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

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.