Distributed Parameter Systems, Optimal Control And Domain Decomposition Algorithm And Its Application

In view of problems on solving parabolic equation with non-differentiability, parameter identification on the problems is discussed in this paper by non-overlapping domain decomposition method. Main theoretic results are as following.1. Through introducing an energy transmission function on internal boundary, a distributed parameter identification model is established. In the model state variable is temperature in subdomains, and identification variable is the energy transmission function. Its objective functional is to minimize the sum of the difference between temperatures on the interfaces among all neighbor subdomains.2. Using the property of the bilinear and trilinear form, a priori bound for solutions of a weak formulation is given. Through the priori bound, it is shown that optimal solutions exist.3. With penalty parameter converging to zero in the objective functional, it is shown that optimal solutions of the optimization problem converge to a weak solution of the original problem.Results above are applied to calculation of nonsteady three-dimensional temperature field in transformers.It is very important for design and improvement of transformers to determine temperature field distribution and character in transformers. Problems on temperature field are complicate, especially for large transformers, so they haven't been solved. This paper discusses the numerical simulation model, in which nonsteady three-dimensional temperature field in large oil-immersed self-quenched transformers is the main object.According to the symmetry of structure of the transformer, one fourth of the whole domain is chosen as the numerical calculation domain. This paper presents the three-dimensional nonsteady temperature field equation including transfer of mass and heat, and conditions determining solutions. For overcoming nonsmooth of temperature field, temperature field equations in subdomains are built respectively in rectangular coordinate and in cylindrical coordinate.Based on the numerical simulation algorithm in this paper, numerical results for temperature field are given and analyzed. The results show that the numerical simulation is coincident with the experiments, and that the mathematical model and the domain decomposition method in this paper are corrective and effective.