This thesis aims to determine which reordering and preconditioning techniques best exploit the sparsity and structure of Jacobian matrices arising from the district heating networks of Gradyent, to reduce computation times and enable real-time optimization.
District heating networks play a crucial role in the sustainable urban energy supply. Gradyent aims to improve the efficiency and sustainability of district heating networks using their real-time digital twin model. A key challenge to enable fast and accurate simulations is solving large, sparse, and ill-conditioned linear systems of arising within the Newton-Raphson method efficiently.
The application of suitable, computationally effective and applicable reordering and preconditioning techniques based on the structure of the networks improves the convergence rate of direct and iterative methods. Thus, reduces the computational times of linear solvers. For this thesis, first, a thorough understanding of the structure of the networks is established. Subsequently, different reordering and preconditioning techniques are analysed to determine which can be most effective when applied on the linear systems arising from Gradyent’s district heating networks.
The approach analyses the sparsity and block-structure of the Jacobians to identify suitable reordering and preconditioning techniques. It evaluates the performance of the reordering strategies–Reverse Cuthill–McKee, Approximate Minimum Degree, and Maximum Bipartite Matching–for reducing fill-in, bandwidth, and enhancing diagonal dominance. In addition, it investigates the effectiveness of ILU and block preconditioning methods, as well as hybrid techniques. Both direct (LU) and iterative (GMRES) linear solvers are used for this assessment.