scholarly journals Investigation of High-Efficiency Iterative ILU Preconditioner Algorithm for Partial-Differential Equation Systems

Symmetry ◽  
2019 ◽  
Vol 11 (12) ◽  
pp. 1461 ◽  
Author(s):  
Yan-Hong Fan ◽  
Ling-Hui Wang ◽  
You Jia ◽  
Xing-Guo Li ◽  
Xue-Xia Yang ◽  
...  
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Linear Systems ◽  
High Efficiency ◽  
Iterative Scheme ◽  
Processing Unit ◽  
Matrix Equations ◽  
Partial Differential ◽  
Central Processing ◽  
Ilu Factorization

In this paper, we investigate an iterative incomplete lower and upper (ILU) factorization preconditioner for partial-differential equation systems. We discretize the partial-differential equations into linear equation systems. An iterative scheme of linear systems is used. The ILU preconditioners of linear systems are performed on the different computation nodes of multi-central processing unit (CPU) cores. Firstly, the preconditioner of general tridiagonal matrix equations is tested on supercomputers. Then, the effects of partial-differential equation systems on the speedup of parallel multiprocessors are examined. The numerical results estimate that the parallel efficiency is higher than in other algorithms.

scholarly journals Метод восстановления моделей тепломассопереноса по пространственно-временным распределениям параметров

2021 ◽  
Vol 47 (24) ◽  
pp. 9
Author(s):  
Н.Ю. Быков ◽  
А.А. Хватов ◽  
А.В. Калюжная ◽  
А.В. Бухановский
Keyword(s):  
Heat Transfer ◽  
Differential Equation ◽  
Partial Differential Equation ◽  
Phase Transitions ◽  
Laser Radiation ◽  
High Efficiency ◽  
Design Method ◽  
Temperature Dependent ◽  
Partial Differential ◽  
Correct Structure

An algorithm of the generative design method for reconstruction of heat transfer models from the available data is proposed. The method is applied to generate a partial differential equation describing the process of heating and evaporation of a metal, the surface of which is heated by laser radiation. The high efficiency of the method was demonstrated for the purpose of reconstructing the correct structure of the equation, indicating additional processes accompanying heating as phase transitions, and also for determining the values of the temperature-dependent coefficients of the derivatives.

Qxygen transfer in gravity flow sewers

2000 ◽  
Vol 42 (3-4) ◽  
pp. 417-422 ◽  
Author(s):  
T.Y. Pai ◽  
C.F. Ouyang ◽  
Y.C. Liao ◽  
H.G. Leu
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Dissolved Oxygen ◽  
Flow Velocity ◽  
Molecular Diffusion ◽  
Eddy Diffusion ◽  
Partial Differential ◽  
Diffusion Term ◽  
Sewer Pipes ◽  
Gravity Sewer

Oxygen diffused to water in gravity sewer pipes was studied in a 21 m long, 0.15 m diameter model sewer. At first, the sodium sulfide was added into the clean water to deoxygenate, then the pump was started to recirculate the water and the deoxygenated water was reaerated. The dissolved oxygen microelectrode was installed to measure the dissolved oxygen concentrations varied with flow velocity, time and depth. The dissolved oxygen concentration profiles were constructed and observed. The partial differential equation diffusion model that considered Fick's law including the molecular diffusion term and eddy diffusion term were derived. The analytic solution of the partial differential equation was used to determine the diffusivities by the method of nonlinear regression. The diffusivity values for the oxygen transfer was found to be a function of molecular diffusion, eddy diffusion and flow velocity.

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