In this paper, we introduce a mathematical framework for analyzing and optimizing district heating networks by leveraging the Green's function method. Traditional numerical methods for simulating district heating networks often face computational challenges and lack transparency in revealing cause-and-effect relationships in heat propagation. By treating temperature as a scalar field, we employ Green's function methods to derive analytical solutions that provide a more transparent and intuitive understanding of how heat propagates through the network in response to various inputs. We demonstrate the application of this framework through two numerical examples involving heating networks. Comparative results show that, under identical hardware conditions, the Green's function method requires only about one-fifth of the computational time compared to the finite element method for the same case. This approach offers distinct advantages in terms of computational efficiency, accuracy, and interpretability, enabling more effective design, optimization, and control of sustainable district heating systems. [ABSTRACT FROM AUTHOR]

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