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A sparse-grid isogeometric solver
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DOI：10.1016/j.cma.2018.02.017.png)
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摘要
En 中文
Isogeometric Analysis (IGA) typically adopts tensor-product splines and NURBS as a basis for the approximation of the solution of PDEs. In this work, we investigate to which extent IGA solvers can benefit from the so-called sparse-grids construction in its combination technique form, which was first introduced in the early 90s in the context of the approximation of high-dimensional PDEs. The tests that we report show that, in accordance to the literature, a sparse-grid construction can indeed be useful if the solution of the PDE at hand is sufficiently smooth. Sparse grids can also be useful in the case of non-smooth solutions when some a-priori knowledge on the location of the singularities of the solution can be exploited to devise suitable non-equispaced meshes. Finally, we remark that sparse grids can be seen as a simple way to parallelize pre-existing serial IGA solvers in a straightforward fashion, which can be beneficial in many practical situations. (C) 2018 Elsevier B.V. All rights reserved.
Keyword:
Isogeometric analysis
B-splines
NURBS
Sparse grids
Combination technique
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IF:
7.3
论文数:
1.3W
被引数:
5.6W
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分享收藏Higher order sparse grid methods for elliptic partial differential equations with variable coefficients.png)
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