arXiv subjects

Guoyi Ke

Publications and source records attributed to Guoyi Ke.

3 recordsLinked to original sources

arXiv2019

A computational study of preconditioning techniques for the stochastic diffusion equation with lognormal coefficient

We present a computational study of several preconditioning techniques for the GMRES algorithm applied to the stochastic diffusion equation with a lognormal coefficient discretized with the stochastic Galerkin method. The clear block structure of the system matrix arising from this type of discretization motivates the analysis of preconditioners designed according to a field-splitting strategy of the stochastic variables. This approach is inspired by a similar procedure used within the framework of physics based preconditioners for deterministic problems, and its application to stochastic PDEs represents the main novelty of this work. Our numerical investigation highlights the superior properties of the field-split type preconditioners over other existing strategies in terms of computational time and stochastic parameter dependence.

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arXiv2019

A field-split preconditioning technique for fluid-structure interaction problems with applications in biomechanics

We present a novel preconditioning technique for Krylov subspace algorithms to solve fluid-structure interaction (FSI) linearized systems arising from finite element discretizations. An outer Krylov subspace solver preconditioned with a geometric multigrid (GMG) algorithm is used, where for the multigrid level sub-solvers, a field-split (FS) preconditioner is proposed. The block structure of the FS preconditioner is derived using the physical variables as splitting strategy. To solve the subsystems originated by the FS preconditioning, an additive Schwarz (AS) block strategy is employed. The proposed field-split preconditioner is tested on biomedical FSI applications. Both 2D and 3D simulations are carried out considering aneurysm and venous valve geometries. The performance of the FS preconditioner is compared with that of a second preconditioner of pure domain decomposition type.

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arXiv2018

Construction of h-refined continuous finite element spaces with arbitrary hanging node configurations and applications to multigrid algorithms

We present a novel approach for the construction of basis functions to be employed in selective or adaptive h-refined finite element applications with arbitrary-level hanging node configurations. Our analysis is not restricted to $1$-irregular meshes, as it is usually done in the literature, allowing our results to be applicable to a broader class of local refinement strategies. The proposed method does not require the solution of any linear system to obtain the constraints necessary to enforce continuity of the basis functions and it can be easily implemented. A mathematical analysis is carried out to prove that the proposed basis functions are continuous and linearly independent. Finite element spaces are then defined as the spanning sets of such functions, and the implementation of a multigrid algorithm built on these spaces is discussed. A spectral analysis of the multigrid algorithm highlights superior convergence properties of the proposed method over existing strategies based on a local smoothing procedure. Finally, linear and nonlinear numerical examples are tested to show the robustness and versatility of the multigrid algorithm.

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