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Efficient algorithm for equivalent transformations of grid models. (English. Russian original) Zbl 0606.65083

Cybernetics 21, 747-752 (1985); translation from Kibernetika 1985, No. 6, 24-27 (1985).
Mathematical methods of processing of physical experimental results have reached an advanced level of theoretical development and are widely used in practice. However, the application of these methods to the solution of boundary-value inverse problems of heat conduction runs into considerable difficulties, both in the modeling stage and in the model interpretation stage.
For three-dimensional objects of complex geometrical configuration, these inverse problems are solved numerically using grid models. When solving the direct problems, it is useful to transform to homogeneous boundary conditions, using the surface temperatures of the object under study as the determining variables. Then, using the equivalent transformation (ET) approach, we can obtain an easily identifiable solution, which is linked in a straightforward manner with the experimentally measured quantities. In this way, the unknown boundary conditions can be subsequently defined using prior information.
The temperatures and the thermal fluxes are mostly measured at technically accessible points inside the measurement region and sometimes on its boundary. In order to avoid distorting the temperature field of the measured object, a limited number of temperature and thermal flux sensors may be used.
In this paper we describe an efficient ET algorithm which can be used to generate the equivalent matrix of a grid model. Then the thermal fluxes at the boundary of the observed body are calculated in explicit form as functions of the boundary temperatures.

MSC:

65Z05 Applications to the sciences
65N22 Numerical solution of discretized equations for boundary value problems involving PDEs
35R30 Inverse problems for PDEs
35K05 Heat equation
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