In this work, a novel Robin transmission condition (RTC)-enhanced discontinuous Galerkin (DG) method is proposed for the dc IR-drop analysis of power distribution networks with Joule heating effects included. Unlike the conventional DG method, the proposed DG method straightforwardly applied to discretize the second-order spatial partial differential governing equations for the electrostatic potential $\Phi $ and the steady-state temperature $T$. The numerical flux in DG used to facilitate the information exchange among neighboring subdomains introduces two additional variables: the current density $J$ for the electrical potential equation and the thermal flux $q$ for the thermal equation. To solve them, at the interface of neighboring subdomains, an RTC is presented as the second equation to establish another connection for solutions in neighboring subdomains. With this strategy, the number of degrees of freedom (DoFs) involved in the proposed RTC-DG method is dramatically reduced compared with the traditional DG method. The finalized matrix system is solved in a finite-element tearing and interconnecting (FETI)-like procedure, namely the unknowns are obtained in a subdomain-by-subdomain scheme. Finally, the accuracy and the efficiency of the proposed RTC-DG method are validated by several representative examples.


Electrical and Computer Engineering


National Natural Science Foundation of China, Grant 62071290

Keywords and Phrases

DC IR-drop; discontinuous Galerkin~(DG) method; domain decomposition method (DDM); electrical-thermal cosimulation; Robin transmission condition (RTC)

International Standard Serial Number (ISSN)

2156-3985; 2156-3950

Document Type

Article - Journal

Document Version


File Type





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Publication Date

01 Jan 2022