scholarly journals Eigenvalue estimates and differential form Laplacians on Alexandrov spaces

2018 ◽  
Vol 371 (3-4) ◽  
pp. 1737-1767 ◽  
Author(s):  
John Lott
Keyword(s):  
Differential Form ◽  
Alexandrov Spaces ◽  
Eigenvalue Estimates

scholarly journals Extending the global-direction stencil with “face-area-weighted centroid” to unstructured finite volume discretization from integral form

2020 ◽  
Vol 2 (1) ◽  
Author(s):  
Lingfa Kong ◽  
Yidao Dong ◽  
Wei Liu ◽  
Huaibao Zhang
Keyword(s):  
Convergence Rate ◽  
Finite Volume ◽  
Differential Form ◽  
Integral Form ◽  
Finite Volume Methods ◽  
Reconstruction Method ◽  
Computational Accuracy ◽  
Face Area ◽  
Finite Volume Discretization ◽  
Skewness Reduction

AbstractAccuracy of unstructured finite volume discretization is greatly influenced by the gradient reconstruction. For the commonly used k-exact reconstruction method, the cell centroid is always chosen as the reference point to formulate the reconstructed function. But in some practical problems, such as the boundary layer, cells in this area are always set with high aspect ratio to improve the local field resolution, and if geometric centroid is still utilized for the spatial discretization, the severe grid skewness cannot be avoided, which is adverse to the numerical performance of unstructured finite volume solver. In previous work [Kong, et al. Chin Phys B 29(10):100203, 2020], we explored a novel global-direction stencil and combined it with the face-area-weighted centroid on unstructured finite volume methods from differential form to realize the skewness reduction and a better reflection of flow anisotropy. Greatly inspired by the differential form, in this research, we demonstrate that it is also feasible to extend this novel method to the unstructured finite volume discretization from integral form on both second and third-order finite volume solver. Numerical examples governed by linear convective, Euler and Laplacian equations are utilized to examine the correctness as well as effectiveness of this extension. Compared with traditional vertex-neighbor and face-neighbor stencils based on the geometric centroid, the grid skewness is almost eliminated and computational accuracy as well as convergence rate is greatly improved by the global-direction stencil with face-area-weighted centroid. As a result, on unstructured finite volume discretization from integral form, the method also has superiorities on both computational accuracy and convergence rate.

scholarly journals The Riemannian structure of Alexandrov spaces

1994 ◽  
Vol 39 (3) ◽  
pp. 629-658 ◽  
Author(s):  
Yukio Otsu ◽  
Takashi Shioya
Keyword(s):  
Riemannian Structure ◽  
Alexandrov Spaces

scholarly journals ON EIGENVALUE ESTIMATES FOR THE SUBMANIFOLD DIRAC OPERATOR

2002 ◽  
Vol 13 (05) ◽  
pp. 533-548 ◽  
Author(s):  
NICOLAS GINOUX ◽  
BERTRAND MOREL
Keyword(s):  
Dirac Operator ◽  
Lower Bounds ◽  
Dirac Operators ◽  
Extrinsic Curvature ◽  
Eigenvalue Estimates ◽  
Killing Spinors ◽  
Spinor Fields ◽  
Twisted Dirac Operators

We give lower bounds for the eigenvalues of the submanifold Dirac operator in terms of intrinsic and extrinsic curvature expressions. We also show that the limiting cases give rise to a class of spinor fields generalizing that of Killing spinors. We conclude by translating these results in terms of intrinsic twisted Dirac operators.

scholarly journals Extension of Reilly formula with applications to eigenvalue estimates for drifting Laplacians

2010 ◽  
Vol 348 (21-22) ◽  
pp. 1203-1206 ◽  
Author(s):  
Li Ma ◽  
Sheng-Hua Du
Keyword(s):  
Eigenvalue Estimates
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