On the Use of Discrete Laplace Operator for Preconditioning Kernel Matrices

2013 ◽  
Vol 35 (2) ◽  
pp. A577-A602 ◽  
Author(s):  
Jie Chen
Keyword(s):  
Laplace Operator ◽  
Discrete Laplace Operator

scholarly journals Adaptive Discrete Laplace Operator

2011 ◽  
pp. 377-386 ◽  
Author(s):  
Christophe Fiorio ◽  
Christian Mercat ◽  
Frédéric Rieux
Keyword(s):  
Laplace Operator ◽  
Discrete Laplace Operator

Discrete Laplace operator of 3-cochains

2020 ◽  
pp. 2150001
Author(s):  
Azeddine Baalal ◽  
Khalid Hatim
Keyword(s):  
Simplicial Complex ◽  
Essential Spectrum ◽  
Laplace Operator ◽  
Upper Bound ◽  
Discrete Laplacian ◽  
Discrete Laplace Operator

In this paper, we use the Nelson lemma to give a new proof for the essential self-adjointness of the discrete Laplace operator acting on 3-cochains, which we are defined in our previous paper [A. Baalal and K. Hatim, The discrete Laplacian of a 3-simplicial complex (2019), https://hal.archives-ouvertes.fr/hal-02105789 ]. Moreover, we establish on the infimum of the essential spectrum an upper bound.

scholarly journals Benchmark Problems for the Numerical Discretization of the Cahn–Hilliard Equation with a Source Term

2021 ◽  
Vol 2021 ◽  
pp. 1-11
Author(s):  
Sungha Yoon ◽  
Hyun Geun Lee ◽  
Yibao Li ◽  
Chaeyoung Lee ◽  
Jintae Park ◽  
...  
Keyword(s):  
Laplace Operator ◽  
Source Term ◽  
Orientation Dependence ◽  
Benchmark Problems ◽  
Hilliard Equation ◽  
Growth Phenomenon ◽  
Discrete Laplace Operator ◽  
Space Discretization ◽  
Numerical Discretization ◽  
Cahn Hilliard Equation

In this paper, we present benchmark problems for the numerical discretization of the Cahn–Hilliard equation with a source term. If the source term includes an isotropic growth term, then initially circular and spherical shapes should grow with their original shapes. However, there is numerical anisotropic error and this error results in anisotropic evolutions. Therefore, it is essential to use isotropic space discretization in the simulation of growth phenomenon such as tumor growth. To test numerical discretization, we present two benchmark problems: one is the growth of a disk or a sphere and the other is the growth of a rotated ellipse or a rotated ellipsoid. The computational results show that the standard discrete Laplace operator has severe grid orientation dependence. However, the isotropic discrete Laplace operator generates good results.

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