An efficient preconditioner for monolithically-coupled large-displacement fluid–structure interaction problems with pseudo-solid mesh updates

We present a block preconditioner for the efficient solution of the linear systems that arise when employing Newton’s method to solve monolithically-coupled large-displacement fluid–structure interaction problems in which the update of the moving fluid mesh is performed by the equations of large-displacement elasticity. Following a theoretical analysis of the preconditioner, we propose an efficient implementation that yields a solver with near-optimal computational cost, in the sense that the time for the solution of the linear systems scales approximately linearly with the number of unknowns. We evaluate the performance of the preconditioner in selected two- and three-dimensional test problems.