Local Fourier analysis of block-structured multigrid relaxation schemes for the Stokes equations

2018 ◽  
Vol 25 (3) ◽  
pp. e2147 ◽  
Author(s):  
Yunhui He ◽  
Scott P. MacLachlan
Keyword(s):  
Fourier Analysis ◽  
Stokes Equations ◽  
Relaxation Schemes ◽  
Local Fourier Analysis ◽  
Block Structured

scholarly journals Remarks on the Systems of Semilinear Fractional Rayleigh-Stokes Equation

2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Le Dinh Long
Keyword(s):  
Cauchy Problem ◽  
Fourier Analysis ◽  
Stokes Equation ◽  
Stokes Equations ◽  
Newtonian Fluids ◽  
System Of Equations ◽  
Main Technique ◽  
The Cauchy Problem ◽  
The Stability

In this paper, we study the Cauchy problem for a system of Rayleigh-Stokes equations. In this system of equations, we use derivatives in the classical Riemann-Liouville sense. This system has many applications in some non-Newtonian fluids. We obtained results for the existence, uniqueness, and frequency of the solution. We discuss the stability of the solutions and find the solution spaces. Our main technique is to use the Banach mapping theorem combined with some techniques in Fourier analysis.

Developing an Efficient Multigrid Strategy for Solving Incompressible Flow

2004 ◽  
Author(s):  
Masoud Darbandi ◽  
Gerry E. Schneider ◽  
Arash Taheri
Keyword(s):  
Finite Element ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Computational Time ◽  
Fine Grid ◽  
Algebraic Set ◽  
Acceleration Technique ◽  
Relaxation Schemes ◽  
Relaxation Procedure ◽  
Benchmark Solutions

In this work, a multigrid acceleration technique is suitably developed for solving the two-dimensional incompressible Navier-Stokes equations using an implicit finite element volume method. In this regard, the solution domain is broken into a huge number of quadrilateral finite elements. The accurate numerical solution of a flow field can be achieved if very fine grid resolutions are utilized. Unfortunately, the standard implicit solvers need more computational time to solve larger size of algebraic set of equations which normally arise if fine grid distributions are used. Past experience has shown that the convergence of classical relaxation schemes perform an initial rapid decrease of residuals followed by a slower rate of decrease. This point indicates that a relaxation procedure is efficient for eliminating only the high frequency components of the residuals. This problem can be overcome using multigrid method, i.e., carrying out the relaxation procedure on a series of different grid sizes. There are different prolongation operators to establish a multigrid procedure. A new prolongation expression is suitably developed in this work. It needs constructing data during refining and coarsening stages which is fulfilled using suitable finite element interpolators. The extended formulations are finally used to test several different problems with available benchmark solutions. The results indicate that the current multigrid strategy effectively improves the bandit solver performance.

scholarly journals On Local Fourier Analysis of Multigrid Methods for PDEs with Jumping and Random Coefficients

2019 ◽  
Vol 41 (3) ◽  
pp. A1385-A1413 ◽  
Author(s):  
Prashant Kumar ◽  
Carmen Rodrigo ◽  
Francisco J. Gaspar ◽  
Cornelis W. Oosterlee
Keyword(s):  
Fourier Analysis ◽  
Multigrid Methods ◽  
Random Coefficients ◽  
Local Fourier Analysis
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