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A field-split preconditioning technique for fluid-structure interaction problems with applications in biomechanics.

Sara Calandrini1, Eugenio Aulisa2, Guoyi Ke3

  • 1Department of Scientific Computing, Florida State University, Tallahassee, Florida.

International Journal for Numerical Methods in Biomedical Engineering
|December 29, 2019
PubMed
Summary

A new field-split (FS) preconditioner enhances Krylov subspace algorithms for fluid-structure interaction (FSI) problems. This method, using geometric multigrid (GMG) and additive Schwarz (AS), shows promise for biomedical applications.

Keywords:
additive Schwarz preconditionerfield-split preconditionerfluid-structure interactionhemodynamics

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Area of Science:

  • Computational fluid dynamics
  • Biomedical engineering
  • Numerical analysis

Background:

  • Fluid-structure interaction (FSI) simulations are crucial for understanding complex biomechanical systems.
  • Solving large, linearized FSI systems efficiently is computationally demanding.
  • Existing preconditioning techniques may not fully capture the coupled physics in FSI.

Purpose of the Study:

  • To introduce a novel field-split (FS) preconditioning technique for Krylov subspace solvers applied to FSI problems.
  • To evaluate the effectiveness of the proposed FS preconditioner in biomedical FSI simulations.
  • To compare the performance of the FS preconditioner against a standard domain decomposition method.

Main Methods:

  • Development of a novel FS preconditioner utilizing physical variables for block splitting.
  • Integration of the FS preconditioner with a geometric multigrid (GMG) outer solver.
  • Application of an additive Schwarz (AS) block strategy to solve subsystems within the FS preconditioner.
  • Testing on 2D and 3D finite element discretizations of biomedical FSI problems (aneurysm, venous valve).

Main Results:

  • The proposed FS preconditioner demonstrates effective performance in solving FSI linearized systems.
  • Simulations involving aneurysm and venous valve geometries show the applicability of the method.
  • Comparative analysis indicates competitive or superior performance against pure domain decomposition preconditioners.

Conclusions:

  • The novel FS preconditioner is a viable and efficient technique for tackling complex FSI problems in biomedical engineering.
  • The combination of GMG and FS preconditioning offers a robust approach for FSI simulations.
  • Further research can explore extensions of this technique to other coupled physics problems.