Stabilizing and Accelerating Solution of Harmonic Balance Equation System Using the LU-SGS and Block Jacobi Methods

2016 ◽  
Author(s):  
Xiuquan Huang ◽  
Ding Xi Wang
Keyword(s):  
Balance Equation ◽  
Harmonic Balance ◽  
Equation System ◽  
Jacobi Method ◽  
Implicit Time ◽  
Solution Stability ◽  
Reduced Frequency ◽  
Solution Convergence ◽  
Time Marching ◽  
Jacobi Iterations

The paper presents the combination of the Lower Upper Symmetric Gauss Seidel (LU-SGS) method and the block Jacobi method for stabilizing and accelerating the solution of a harmonic balance equation system. First the baseline LU-SGS procedure for a harmonic balance equation system with explicit discretization of the time spectral source term is derived. The LU-SGS method, different from its original application as an implicit time marching scheme, is used as an implicit residual smoother, allowing big CFL numbers (in order of 1000s), within the Runge-Kutta explicit time marching loops. Then the block Jacobi method is introduced to augment solution stability for the solution of a harmonic balance equation system under situation where grid reduced frequency is in the order of 10. Results are presented to show the effectiveness of the combination of LU-SGS and the block Jacobi method on the solution stabilization and acceleration. The influence of the number of Jacobi iterations on solution convergence is also investigated.

Solution Stabilization and Convergence Acceleration for the Harmonic Balance Equation System

2017 ◽  
Vol 139 (9) ◽  
Author(s):  
Ding Xi Wang ◽  
Xiuquan Huang
Keyword(s):  
Balance Equation ◽  
Harmonic Balance ◽  
Source Term ◽  
Equation System ◽  
Jacobi Method ◽  
Implicit Time ◽  
Transonic Compressor ◽  
Blade Row ◽  
Jacobi Iterations ◽  
Blade Row Interaction

This paper presents an efficient approach for stabilizing solution and accelerating convergence of a harmonic balance equation system for an efficient analysis of turbomachinery unsteady flows due to flutter and blade row interaction. The proposed approach combines the Runge–Kutta method with the lower upper symmetric Gauss Seidel (LU-SGS) method and the block Jacobi method. The LU-SGS method, different from its original application as an implicit time marching scheme, is used as an implicit residual smoother with under-relaxation, allowing big Courant–Friedrichs–Lewy (CFL) numbers (in the order of hundreds), leading to significant convergence speedup. The block Jacobi method is introduced to implicitly integrate the time spectral source term of a harmonic balance equation system, in order to reduce the complexity of the direct implicit time integration by the LU-SGS method. The implicit treatment of the time spectral source term thus greatly augments the stability region of a harmonic balance equation system in the case of grid-reduced frequency well above ten. Validation of the harmonic balance flow solver was carried out using linear cascade test data. Flutter analysis of a transonic rotor and blade row interaction analyses for a transonic compressor stage were presented to demonstrate the stabilization and acceleration effect by the combination of the LU-SGS and the block Jacobi methods. The influence of the number of Jacobi iterations on solution stabilization is also investigated, showing that two Jacobi iterations are sufficient for stability purpose, which is much more efficient than existing methods of its kind in the open literature.

scholarly journals Geodesic Distance on Riemannian Manifold using Jacobi Iterations in 3D Face Recognition System

2017 ◽  
Vol 6 (1) ◽  
pp. 10
Author(s):  
Rachid Ahdid ◽  
Said Safi ◽  
Mohamed Fakir ◽  
Bouzid Manaut
Keyword(s):  
Face Recognition ◽  
Riemannian Manifold ◽  
Eikonal Equation ◽  
Geodesic Distance ◽  
Recognition System ◽  
Support Vector ◽  
3D Face Recognition ◽  
3D Face ◽  
Face Recognition System ◽  
Jacobi Iterations

In this paper, we present an automatic application of 3D face recognition system using geodesic distance in Riemannian geometry. We consider, in this approach, the three dimensional face images as residing in Riemannian manifold and we compute the geodesic distance using the Jacobi iterations as a solution of the Eikonal equation. The problem of solving the Eikonal equation, unstructured simplified meshes of 3D face surface, such as tetrahedral and triangles are important for accurately modeling material interfaces and curved domains, which are approximations to curved surfaces in R<sup>3</sup>. In the classifying steps, we use: Neural Networks (NN), K-Nearest Neighbor (KNN) and Support Vector Machines (SVM). To test this method and evaluate its performance, a simulation series of experiments were performed on 3D Shape REtrieval Contest 2008 database (SHREC2008).<strong></strong>

scholarly journals Optimal control computation for cascade systems by structured Jacobi iterations

2019 ◽  
Vol 52 (20) ◽  
pp. 291-296 ◽  
Author(s):  
Armaghan Zafar ◽  
Michael Cantoni ◽  
Farhad Farokhi
Keyword(s):  
Optimal Control ◽  
Cascade Systems ◽  
Jacobi Iterations
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