Iterative solution methods
Block-Triangular Preconditioners for Saddle Point Problems with a Penalty Term
SIAM Journal on Scientific Computing
Nonlinearly Preconditioned Inexact Newton Algorithms
SIAM Journal on Scientific Computing
Block triangular preconditioners for symmetric saddle-point problems
Applied Numerical Mathematics - Numerical algorithms, parallelism and applications
Block Preconditioners Based on Approximate Commutators
SIAM Journal on Scientific Computing
Fluid-structure partitioned procedures based on Robin transmission conditions
Journal of Computational Physics
Splitting Methods Based on Algebraic Factorization for Fluid-Structure Interaction
SIAM Journal on Scientific Computing
Algebraic multigrid preconditioners for the bidomain reaction--diffusion system
Applied Numerical Mathematics
Journal of Computational Physics
A Newton method using exact jacobians for solving fluid-structure coupling
Computers and Structures
Robin Based Semi-Implicit Coupling in Fluid-Structure Interaction: Stability Analysis and Numerics
SIAM Journal on Scientific Computing
Two-Level Newton and Hybrid Schwarz Preconditioners for Fluid-Structure Interaction
SIAM Journal on Scientific Computing
On the physical consistency between three-dimensional and one-dimensional models in haemodynamics
Journal of Computational Physics
On the continuity of mean total normal stress in geometrical multiscale cardiovascular problems
Journal of Computational Physics
Journal of Computational and Applied Mathematics
Hi-index | 0.02 |
The increasing computational load required by most applications and the limits in hardware performances affecting scientific computing contributed in the last decades to the development of parallel software and architectures. In fluid-structure interaction (FSI) for haemodynamic applications, parallelization and scalability are key issues (see [L. Formaggia, A. Quarteroni, and A. Veneziani, eds., Cardiovascular Mathematics: Modeling and Simulation of the Circulatory System, Modeling, Simulation and Applications 1, Springer, Milan, 2009]). In this work we introduce a class of parallel preconditioners for the FSI problem obtained by exploiting the block-structure of the linear system. We stress the possibility of extending the approach to a general linear system with a block-structure, then we provide a bound in the condition number of the preconditioned system in terms of the conditioning of the preconditioned diagonal blocks, and finally we show that the construction and evaluation of the devised preconditioner is modular. The preconditioners are tested on a benchmark three-dimensional (3D) geometry discretized in both a coarse and a fine mesh, as well as on two physiological aorta geometries. The simulations that we have performed show an advantage in using the block preconditioners introduced and confirm our theoretical results.