A Schur complement formulation for solving free-boundary, Stefan problems of phase change

Lun, Lisa; Yeckel, Andrew; Derby, Jeffrey J.

doi:10.1016/j.jcp.2010.06.046

Cited by 3 publications

(2 citation statements)

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“…If one can solve the sub-matrices A and S to a prescribed tolerance, the matrix A is solved in one pass without generating a Krylov subspace. This is commonly known as the Schur complement reduction (SCR) or segregated approach [6,24,25,26]. In contrast, the aforementioned strategy, where A is solved by a preconditioned iterative method, is referred to as the coupled approach [6].…”

Section: Projection Methods and Block Preconditionersmentioning

confidence: 99%

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A robust and efficient iterative method for hyper-elastodynamics with nested block preconditioning

Marsden

2019

Journal of Computational Physics

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We develop a robust and efficient iterative method for hyper-elastodynamics based on a novel continuum formulation recently developed in [1]. The numerical scheme is constructed based on the variational multiscale formulation and the generalized-α method. Within the nonlinear solution procedure, a block factorization is performed for the consistent tangent matrix to decouple the kinematics from the balance laws. Within the linear solution procedure, another block factorization is performed to decouple the mass balance equation from the linear momentum balance equations. A nested block preconditioning technique is proposed to combine the Schur complement reduction approach with the fully coupled approach. This preconditioning technique, together with the Krylov subspace method, constitutes a novel iterative method for solving hyper-elastodynamics. We demonstrate the efficacy of the proposed preconditioning technique by comparing with the SIMPLE preconditioner and the one-level domain decomposition preconditioner. Two representative examples are studied: the compression of an isotropic hyperelastic cube and the tensile test of a fully-incompressible anisotropic hyperelastic arterial wall model. The robustness with respect to material properties and the parallel performance of the preconditioner are examined.

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Section: Projection Methods and Block Preconditionersmentioning

confidence: 99%

“…The upper triangular block matrix problem can be solved by a back substitution. Consequently, the solution procedure for Ax = r can be summarized as the following segregated algorithm [24,25,26].…”

Section: Schur Complement Reductionmentioning

confidence: 99%