TY - JOUR

T1 - Space/time multigrid for a fluid-structure-interaction problem

AU - Brummelen, van, E.H.

AU - Zee, van der, K.G.

AU - Borst, de, R.

PY - 2008

Y1 - 2008

N2 - The basic iterative method for solving fluid–structure-interaction problems is a defect-correction process based on a partitioning of the underlying operator into a fluid part and a structural part. In the present work we establish for a prototypical model problem that this defect-correction process yields an excellent smoother for multigrid, on account of the relative compactness of the fluid part of the operator with respect to the structural part. We show that the defect-correction process in fact represents an asymptotically-perfect smoother, i.e., the effectiveness of the smoother increases as the mesh is refined. Consequently, on sufficiently fine meshes the fluid–structure-interaction problem can be solved to arbitrary accuracy by one iteration of the defect-correction process followed by a coarse-grid correction. Another important property of the defect-correction process is that it smoothens the error in space/time, so that the coarsening in the multigrid method can be applied in both space and time.

AB - The basic iterative method for solving fluid–structure-interaction problems is a defect-correction process based on a partitioning of the underlying operator into a fluid part and a structural part. In the present work we establish for a prototypical model problem that this defect-correction process yields an excellent smoother for multigrid, on account of the relative compactness of the fluid part of the operator with respect to the structural part. We show that the defect-correction process in fact represents an asymptotically-perfect smoother, i.e., the effectiveness of the smoother increases as the mesh is refined. Consequently, on sufficiently fine meshes the fluid–structure-interaction problem can be solved to arbitrary accuracy by one iteration of the defect-correction process followed by a coarse-grid correction. Another important property of the defect-correction process is that it smoothens the error in space/time, so that the coarsening in the multigrid method can be applied in both space and time.

U2 - 10.1016/j.apnum.2007.11.012

DO - 10.1016/j.apnum.2007.11.012

M3 - Article

SN - 0168-9274

VL - 58

SP - 1951

EP - 1971

JO - Applied Numerical Mathematics

JF - Applied Numerical Mathematics

IS - 12

ER -