A semi-local spectral/hp element solver for linear elasticity problems. (English) Zbl 1352.74476
Summary: We develop an efficient semi-local method for speeding up the solution of linear systems arising in spectral/hp element discretization of the linear elasticity equations. The main idea is to approximate the element-wise residual distribution with a localization operator we introduce in this paper, and subsequently solve the local linear system. Additionally, we decouple the three directions of displacement in the localization operator, hence enabling the use of an efficient low energy preconditioner for the conjugate gradient solver. This approach is effective for both nodal and modal bases in the spectral/hp element method, but here, we focus on the modal hierarchical basis. In numerical tests, we verify that there is no loss of accuracy in the semi-local method, and we obtain good parallel scalability and substantial speed-up compared to the original formulation. In particular, our tests include both structure-only and fluid-structure interaction problems, with the latter modeling a 3D patient-specific brain aneurysm.
MSC:
| 74S25 | Spectral and related methods applied to problems in solid mechanics |
| 74L15 | Biomechanical solid mechanics |
| 76Z05 | Physiological flows |
| 65M70 | Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs |
| 65M60 | Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs |
| 74B05 | Classical linear elasticity |
| 74S05 | Finite element methods applied to problems in solid mechanics |
Keywords:
spectral element method; high-order; preconditioner; FSI; flexible brain arteries; patient-specific aneurysmReferences:
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