scholarly journals Spectral discretization errors in filtered subspace iteration

2019 ◽  
Vol 89 (321) ◽  
pp. 203-228 ◽  
Author(s):  
Jay Gopalakrishnan ◽  
Luka Grubišić ◽  
Jeffrey Ovall
Keyword(s):  
Subspace Iteration ◽  
Discretization Errors ◽  
Spectral Discretization

Spectral Methods

2018 ◽  
Author(s):  
S. G. Rajeev
Keyword(s):  
Simple Model ◽  
Differential Equations ◽  
Boundary Conditions ◽  
Linear Algebra ◽  
Spectral Methods ◽  
Differential Operators ◽  
Higher Dimensions ◽  
Standard Linear ◽  
Sommerfeld Equation ◽  
Spectral Discretization

Thenumerical solution of ordinary differential equations (ODEs)with boundary conditions is studied here. Functions are approximated by polynomials in a Chebychev basis. Sections then cover spectral discretization, sampling, interpolation, differentiation, integration, and the basic ODE. Following Trefethen et al., differential operators are approximated as rectangular matrices. Boundary conditions add additional rows that turn them into square matrices. These can then be diagonalized using standard linear algebra methods. After studying various simple model problems, this method is applied to the Orr–Sommerfeld equation, deriving results originally due to Orszag. The difficulties of pushing spectral methods to higher dimensions are outlined.

scholarly journals Scaling behavior of discretization errors in renormalization and improvement constants

2006 ◽  
Vol 73 (11) ◽  
Author(s):  
Tanmoy Bhattacharya ◽  
Rajan Gupta ◽  
Weonjong Lee ◽  
Stephen R. Sharpe
Keyword(s):  
Scaling Behavior ◽  
Discretization Errors

scholarly journals An Acceleration Method for the Subspace Iteration

1989 ◽  
Vol 121 ◽  
pp. 643-648
Author(s):  
J.I. Llorente ◽  
R. Avilés ◽  
M.B. Ajuria ◽  
E. Amezua
Keyword(s):  
Subspace Iteration ◽  
Acceleration Method

Robustness of Natural Controls of Distributed-Parameter Systems

1996 ◽  
Vol 118 (1) ◽  
pp. 56-63 ◽  
Author(s):  
Jai Hyuk Hwang ◽  
Doo Man Kim ◽  
Kyoung Ho Lim
Keyword(s):  
Closed Loop ◽  
Distributed Parameter Systems ◽  
Distributed Parameter ◽  
Control Force ◽  
Spatial Discretization ◽  
Actual System ◽  
Discretization Errors

In this paper, the effect of parameter and spatial discretization errors on the closed-loop behavior of distributed-parameter systems is analyzed for natural controls. If the control force designed on the basis of the postulated system with the parameter and discretization errors is applied to control the actual system, the closed-loop performance of the actual system will be degraded depending on the degree of the errors. The extent of deviation of the closed-loop performance from the expected one is derived and evaluated using operator techniques. It has been found that the extent of the deviation is proportional to the magnitude of the parameter and discretization errors, and that the proportional coeffecient depends on the structures of the natural controls.

scholarly journals An accelerated Poisson solver based on multidomain spectral discretization

2018 ◽  
Vol 58 (4) ◽  
pp. 851-879 ◽  
Author(s):  
Tracy Babb ◽  
Adrianna Gillman ◽  
Sijia Hao ◽  
Per-Gunnar Martinsson
Keyword(s):  
Poisson Solver ◽  
Spectral Discretization
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