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A method is presented that reduces the degrees of freedom (DoFs) in linear subdomains in transient non-linear electro-quasistatic (EQS) field finite-element method (FEM) simulations. The electro-quasistatic field model yields a suitable approximation to simulate high-voltage devices such as insulators or surge arresters featuring non-linear resistive field grading materials. These materials are usually applied as thin layers, i.e., they represent only a very small volume part in the overall model. Despite the application of unstructured FEM meshes, commonly most of the DoFs are located in the domain with constant material parameters. The non-linear subdomain is much smaller with respect to the number of DoFs than the part with constant materials. The application of model order reduction techniques, in particular proper orthogonal decomposition (POD), is proposed to minimize the DoFs in the linear subdomain of the simulation model. POD captures the dynamic in the linear subdomain. Large reduction factors can be achieved for low dynamic exterior domains, thus considerably reducing the computational costs. Numerical results are presented for an IEC norm surge arrester and a typical 11 kV insulator design with a field grading inlay.