Numerical solution of an axisymmetric inverse heat conduction problem
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Ibtissem Djerrar
Abstract
In this paper we are considering a boundary value axisymmetric inverse heat conduction problem inside the cylinder 0 ≤ r ≤ b. Our aim is to reconstruct the temperature f (t) = u(b, t) on the boundary r = b from measured temperature gδ(t) in the interior point 0 < r1 < b. Using Laplace transform, for the direct problem the solution will be represented as a Fourier Bessel series. Then the inverse problem is reduced to an integral equation of type Af = gδ. Such an equation is ill-posed, hence we use the Tikhonov regularization method. Finally, we conclude with numerical examples.
Abstract
In this paper we are considering a boundary value axisymmetric inverse heat conduction problem inside the cylinder 0 ≤ r ≤ b. Our aim is to reconstruct the temperature f (t) = u(b, t) on the boundary r = b from measured temperature gδ(t) in the interior point 0 < r1 < b. Using Laplace transform, for the direct problem the solution will be represented as a Fourier Bessel series. Then the inverse problem is reduced to an integral equation of type Af = gδ. Such an equation is ill-posed, hence we use the Tikhonov regularization method. Finally, we conclude with numerical examples.
Kapitel in diesem Buch
- Frontmatter I
- Preface V
- Acknowledgment VII
- Contents IX
- Elliptic differential operators with periodic and oscillating decaying coefficients 1
- Locally finite extensions and Gesztesy–Šeba realizations for the Dirac operator on a metric graph 25
- Double lacunary statistically convergent sequences of weight g 55
- Riesz probability distributions on symmetric cones 63
- A note on traces of forms with applications to the Bessel operator 75
- Pseudospectra of multivalued linear operators 85
- On the frame properties of exponentials associated to analytic families of operators and application 101
- Invariance of essential spectrum by means of generalized weak demicompactness 115
- Some results of S-pseudospectra of bounded operators in a Hilbert space 121
- Stabilization of a marine riser system by the use of viscoelastic material 131
- Sequence of linear operators converging in the generalized sense and its essential pseudospectra 147
- Left–right essential spectra of one-sided operator matrix and application 157
- Existence of Solutions for an integral equation of Chandrasekhar type in Banach algebras with respect to the weak topology 177
- Strong evolution problems in Musielak spaces 183
- Numerical solution of an axisymmetric inverse heat conduction problem 199
- Multiple solutions for nonlocal elliptic problems with concave–convex nonlinearities and weights 207
Kapitel in diesem Buch
- Frontmatter I
- Preface V
- Acknowledgment VII
- Contents IX
- Elliptic differential operators with periodic and oscillating decaying coefficients 1
- Locally finite extensions and Gesztesy–Šeba realizations for the Dirac operator on a metric graph 25
- Double lacunary statistically convergent sequences of weight g 55
- Riesz probability distributions on symmetric cones 63
- A note on traces of forms with applications to the Bessel operator 75
- Pseudospectra of multivalued linear operators 85
- On the frame properties of exponentials associated to analytic families of operators and application 101
- Invariance of essential spectrum by means of generalized weak demicompactness 115
- Some results of S-pseudospectra of bounded operators in a Hilbert space 121
- Stabilization of a marine riser system by the use of viscoelastic material 131
- Sequence of linear operators converging in the generalized sense and its essential pseudospectra 147
- Left–right essential spectra of one-sided operator matrix and application 157
- Existence of Solutions for an integral equation of Chandrasekhar type in Banach algebras with respect to the weak topology 177
- Strong evolution problems in Musielak spaces 183
- Numerical solution of an axisymmetric inverse heat conduction problem 199
- Multiple solutions for nonlocal elliptic problems with concave–convex nonlinearities and weights 207
