GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems
SIAM Journal on Scientific and Statistical Computing
Viscous flow with large free surface motion
Computer Methods in Applied Mechanics and Engineering
A three-dimensional computational method for blood flow in the heart. II. contractile fibers
Journal of Computational Physics
Stability of higher-order Hood-Taylor methods
SIAM Journal on Numerical Analysis
A Note on Preconditioning for Indefinite Linear Systems
SIAM Journal on Scientific Computing
Efficient preconditioning of the linearized Navier—Stokes equations for incompressible flow
Journal of Computational and Applied Mathematics - Special issue on numerical analysis 2000 Vol. VII: partial differential equations
A Preconditioner for the Steady-State Navier--Stokes Equations
SIAM Journal on Scientific Computing
A three-dimensional computer model of the human heart for studying cardiac fluid dynamics
ACM SIGGRAPH Computer Graphics
Multilevel First-Order System Least Squares for Elliptic Grid Generation
SIAM Journal on Numerical Analysis
Multilevel First-Order System Least Squares for Nonlinear Elliptic Partial Differential Equations
SIAM Journal on Numerical Analysis
Adaptive tetrahedral meshing in free-surface flow
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
Sharp interface Cartesian grid method III: Solidification of pure materials and binary solutions
Journal of Computational Physics
Comparison of various fluid-structure interaction methods for deformable bodies
Computers and Structures
Triangulation of p-Order Parametric Surfaces
Journal of Scientific Computing
SIAM Journal on Scientific Computing
Splitting Methods Based on Algebraic Factorization for Fluid-Structure Interaction
SIAM Journal on Scientific Computing
A Newton method using exact jacobians for solving fluid-structure coupling
Computers and Structures
Fluid-structure interaction in blood flows on geometries based on medical imaging
Computers and Structures
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This paper presents an efficient numerical solver for the finite element approximation of the incompressible Navier-Stokes equations within a moving three-dimensional domain. The moving domain is modeled using the arbitrary Lagrangian-Eulerian (ALE) formulation. Applying a finite element approximation leads to the solution of a large sparse system of equations. In this work we look at the application of the $Fp$ preconditioner within GMRES for efficiently solving such systems. Numerical results are presented for tetrahedral and hexahedral elements, and both structured and unstructured meshes. In all cases GMRES convergence rates are seen to be independent of mesh size. Finally, we show an application of this problem for modeling fluid flow within the heart.