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- Reduced Basis Modeling of Hierarchical Flow Systems
(147044/431) is funded by The Research
Council of Norway under the program
BeMatA
for the period 2002-2006.
- Project Description:
- Reduced basis methods are particularly attractive to use in
order to reduce the number of degrees-of-freedom associated
with a given numerical approximation to a set of partial
differential equations; the computational complexity can be
reduced to a level where potentially very complex systems
can be simulated. The main idea is to construct basis
functions with a large information content in order to
reduce the number of basis coefficients needed to reach a
certain level of accuracy in the outputs of interest. In
this project, we propose to develop and analyze reduced
basis methods for simulating hierarchical flow systems,
which is of relevance for studying flow in a set of arteries
or veins, flow in a respiratory system, or flow in a network
of pipes. We propose to decompose the geometry into generic
parts (e.g., pipes and bifurcations), and to construct a
reduced basis for these generic parts by considering
representative geometric snapshots. The global system will
be constructed by gluing the individual basis solutions
together via Lagrange multipliers. As far as we know, the
use of reduced basis methods have previously benn limited to
finite-dimensional parameter spaces; defining the geometry
as a generic "parameter" appears to be new. For more
detailed information, dowload
the original proposal and project description.
- Project Manager:
- Professor Einar
M. Rønquist, Norwegian University of Science and
Technology, Department of Mathematics; ronquist@math.ntnu.no
- PhD Candidate:
- Alf Emil Løvgren , Norwegian
University of Science and Technology, Department of
Mathematics; alfemil@math.ntnu.no
- Publications:
- Y. Maday and E.M. Rønquist, A reduced-basis element method,
C. R. Acad. Sci. Paris, Ser. I, Vol. 335, pp. 195-200, 2002.
- Y. Maday and E.M. Rønquist, A Reduced-Basis Element Method,
J. Sci. Comput., Vol. 17(1-4):447-459, 2002.
- Y. Maday and E.M. Rønquist, The Reduced-Basis Element
Method: Application to a Thermal Fin Problem,
Preprint Numerics No. 6/2002, NTNU,
to appear in SIAM Journal on Scientific Computing.
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