| 1. |
- Ranjbar, Zohreh, et al.
(författare)
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A Preconditioned GMRES Method for Solving a 1D Sideways Heat Equation
- 2010
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- The sideways Heat equation (SHE) is a model of the problem of determining the temperature on the surface of a body from the interior measurements. Mathematically it can be formulated as a non-characteristic Cauchy problem for a parabolic partial differential equation. This problem is severely ill-posed: the solution does not depend continuously on the data. We use a preconditioned Generalized Minimum Residuals Method (GMRES) to solve a 1D SHE. Regularization is used in the preconditioner as well as truncating the GMRES algorithm. Numerical experiments demonstrate that the proposed method works well.
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| 2. |
- Ranjbar, Zohreh, et al.
(författare)
-
A Preconditioned GMRES Method for Solving a Sideways Parabolic Equation in Two Space Dimensions
- 2010
-
Rapport (övrigt vetenskapligt/konstnärligt)abstract
- The sideways parabolic equation (SPE) is a model of the problem of determining the temperature on the surface of a body from the interior measurements. Mathematically it can be formulated as a non-characteristic Cauchy problem for a parabolic partial differential equation. This problem is severely ill-posed: the solution does not depend continuously on the data. We consider both one and two-dimensional SPE with both constant and variable coefficients. We apply the preconditioned Generalized Minimum Residuals Method (GMRES) on these problems. Preconditioners are chosen in ways that allow efficient implementation using the Fast Fourier Transform (FFT). Regularization is used in the preconditioner as well as truncating the GMRES algorithm. Numerical experiments demonstrate that the proposed method works well.
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| 3. |
- Ranjbar, Zohreh, 1977-, et al.
(författare)
-
A Sideways Heat Equation Applied to the Measurement of the Gas Temperature in a Combustion Chamber
- 2010
-
Rapport (övrigt vetenskapligt/konstnärligt)abstract
- We consider a Cauchy problem for a parabolic equation as a mathematical model of the temperature development inside a suction pyrometer. Such devices are often used to calibrate the temperature sensor in a combustion chamber. Mathematically the problem is severely ill-posed and needs to be regularized. The model is simplified to make it one-dimensional in space. The temperature measurements are done in two steps. First, the heat transfer coefficient is approximated via a calibration experiment. Then the gas temperature in the combustion chamber is computed using a convection boundary condition. In both steps one computes the surface temperature and heat flux based on interior measurements in the thermocouple. Numerical examples are presented to test the proposed approach.
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