DISTRIBUTED ALGORITHMS FOR SOLVING APPLIED PROBLEMS IN AN EXTREME SETTING (Modern Problems of Metallurgy, 2021)
The corresponding class of mathematical models was derived from studying the thermophysical properties of materials using inverse methods. It was shown that one-dimensional formulation of thermal conductivity problems is the primary computational mathematical model, which requires building effective solutions of the inverse thermal conductivity problem and algorithms for processing experimental data to determine the material's thermophysical features. The processing mathematical models procedure is reduced to an extreme formulation allowing to development of practical algorithms for solving coefficient problems of arbitrary order of accuracy. Herein, the algorithm's variety of accurate input data entirely coincides with the exact result of analytical solutions, and the computational results errors of the recoverable causal features, including the input data error, are approximately equal to the original data errors. The paper presents the results of solving test problems based on the proposed approach. Additional conditions are derived, dividing the studied problem into two tasks: a) temperature; b) streaming. The first allows solving the coefficient problem over the entire given range of temperature changes by the control parameter as the diffusion coefficient (model 1); the other aims at determining the coefficients of thermal conductivity or heat capacity (model 2). Studies of mathematical models 1 and 2 were performed by the direct method. The proposed models allow solving problems in extreme situations. That approach is that the heat transfer process' desired causal features are considered the control parameters that are part of the direct problems solution. To solve the given problems by mathematical modeling methods, we developed a package of applied problems, which primary purpose was to provide practical assistance to the researcher at all experimental data processing stages. The package covered the requirements for object-oriented programming. The simulation procedure was implemented based on the multiprocessor computing system. The application package is designed to process thermophysical experiments by inverse methods.
Keywords: coefficient problems; extreme formulation; mathematical models; thermal conductivity; heat transfer