Algebraic multigrid preconditioning of high-order spectral elements for elliptic problems on a simplicial mesh

Olson L

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Algebraic multigrid preconditioning of high-order spectral elements for elliptic problems on a simplicial mesh

机译：简单网格上椭圆问题的高阶谱元代数多重网格预处理

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Algebraic multigrid is investigated as a solver for linear systems that arise from high-order spectral element discretizations. An algorithm is introduced that utilizes the efficiency of low-order finite elements to precondition the high-order method in a multilevel setting. In particular, the efficacy of this approach is highlighted on simplexes in two and three dimensions with nodal spectral elements up to order n = 11. Additionally, a hybrid preconditioner is also developed for use with discontinuous spectral element methods. The latter approach is verified for the discontinuous Galerkin method on elliptic problems.

机译：研究代数多重网格作为线性系统的求解器，该线性系统由高阶频谱元素离散化产生。引入了一种算法，该算法利用低阶有限元的效率在多级设置中对高阶方法进行预处理。特别是，这种方法的有效性在二维和三维单纯形上得到了强调，其中节点频谱元素的阶数为n =11。此外，还开发了一种混合预处理器，用于不连续频谱元素方法。对于椭圆问题的不连续Galerkin方法，验证了后一种方法。

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《SIAM Journal on Scientific Computing》 |2007年第5期|共21页
作者
Olson L;
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正文语种 eng
中图分类工程基础科学;
关键词
spectral element; discontinuous Galerkin; algebraic multigrid; DISCONTINUOUS GALERKIN METHODS; EQUATIONS; APPROXIMATIONS; INTERPOLATION; SIMPLEX; FEKETE;

机译：光谱元素;间断Galerkin;代数多重网格;间断Galerkin方法;方程;逼近;插值;简单;FEKETE;

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1. ALGEBRAIC MULTIGRID PRECONDITIONING OF HIGH-ORDER SPECTRAL ELEMENTS FOR ELLIPTIC PROBLEMS ON A SIMPLICIAL MESH [J] . LUKE OLSON SIAM Journal on Scientific Computing . 2008,第5期

机译：简单网格上椭圆问题的高阶谱元素的代数多重网格预处理
2. Algebraic Multigrid Preconditioning for 3-D Magnetic Finite-Element Analyses Using Nodal Elements and Edge Elements [J] . Takeshi Mifune, Satoshi Isozaki, Takeshi Iwashita, IEEE Transactions on Magnetics . 2006,第4期

机译：使用节点元素和边缘元素进行3-D磁性有限元分析的代数多重网格预处理
3. PRECONDITIONING HIGHER ORDER FINITE ELEMENT SYSTEMS BY ALGEBRAIC MULTIGRID METHOD OF LINEAR ELEMENTS [J] . Yun-qing Huang, Shi Shu, Xi-jun Yu Journal of Computational Mathematics . 2006,第5期

机译：线性单元的代数多重网格法预处理高阶有限元系统
4. Spectral Element Agglomerate Algebraic Multigrid Methods for Elliptic Problems with High-Contrast Coefficients [C] . Yalchin Efendiev, Juan Galvis, Panayot S. Vassilevski International conference on domain decomposition . 2011

机译：光谱元素集聚代数多重射线多重型方法，用于高对比度系数的椭圆问题
5. Element-based algebraic multigrid (AMGe) and spectral AMGe. [D] . Chartier, Timothy P. 2001

机译：基于元素的代数多重网格（AMGe）和频谱AMGe。
6. Algebraic Multigrid Preconditioner for the Cardiac Bidomain Model [O] . Gernot Plank, Manfred Liebmann, Rodrigo Weber dos Santos, -1

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7. A Parallel Algebraic Multigrid Preconditioner Using Algebraic Multicolor Ordering for Magnetic Finite Element Analyses [O] . Mifune T., Obata N., Iwashita T., 2006

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Algebraic multigrid preconditioning of high-order spectral elements for elliptic problems on a simplicial mesh

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