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THE GALERKIN LUMPED PARAMETER METHOD FOR THERMAL PROBLEMS

机译:Galerkin集成的热问题参数方法

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In this contribution, we present a method called Galerkin lumped parameter (GLP) method, as a generalization of the lumped parameter models used in engineering. This method can also be seen as a model-order reduction method. Similarities and differences are discussed. In the GLP method, introduced in [1], domain is decomposed into several sub-domains and a time-independent adapted reduced basis is calculated solving elliptic problems in each sub-domain. The method seeks a global solution in the space spanned by this basis, by solving an ordinary differential system. This approach is useful for electric motors, since the decomposition into several pieces is natural. Numerical results concerning heat equation are presented. Firstly, the comparison with an analytic solution is shown to check the implementation of the numerical algorithm. Secondly, the thermal behavior of an electric motor is simulated, assuming that the electric losses are known. A comparison with the solution obtained by the finite element method is shown.
机译:在这一贡献中,我们提出了一种称为Galerkin集总参数(GLP)方法的方法,作为工程中使用的集总参数模型的概括。该方法也可以被视为模型顺序减少方法。讨论了相似之处和差异。在[1]中引入的GLP方法中,域被分解成几个子域,并且计算了每个子域中的椭圆问题的求解椭圆问题。该方法通过解决普通的差分系统来寻求在此基础上跨越空间的全局解决方案。这种方法对于电动机是有用的,因为分解成几块是自然的。提出了关于热方程的数值结果。首先,与分析解决方案的比较显示检查数值算法的实现。其次,模拟电动机的热行为,假设是已知的电损耗。示出了与通过有限元方法获得的溶液的比较。

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