Domain Decomposition Preconditioners for the System Generated by Discontinuous Galerkin Discretization of 2D-3T Heat Conduction Equations

2017 ◽  
Vol 22 (4) ◽  
pp. 1069-1100 ◽  
Author(s):  
Qiya Hu ◽  
Lin Zhao
Keyword(s):  
Heat Conduction ◽  
Domain Decomposition ◽  
Discontinuous Galerkin ◽  
Discrete System ◽  
Two Dimensions ◽  
Time Dependent ◽  
Matrix Size ◽  
Time Dependent Problem ◽  
Dg Methods ◽  
Small Overlap

AbstractIn this paper we are concerned with numerical methods for nonlinear time-dependent problem coupled by electron, ion and photon temperatures in two dimensions, which is called the 2D-3T heat conduction equations. We propose discontinuous Galerkin (DG) methods for the discretization of the equations. For solving the resulting discrete system, we employ two domain decomposition (DD) preconditioners, one of which is associated with the non-overlapping DDM and the other is based on DDM with small overlap. The preconditioners are constructed by dropping the couplings between particles and each preconditioner consists of three preconditioners with smaller matrix size. To gauge the efficiency of the preconditioners, we test two examples and make different settings of parameters. Numerical results show that the proposed preconditioners are very effective to the 2D-3T problem.

Application of Domain Decomposition in Modelling Flow and Heat Transfer Problems

1996 ◽  
Vol 210 (6) ◽  
pp. 519-528 ◽  
Author(s):  
K Muralidhar ◽  
A Chatterjee ◽  
B V Nagabhushana Rao
Keyword(s):  
Heat Transfer ◽  
Heat Conduction ◽  
Domain Decomposition ◽  
Oil Recovery ◽  
Transient Flow ◽  
Two Dimensions ◽  
Processing Unit ◽  
Central Processing ◽  
Flow And Heat Transfer ◽  
Transfer Problems

The present work is concerned with the application of the domain decomposition technique for modelling transient flow and heat transfer problems. The solutions obtained within each subdomain are matched at the interfaces using Uzawa's algorithm. This algorithm has been originally developed in the context of steady heat conduction. The objective of the present study is to test and extend the algorithm to a wider class of problems. Examples considered are non-linear heat conduction in one and two dimensions, simulation of oil recovery from porous formations using water injection, movement of a plane thermal front and heat transfer from a cylinder placed in Darcian flow. The suitability of Uzawa's algorithm for interface treatment with up to nine subdomains has been studied. The method is found to converge to the full-domain solution in all cases considered. Besides this, results show that there are additional advantages which include the generation of small matrices and, in certain cases, a marginal reduction in CPU (central processing unit) time, even on sequential machines.

scholarly journals Stable Filtering Procedures for Nodal Discontinuous Galerkin Methods

2021 ◽  
Vol 87 (1) ◽  
Author(s):  
Jan Nordström ◽  
Andrew R. Winters
Keyword(s):  
Discontinuous Galerkin ◽  
Discontinuous Galerkin Methods ◽  
Finite Difference Methods ◽  
Basis Functions ◽  
Galerkin Methods ◽  
Theoretical Discussion ◽  
Numerical Tests ◽  
Dg Methods ◽  
Theoretical Results ◽  
Filtering Procedure

AbstractWe prove that the most common filtering procedure for nodal discontinuous Galerkin (DG) methods is stable. The proof exploits that the DG approximation is constructed from polynomial basis functions and that integrals are approximated with high-order accurate Legendre–Gauss–Lobatto quadrature. The theoretical discussion re-contextualizes stable filtering results for finite difference methods into the DG setting. Numerical tests verify and validate the underlying theoretical results.

Time-dependent Landau system and non-adiabatic Berry phase in two dimensions

2000 ◽  
Vol 9 (7) ◽  
pp. 481-484 ◽  
Author(s):  
Jing Hui ◽  
Wu Jian-sheng
Keyword(s):  
Berry Phase ◽  
Two Dimensions ◽  
Time Dependent

scholarly journals Thermomechanical coupling of ice flow with the bedrock

2003 ◽  
Vol 37 ◽  
pp. 390-396 ◽  
Author(s):  
Richard C.A. Hindmarsh
Keyword(s):  
Temperature Distribution ◽  
Horizontal Velocity ◽  
Time Dependent ◽  
Thermomechanical Coupling ◽  
Positive Anomaly ◽  
Thermal Coupling ◽  
Steady Temperature ◽  
Ice Flow ◽  
Time Dependent Problem ◽  
Geomorphological Processes

AbstractTwo aspects of thermal coupling with bedrock are considered: the coupled time-dependent problem of co-evolving temperatures in lithosphere and ice; and the influence of basal topography on steady temperature distribution within the ice. The nature of the time-dependent coupling is found to depend on the horizontal velocity. As has been suggested, there is a cooling of steady temperatures on bedrock highs, but this is phase-shifted downstream when horizontal velocities increase. This observation may have consequences for geomorphological processes such as plucking and protection. The effect of bedrock channelling on steady temperature is considered. The positive anomaly of basal temperature due to channelling increases as the transverse wavelength decreases, but not monotonically, reaching a plateau when both the wavelengths of the basal topography are around 100 km.

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