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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
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