Connections Between the Meshfree Peridynamics Discretization and Graph Laplacian for Transient Diffusion Problems

2021 ◽  
Author(s):  
Longzhen Wang ◽  
Florin Bobaru
Keyword(s):  
Graph Laplacian ◽  
Transient Diffusion ◽  
Diffusion Problems

scholarly journals Rational Krylov methods for fractional diffusion problems on graphs

2021 ◽  
Author(s):  
Michele Benzi ◽  
Igor Simunec
Keyword(s):  
Analytic Function ◽  
Diffusion Equation ◽  
Graph Laplacian ◽  
Fractional Diffusion ◽  
Singular Matrix ◽  
Krylov Methods ◽  
Fractional Powers ◽  
Directed Networks ◽  
Rank One ◽  
Diffusion Problems

AbstractIn this paper we propose a method to compute the solution to the fractional diffusion equation on directed networks, which can be expressed in terms of the graph Laplacian L as a product $$f(L^T) \varvec{b}$$ f ( L T ) b , where f is a non-analytic function involving fractional powers and $$\varvec{b}$$ b is a given vector. The graph Laplacian is a singular matrix, causing Krylov methods for $$f(L^T) \varvec{b}$$ f ( L T ) b to converge more slowly. In order to overcome this difficulty and achieve faster convergence, we use rational Krylov methods applied to a desingularized version of the graph Laplacian, obtained with either a rank-one shift or a projection on a subspace.

A METHOD FOR SOLVING TRANSIENT DIFFUSION PROBLEMS

1986 ◽  
Vol 9 (6) ◽  
pp. 663-676 ◽  
Author(s):  
Yi-Hsu Ju ◽  
Wen-Chien Lee
Keyword(s):  
Transient Diffusion ◽  
Diffusion Problems
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