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Mechanics and High Performance Computing
Parallel algorithms and high performance computing in computational continuum mechanics
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Research activities of the Mechanics & High Performance Computing Group in 2017 covered a
range of topics in computational modeling and algorithm development in the area of multifield phe-
nomena, highly efficient parallel solution methods, model reduction, inverse analysis and uncertainty
quantification. Applications focused on mechanical models of the heart and the circulatory system,
the mechanobiology of atherosclerosis and abdominal aortic aneursyms and lately on the integration
and optimization of control algorithms with large-scale nonlinear computational models.
Hybrid Preconditioning for Surface-Coupled Problems
When solving coupled problems in a monolithic fashion,
powerful preconditioning techniques are crucial to obtain
an efficient solution scheme. In our group, we are inter-
ested in monolithic solvers for fluid-structure interaction
problems, where a fluid and a solid domain exchange
coupling information at their common coupling surface.
Starting from well-established physics-based block
preconditioners, that are known to accumulate the error
at the coupling surface, we developed a novel hybrid
preconditioner. It is based on an overlapping domain
decomposition, that purposely exhibits subdomains that
span across the fluid-structure interface. By performing
cheap but accurate subdomain solves in an additive
Schwarz manner in combination with the existing phys-
ics-based block preconditioners, the number of iterations
of the linear solver as well as the total solution time could
be reduced remarkably. Furthermore, scalability of the
proposed methods has been demonstrated.
Overlapping domain decomposition for hybrid FSI preconditioner
Uncertainty Quantification in Cardiovascular Mechanics
Personalized computational models in cardiovascular
mechanics as a predictive simulation tool represent a
promising approach for diagnosis and decision making in
clinical practice. Such models, however, require precise
knowledge about the individual geometry, boundary
conditions and material parameters. Since it is impossible
to exactly specify a simulation model on a patient-specific
basis, the best one can do is to incorporate all available
information into the model in a probabilistic manner. This
knowledge often stems from noisy input parameters or
is based on posterior statistic from Bayesian inference.
We are working on efficient UQ strategies that are able to
represent uncertainties in personalized simulations and
quantify their effects on the quantities of interest.
Predicted mean, confidence interval and reference solution for the peak
wall stress (PWS) of a personalized abdominal aortic aneurysm model. The
surrogate model was built from reference data points for an uncertain wall
thickness and can be used for rupture risk estimation.