GMRES Solver for MLPG Method Applied to Heat Conduction

2020 ◽  
Author(s):  
Abhishek Kumar Singh ◽  
Krishna Mohan Singh
Keyword(s):  
Heat Conduction ◽  
Three Dimensional ◽  
Computation Time ◽  
Symmetric System ◽  
Algebraic Equations ◽  
Relaxation Methods ◽  
Convergence Behaviour ◽  
Mlpg Method ◽  
Steady State Heat ◽  
Successive Over Relaxation

Abstract In recent years, meshless local Petrov-Galerkin (MLPG) method has emerged as the promising choice for solving variety of scientific and engineering problems. MLPG formulation leads to a non-symmetric system of algebraic equations. Iterative methods (such as GMRES and BiCGSTAB methods) are more competent than the direct solvers for solving a general linear system of larger size (order of millions or billions). This paper presents the use of GMRES solver with MLPG method for the very first time. The restarted version of the GMRES method is applied in connection with the interpolating MLPG method, to solve steady-state heat conduction in three-dimensional regular geometry. The performance of GMRES solver (with and without preconditioner) has been compared with the preconditioned BiCGSTAB method in terms of computation time and convergence behaviour. Jacobi and successive over-relaxation methods have been used as preconditioners in both the solvers. The results show that GMRES solver takes about 18 to 20% less CPU time than the BiCGSTAB solver along with better convergence behaviour.

Three-Dimensional, Steady-State Heat Conduction in Cylinders of General Anisotropic-Media

1979 ◽  
Vol 101 (3) ◽  
pp. 548-553 ◽  
Author(s):  
Y. P. Chang ◽  
K. C. Poon
Keyword(s):  
Heat Conduction ◽  
Steady State ◽  
Fourier Transforms ◽  
Coupling Effect ◽  
Three Dimensional ◽  
Anisotropic Media ◽  
State Heat ◽  
Change Of Variables ◽  
Steady State Heat ◽  
Kummer's Equation

This paper provides the analytical solution of three-dimensional steady-state heat conduction in solid and hollow cylinders of general anisotropic-media. By the use of Fourier transforms and a change of variables the partial differential equation is reduced to Kummer’s equation. Some calculated results for a solid cylinder are shown and discussed. A parameter γ is found to represent the coupling effect of three-dimensional anisotropy. For small values of γ, an approximate solution is recommended. The inequality σ > 0 which was found in an earlier paper is further discussed.

Heat Conduction in Three Dimensional Stacked Packages

2005 ◽  
Author(s):  
Anand Desai ◽  
James Geer ◽  
Bahgat Sammakia
Keyword(s):  
Heat Conduction ◽  
Thermal Management ◽  
Heat Generation ◽  
Analytical Study ◽  
Three Dimensional ◽  
The Other ◽  
Heat Generation Rate ◽  
Potential Applications ◽  
Steady State Heat ◽  
Spatially Varying

This paper presents the results of an analytical study of steady state heat conduction in multiple rectangular domains. Any finite number of such domains may be considered in the current study. The thermal conductivity and thickness of these domains may be different. The entire geometry composed of these connected domains is considered as adiabatic on the lateral surfaces and can be subjected to uniform convective cooling at one end. The other end of the geometry may be adiabatic and a specified, spatially varying heat generation rate can be applied in each of the domains. The solutions are found to be in agreement with known solutions for simpler geometries. The analytical solution presented here is very general in that it takes into account the interface resistances between the layers. One application of this analytical study relates to the thermal management of a 3-D stack of devices and interconnect layers. Another possible application is to the study of hotspots in a chip stack with non uniform heat generation. Many other potential applications may also be simulated.

Heat Conduction in a Rectangular Tube With Eccentric Hot Spots

2010 ◽  
Author(s):  
Bo Dan ◽  
James F. Geer ◽  
Bahgat G. Sammakia
Keyword(s):  
Heat Conduction ◽  
Hot Spots ◽  
Analytical Study ◽  
Three Dimensional ◽  
Rectangular Domain ◽  
Current Paper ◽  
Dominant Factor ◽  
Rectangular Tube ◽  
Convection Boundary ◽  
Steady State Heat

The current paper presents the results of an analytical study of steady state heat conduction in a rectangular tube with eccentric hot spots on both the top and the bottom surfaces. The rectangular domain is assumed to be adiabatic on the lateral surfaces and a single or multiple eccentric hot spots can be applied on the top and bottom surfaces. Isothermal, heat flux or convection boundary conditions can be applied on the hot spots. Because the hot spots are eccentric, the spreading resistance becomes a dominant factor in heat conduction in the tube. The multiple hot spots, multiple layer and combination problems are also studied in the current paper. The solutions can be applied to the thermal management of three-dimensional stacks of electronic devices, the interconnect layers and the thermoelectric devices.

Experimental Measurements of Temperature Distribution in Three Dimensional Stacked Package

2007 ◽  
Author(s):  
Anand Desai ◽  
James Geer ◽  
Bahgat Sammakia
Keyword(s):  
Experimental Study ◽  
Heat Conduction ◽  
Steady State ◽  
Temperature Distribution ◽  
Numerical Model ◽  
Analytical Solution ◽  
Three Dimensional ◽  
Power Input ◽  
Experimental Measurements ◽  
Steady State Heat

This paper presents the results of an experimental study of steady state heat conduction in a three dimensional stack package. The temperatures are measured at different interfaces within the stacked package. Delphi devices are used in the experiment which enables controlled power input and surface temperature of the devices. The experiment is carried out for three different boundary conditions on the package. The power input in varied to study its effects. A numerical model is created to compare to the experimental results. The results are also compared with the analytical solution presented in Desai et al [5] and Geer et al [6]. The results indicate that the experimental, numerical and analytical solutions follow the same trend. The agreement between the experimental and numerical results improves when the lateral losses are taken into account.

Calculation of three-dimensional nearly singular boundary element integrals for steady-state heat conduction

2015 ◽  
Vol 60 ◽  
pp. 137-143 ◽  
Author(s):  
Guizhong Xie ◽  
Liangwen Wang ◽  
Jianming Zhang ◽  
Dehai Zhang ◽  
Hao Li ◽  
...  
Keyword(s):  
Heat Conduction ◽  
Steady State ◽  
Boundary Element ◽  
Three Dimensional ◽  
Singular Boundary ◽  
State Heat ◽  
Steady State Heat
Sign in / Sign up

Export Citation Format

Share Document