Efficient Numerical Methods for Non-local Operators

10.4171/091 ◽  
2010 ◽  
Author(s):  
Steffen Börm
Keyword(s):  
Numerical Methods ◽  
Local Operators ◽  
Non Local

scholarly journals Fast Numerical Methods for Non-local Operators

2004 ◽  
pp. 1747-1788
Author(s):  
Wolfgang Hackbusch ◽  
Stefan Sauter ◽  
Christoph Schwab
Keyword(s):  
Numerical Methods ◽  
Local Operators ◽  
Non Local

scholarly journals Conformally invariant non-local operators

2001 ◽  
Vol 201 (1) ◽  
pp. 19-60 ◽  
Author(s):  
Thomas Branson ◽  
A. Rod Gover
Keyword(s):  
Conformally Invariant ◽  
Local Operators ◽  
Non Local

scholarly journals Simulation of Solar Magnetoconvection

2003 ◽  
Vol 210 ◽  
pp. 157-167 ◽  
Author(s):  
A. Vögler ◽  
S. Shelyag ◽  
M. Schüssler ◽  
F. Cattaneo ◽  
T. Emonet ◽  
...  
Keyword(s):  
Numerical Methods ◽  
Radiative Transfer ◽  
Transfer Test ◽  
Parallel Computers ◽  
Plage Region ◽  
First Results ◽  
Non Local ◽  
Efficient Parallelization

We present a new 3D MHD code for the simulation of solar magnetoconvection. The code is designed for use on parallel computers and in the choice of methods emphasis has been laid on efficient parallelization. We give a description of the numerical methods and discuss the non-local and non-grey treatment of the radiative transfer. Test calculations underlining the importance of non-grey effects and first results of the simulation of a solar plage region are shown.

The bond-based peridynamic system with Dirichlet-type volume constraint

2014 ◽  
Vol 144 (1) ◽  
pp. 161-186 ◽  
Author(s):  
Tadele Mengesha ◽  
Qiang Du
Keyword(s):  
Poisson Ratio ◽  
Variational Problems ◽  
Compact Embedding ◽  
Volume Constraint ◽  
Positive Definite Kernels ◽  
Local Boundary ◽  
Local Operators ◽  
Non Local ◽  
Poincaré Type Inequalities ◽  
Non Locality

In this paper, the bond-based peridynamic system is analysed as a non-local boundary-value problem with volume constraint. The study extends earlier works in the literature on non-local diffusion and non-local peridynamic models, to include non-positive definite kernels. We prove the well-posedness of both linear and nonlinear variational problems with volume constraints. The analysis is based on some non-local Poincaré-type inequalities and the compactness of the associated non-local operators. It also offers careful characterizations of the associated solution spaces, such as compact embedding, separability and completeness. In the limit of vanishing non-locality, the convergence of the peridynamic system to the classical Navier equations of elasticity with Poisson ratio ¼ is demonstrated.

scholarly journals Decay properties for evolution-parabolic coupled systems related to thermoelastic plate equations

2021 ◽  
Vol 7 (1) ◽  
pp. 260-275
Author(s):  
Zihan Cai ◽  
◽  
Yan Liu ◽  
Baiping Ouyang ◽  
Keyword(s):  
Cauchy Problem ◽  
Phase Space ◽  
Coupled Systems ◽  
Decay Properties ◽  
Representation Of Solutions ◽  
The Cauchy Problem ◽  
Plate Equations ◽  
Thermoelastic Plate ◽  
Local Operators ◽  
Non Local

<abstract><p>In this paper, we consider the Cauchy problem for a family of evolution-parabolic coupled systems, which are related to the classical thermoelastic plate equations containing non-local operators. By using diagonalization procedure and WKB analysis, we derive representation of solutions in the phase space. Then, sharp decay properties in a framework of $ L^p-L^q $ are investigated via these representations. Particularly, some thresholds for the regularity-loss type decay properties are found.</p></abstract>

scholarly journals Decay properties for evolution-parabolic coupled systems related to thermoelastic plate equations

2021 ◽  
Author(s):  
Yan Liu ◽  
Zihan Cai ◽  
Shuanghu Zhang
Keyword(s):  
Cauchy Problem ◽  
Phase Space ◽  
Coupled Systems ◽  
Decay Properties ◽  
Representation Of Solutions ◽  
The Cauchy Problem ◽  
Plate Equations ◽  
Thermoelastic Plate ◽  
Local Operators ◽  
Non Local

In this paper, we consider the Cauchy problem for a family of evolution-parabolic coupled systems, which are related to the classical thermoelastic plate equations containing non-local operators. By using diagonalization procedure and WKB analysis, we derive representation of solutions in the phase space. Then, sharp decay properties in a framework of $L^p-L^q$ are investigated via these representations. Particularly, some thresholds for the regularity-loss type decay properties are found.

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