A comparison of generalized eigensystem, truncated singular value decomposition, and tikhonov regularization for the steady inverse heat conduction problem*

^*This work was partially supported by grant number BES-9410385 from the National Science Foundation.

Abstract

We present new techniques for solving inverse boundary value problems in steady heat conduction. These new Generalized Eigensystem techniques are vector expansion methods which have previously been used in inverse electrocardiography applications. We compare the Generalized Eigensystem techniques to truncated singular value decomposition and Tikhonov regularization on two two-dimensional test geometries and four temperature/flux patterns. One of the Generalized Eigensystem methods (GES_L) substantially outperforms the other techniques studied on the majority of the test cases, with inverse errors up to 20 times smaller than other approaches. In addition, even when the number of sensors on the boundary is reduced, GES _L was still comparable to or superior to the other techniques with a full sensor set.

Keywords:

• Inverse boundary value problem
• heat conduction
• Tikhonov
• SVD
• Generalized Eigensystem Method

^*This work was partially supported by grant number BES-9410385 from the National Science Foundation.

^*This work was partially supported by grant number BES-9410385 from the National Science Foundation.

Notes

^*This work was partially supported by grant number BES-9410385 from the National Science Foundation.

Additional information

Notes on contributors

Lorraine Olson

†