Numerical implementations of an iterative method with boundary condition splitting as applied to the nonstationary stokes problem in the gap between coaxial cylinders

2010 ◽  
Vol 50 (11) ◽  
pp. 1895-1913 ◽  
Author(s):  
M. B. Solov’ev
Keyword(s):  
Boundary Condition ◽  
Iterative Method ◽  
Stokes Problem ◽  
Coaxial Cylinders ◽  
Nonstationary Stokes Problem

Approximate Solution of Linear Systems with Laplace-like Operators via Cross Approximation in the Frequency Domain

2019 ◽  
Vol 19 (1) ◽  
pp. 137-145 ◽  
Author(s):  
Ekaterina A. Muravleva ◽  
Ivan V. Oseledets
Keyword(s):  
Approximate Solution ◽  
Iterative Method ◽  
Frequency Domain ◽  
Linear Systems ◽  
Stokes Problem ◽  
Inverse Operator ◽  
Low Rank ◽  
Low Rank Approximation ◽  
Rank Approximation ◽  
Reduced Complexity

AbstractIn this paper we propose an efficient algorithm to compute low-rank approximation to the solution of so-called “Laplace-like” linear systems. The idea is to transform the problem into the frequency domain, and then use cross approximation. In this case, we do not need to form explicit approximation to the inverse operator, and can approximate the solution directly, which leads to reduced complexity. We demonstrate that our method is fast and robust by using it as a solver inside Uzawa iterative method for solving the Stokes problem.

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