(GAIA II).
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Kinematics and Robotics,
rational rigid body motions,
spline-interpolation for industrial robots,
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Differential Geometry,
affine surface theory,
geometrical conditions of contact / Characterization of geometric continuity,
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Geometrical applications of approximation theory,
discussion of approximation orders,
dual bases