Journal of Computational Physics
Choosing the forcing terms in an inexact Newton method
SIAM Journal on Scientific Computing - Special issue on iterative methods in numerical linear algebra; selected papers from the Colorado conference
Journal of Computational Physics
A Restricted Additive Schwarz Preconditioner for General Sparse Linear Systems
SIAM Journal on Scientific Computing
A review of algebraic multigrid
Journal of Computational and Applied Mathematics - Special issue on numerical analysis 2000 Vol. VII: partial differential equations
Iterative Methods for Sparse Linear Systems
Iterative Methods for Sparse Linear Systems
A Dual-Primal FETI method for incompressible Stokes equations
Numerische Mathematik
Splitting Methods Based on Algebraic Factorization for Fluid-Structure Interaction
SIAM Journal on Scientific Computing
Multilevel Additive Schwarz Preconditioners for the Bidomain Reaction-Diffusion System
SIAM Journal on Scientific Computing
Journal of Computational Physics
An Overlapping Schwarz Algorithm for Almost Incompressible Elasticity
SIAM Journal on Numerical Analysis
Journal of Computational Physics
Parallel Algorithms for Fluid-Structure Interaction Problems in Haemodynamics
SIAM Journal on Scientific Computing
Multiphysics simulations: Challenges and opportunities
International Journal of High Performance Computing Applications
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We introduce and study numerically a two-level Schwarz preconditioner for Newton-Krylov methods for fluid-structure interaction, with special consideration of the application area of simulating blood flow. Our approach monolithically couples the fluid to the structure on both fine and coarse grids and in the subdomain solves, insuring that there is multiphysics coupling during all aspects of the algorithm. The fluid-structure system is discretized on unstructured nonnested meshes, with an overlapping additive domain decomposition on both coarse and fine levels and multiplicative Schwarz preconditioning between levels. We investigate the effect of different coarse discretization sizes, solver stopping criteria, and overlap size, and we demonstrate that the method is robust to physical parameters including the structure's Young's modulus and the timestep size. Finally, we show effective preconditioning of the complicated coupled system, with nearly perfect weak scaling to a thousand processors and millions of unknowns.