scholarly journals Adaptive Wavelet Schemes for Parabolic Problems: Sparse Matrices and Numerical Results

2011 ◽  
Vol 49 (1) ◽  
pp. 182-212 ◽  
Author(s):  
Nabi Chegini ◽  
Rob Stevenson
Keyword(s):  
Sparse Matrices ◽  
Numerical Results ◽  
Parabolic Problems ◽  
Adaptive Wavelet

scholarly journals Development of a parallel algorithm based on an implicit scheme for the discontinuous Galerkin method for solving diffusion type equations

2020 ◽  
Vol 22 (1) ◽  
pp. 94-106
Author(s):  
Ruslan V. Zhalnin ◽  
Nikita A. Kuzmin ◽  
Victor F. Masyagin
Keyword(s):  
Galerkin Method ◽  
Parallel Algorithm ◽  
Numerical Study ◽  
Sparse Matrices ◽  
Parabolic Type ◽  
Implicit Scheme ◽  
Basis Functions ◽  
Parabolic Problems ◽  
Diffusion Type ◽  
The Galerkin Method

The paper presents a numerical parallel algorithm based on an implicit scheme for the Galerkin method with discontinuous basis functions for solving diffusion-type equations on triangular grids. To apply the Galerkin method with discontinuous basis functions, the initial equation of parabolic type is transformed to a system of partial differential equations of the first order. To do this, auxiliary variables are introduced, which are the components of the gradient of the desired function. To store sparse matrices and vectors, the CSR format is used in this study. The resulting system is solved numerically using a parallel algorithm based on the Nvidia AmgX library. A numerical study is carried out on the example of solving two-dimensional test parabolic initial-boundary value problems. The presented numerical results show the effectiveness of the proposed algorithm for solving parabolic problems.

scholarly journals CUBIC SPLINE ADAPTIVE WAVELET SCHEME TO SOLVE SINGULARLY PERTURBED REACTION DIFFUSION PROBLEMS

2007 ◽  
Vol 05 (02) ◽  
pp. 317-331 ◽  
Author(s):  
VIVEK KUMAR ◽  
MANI MEHRA
Keyword(s):  
Reaction Diffusion ◽  
Cubic Spline ◽  
Singularly Perturbed ◽  
Reaction Diffusion Equation ◽  
Parabolic Problems ◽  
Adaptive Wavelet ◽  
Cpu Time ◽  
Perturbation Problems ◽  
Adaptive Wavelet Scheme ◽  
Diffusion Problems

In this paper, the collocation method proposed by Cai and Wang1 has been reviewed in detail to solve singularly perturbed reaction diffusion equation of elliptic and parabolic types. The method is based on an interpolating wavelet transform using cubic spline on dyadic points. Adaptive feature is performed automatically by thresholding the wavelet coefficients. Numerical examples are presented for elliptic and parabolic problems. The purposed method comes up as a powerful tool for studying singular perturbation problems in term of effective grid generation and CPU time.

scholarly journals Adaptive wavelet schemes and finite volumes

2021 ◽  
Vol 70 ◽  
pp. 107-123
Author(s):  
Daniele Del Sarto ◽  
Erwan Deriaz ◽  
Xavier Lhebrard ◽  
Mathieu Rigal
Keyword(s):  
Efficient Algorithms ◽  
High Order ◽  
Numerical Results ◽  
Finite Volumes ◽  
Third Order ◽  
Nonuniform Grids ◽  
Adaptive Wavelet ◽  
High Order Finite Volumes

We consider a procedure for combining high order finite volumes and tree-based nonuniform grids. Especially, we focus on efficient algorithms for third order multidimensional volume interpolation and communication between levels of refinement. In the end, numerical results are reviewed to validate our approach.

Effects of stator splitter blades on aerodynamic performance of a single-stage transonic axial compressor

2020 ◽  
Vol 14 (4) ◽  
pp. 7369-7378
Author(s):  
Ky-Quang Pham ◽  
Xuan-Truong Le ◽  
Cong-Truong Dinh
Keyword(s):  
Stokes Equations ◽  
Three Dimensional ◽  
Axial Compressor ◽  
Aerodynamic Performance ◽  
Numerical Results ◽  
Single Stage ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Operating Stability ◽  
Length Coverage

Splitter blades located between stator blades in a single-stage axial compressor were proposed and investigated in this work to find their effects on aerodynamic performance and operating stability. Aerodynamic performance of the compressor was evaluated using three-dimensional Reynolds-averaged Navier-Stokes equations using the k-e turbulence model with a scalable wall function. The numerical results for the typical performance parameters without stator splitter blades were validated in comparison with experimental data. The numerical results of a parametric study using four geometric parameters (chord length, coverage angle, height and position) of the stator splitter blades showed that the operational stability of the single-stage axial compressor enhances remarkably using the stator splitter blades. The splitters were effective in suppressing flow separation in the stator domain of the compressor at near-stall condition which affects considerably the aerodynamic performance of the compressor.

Elasto-plastic state of curve beam system subjected to complex loading

1996 ◽  
Vol 18 (4) ◽  
pp. 14-22
Author(s):  
Vu Khac Bay
Keyword(s):  
Cylindrical Shell ◽  
Solution Method ◽  
Complex Loading ◽  
Numerical Results ◽  
Elastic Solution ◽  
Plastic State ◽  
Curve Beam ◽  
Elastic State ◽  
Elastic Plastic ◽  
Beam System

Investigation of the elastic state of curve beam system had been considered in [3]. In this paper the elastic-plastic state of curve beam system in the form of cylindrical shell is analyzed by the elastic solution method. Numerical results of the problem and conclusion are given.

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