4.6 Article

A IETI-DP method for discontinuous Galerkin discretizations in isogeometric analysis with inexact local solvers

期刊

出版社

WORLD SCIENTIFIC PUBL CO PTE LTD
DOI: 10.1142/S0218202523500495

关键词

Isogeometric analysis; FETI-DP; Fast Diagonalization; preconditioning

向作者/读者索取更多资源

In this paper, we develop solvers for an isogeometric multi-patch discretization using discontinuous Galerkin approach. We solve the resulting linear system using the Dual-Primal IsogEometric Tearing and Interconnecting (IETI-DP) method. We approximate the patch-local problems using the Fast Diagonalization method and introduce an orthogonal splitting of the local function spaces to obtain the tensor structure needed for the Fast Diagonalization method. The numerical experiments confirm the effectiveness of our approach and show good performance in both two-dimensional and three-dimensional problems.
We construct solvers for an isogeometric multi-patch discretization, where the patches are coupled via a discontinuous Galerkin approach, which allows for the consideration of discretizations that do not match on the interfaces. We solve the resulting linear system using a Dual-Primal IsogEometric Tearing and Interconnecting (IETI-DP) method. We are interested in solving the arising patch-local problems using iterative solvers since this allows for the reduction of the memory footprint. We solve the patch-local problems approximately using the Fast Diagonalization method, which is known to be robust in the grid size and the spline degree. To obtain the tensor structure needed for the application of the Fast Diagonalization method, we introduce an orthogonal splitting of the local function spaces. We present a convergence theory for two-dimensional problems that confirms that the condition number of the preconditioned system only grows poly-logarithmically with the grid size. The numerical experiments confirm this finding. Moreover, they show that the convergence of the overall solver only mildly depends on the spline degree. We observe a mild reduction of the computational times and a significant reduction of the memory requirements in comparison to standard IETI-DP solvers using sparse direct solvers for the local subproblems. Furthermore, the experiments indicate good scaling behavior on distributed memory machines. Additionally, we present an extension of the solver to three-dimensional problems and provide numerical experiments assessing good performance also in that setting.

作者

我是这篇论文的作者
点击您的名字以认领此论文并将其添加到您的个人资料中。

评论

主要评分

4.6
评分不足

次要评分

新颖性
-
重要性
-
科学严谨性
-
评价这篇论文

推荐

暂无数据
暂无数据