A reduced computational and geometrical framework for inverse problems in hemodynamics

Lassila, Toni; Manzoni, Andrea; Quarteroni, Alfio; Rozza, Gianluigi

doi:10.1002/cnm.2559

Cited by 104 publications

(112 citation statements)

References 69 publications

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“…• In [147], the authors use the reduced basis method (section 4.3) to create a reduced model of nonlinear viscous flows with varying Young's modulus and varying geometrical parameters, representing arterial wall shape in a fluidstructure interaction problem with a stenosis and a shape optimization process of an arterial bypass. They achieve a reduction from a full model of state dimension 35,000 to a reduced model of state dimension 20 while maintaining accuracy levels of O(10 −2 ) in the vorticity estimates for the shape optimization process, and a reduction from a full model of state dimension 16,000 to a reduced model of state dimension 8 while maintaining accuracy levels of O(10 −2 ) in the viscous energy dissipation estimates for the fluid-structure interaction simulation in presence of a stenosis in the arterial branch.…”

Section: Parametric Model Reduction In Actionmentioning

confidence: 99%

A Survey of Projection-Based Model Reduction Methods for Parametric Dynamical Systems

2015

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Abstract. Numerical simulation of large-scale dynamical systems plays a fundamental role in studying a wide range of complex physical phenomena; however, the inherent large-scale nature of the models often leads to unmanageable demands on computational resources. Model reduction aims to reduce this computational burden by generating reduced models that are faster and cheaper to simulate, yet accurately represent the original large-scale system behavior. Model reduction of linear, nonparametric dynamical systems has reached a considerable level of maturity, as reflected by several survey papers and books. However, parametric model reduction has emerged only more recently as an important and vibrant research area, with several recent advances making a survey paper timely. Thus, this paper aims to provide a resource that draws together recent contributions in different communities to survey the state of the art in parametric model reduction methods. Parametric model reduction targets the broad class of problems for which the equations governing the system behavior depend on a set of parameters. Examples include parameterized partial differential equations and large-scale systems of parameterized ordinary differential equations. The goal of parametric model reduction is to generate low-cost but accurate models that characterize system response for different values of the parameters. This paper surveys state-of-the-art methods in projection-based parametric model reduction, describing the different approaches within each class of methods for handling parametric variation and providing a comparative discussion that lends insights to potential advantages and disadvantages in applying each of the methods. We highlight the important role played by parametric model reduction in design, control, optimization, and uncertainty quantification-settings that require repeated model evaluations over different parameter values.

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Section: Parametric Model Reduction In Actionmentioning

confidence: 99%

A Survey of Projection-Based Model Reduction Methods for Parametric Dynamical Systems

2015

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“…Ad hoc reduced order modelling techniques have recently been proposed for optimal flow control problems [104,108,121], optimal shape design of devices related with fluid flows [6,58,23,88], and the treatment of fluid-structure interaction problems [76,78].…”

Section: Discussionmentioning

confidence: 99%

“…We do not provide any detail about the evaluation of these quantities; the interested reader can refer, for instance, to [76,87,94,124].…”

Section: Certification Of Roms For the Steady Navier-stokes Equationsmentioning

confidence: 99%

Model Order Reduction in Fluid Dynamics: Challenges and Perspectives

Lassila

Manzoni

Quarteroni

et al. 2014

Reduced Order Methods for Modeling and Computational Reduction

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This chapter reviews techniques of model reduction of fluid dynamics systems. Fluid systems are known to be difficult to reduce efficiently due to several reasons. First of all, they exhibit strong nonlinearities -which are mainly related either to nonlinear convection terms and/or some geometric variability -that often cannot be treated by simple linearization. Additional difficulties arise when attempting model reduction of unsteady flows, especially when long-term transient behavior needs to be accurately predicted using reduced order models and more complex features, such as turbulence or multiphysics phenomena, have to be taken into consideration. We first discuss some general principles that apply to many parametric model order reduction problems, then we apply them on steady and unsteady viscous flows modelled by the incompressible Navier-Stokes equations. We address questions of inf-sup stability, certification through error estimation, computational issues and -in the unsteady case -long-time stability of the reduced model. Moreover, we provide an extensive list of literature references.

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“…The integration of the RBF parametrization technique within the reduced basis framework, as well as its application to blood flow simulation on geometries reconstructed from patient data, looks promising in its flexibility and ability to express a variety of shape deformations. Further elements that may be explored deal with the uncertainty quantification [5] and/or robust optimization and control problems [6] for patient-specific scenarios. …”

Section: Discussionmentioning

confidence: 99%

“…In the end, at the outer level a suitable iterative procedure for the optimization is performed. A brief presentation of the whole framework can be found in [8], while a more detailed analysis has been recently addressed in [5,6].…”

Section: A General Strategy For Reduction In Shape Dependent Flowsmentioning

confidence: 99%

Reduction Strategies for Shape Dependent Inverse Problems in Haemodynamics

Lassila

Manzoni

Rozza

2013

IFIP Advances in Information and Communication Technology

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Abstract. This work deals with the development and application of reduction strategies for real-time and many query problems arising in fluid dynamics, such as shape optimization, shape registration (reconstruction), and shape parametrization. The proposed strategy is based on the coupling between reduced basis methods for the reduction of computational complexity and suitable shape parametrizations -such as free-form deformations or radial basis functions -for low-dimensional geometrical description. Our focus is on problems arising in haemodynamics: efficient shape parametrization of cardiovascular geometries (e.g. bypass grafts, carotid artery bifurcation, stenosed artery sections) for the rapid blood flow simulation -and related output evaluation -in domains of variable shape (e.g. vessels in presence of growing stenosis) provide an example of a class of problems which can be recast in the real-time or in the manyquery context.

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A reduced computational and geometrical framework for inverse problems in hemodynamics

Cited by 104 publications

References 69 publications

A Survey of Projection-Based Model Reduction Methods for Parametric Dynamical Systems

A Survey of Projection-Based Model Reduction Methods for Parametric Dynamical Systems

Model Order Reduction in Fluid Dynamics: Challenges and Perspectives

Reduction Strategies for Shape Dependent Inverse Problems in Haemodynamics

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