Free-form deformation of solid geometric models
SIGGRAPH '86 Proceedings of the 13th annual conference on Computer graphics and interactive techniques
The reduced basis method for incompressible viscous flow calculations
SIAM Journal on Scientific and Statistical Computing
A reduced-order method for simulation and control of fluid flows
Journal of Computational Physics
Curves and surfaces for CAGD: a practical guide
Curves and surfaces for CAGD: a practical guide
Spectral Methods: Evolution to Complex Geometries and Applications to Fluid Dynamics (Scientific Computation)
SIAM Journal on Numerical Analysis
Reduced basis methods for Stokes equations in domains with non-affine parameter dependence
Computing and Visualization in Science
Numerical Approximation of Partial Differential Equations
Numerical Approximation of Partial Differential Equations
A Posteriori Error Analysis of the Reduced Basis Method for Nonaffine Parametrized Nonlinear PDEs
SIAM Journal on Numerical Analysis
The BFGS algorithm for a nonlinear least squares problem arising from blood flow in arteries
Computers & Mathematics with Applications
Comparison Between Reduced Basis and Stochastic Collocation Methods for Elliptic Problems
Journal of Scientific Computing
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We present a new model reduction technique for steady fluid-structure interaction problems. When the fluid domain deformation is suitably parametrized, the coupling conditions between the fluid and the structure can be formulated in the low-dimensional space of geometric parameters. Moreover, we apply the reduced basis method to reduce the cost of repeated fluid solutions necessary to achieve convergence of fluid-structure iterations. In this way a reduced order model with reliable a posteriori error bounds is obtained. The proposed method is validated with an example of steady Stokes flow in an axisymmetric channel, where the structure is described by a simple one-dimensional generalized string model. We demonstrate rapid convergence of the reduced solution of the parametrically coupled problem as the number of geometric parameters is increased.