This dissertation, "The Electromagnetic Compatibility and Multi-physics Analysis Based on the PEEC Method" by Ying, Cao,, was obtained from The University of Hong Kong (Pokfulam, Hong Kong) and is being sold pursuant to Creative Commons: Attribution 3.0 Hong Kong License. The content of this dissertation has not been altered in any way. We have altered the formatting in order to facilitate the ease of printing and reading of the dissertation. All rights not granted by the above license are retained by the author. Abstract: In this thesis, it is our biggest interest to develop full-wave based engineering friendly electromagnetic modeling approaches for coupling and radiation problems that are found in multi-physics and electromagnetic compatibility (EMC) applications. The partial element equivalent circuit (PEEC) method, a unique bridging method between electromagnetics and circuit theory, is employed and extended to address new challenges in electromagnetic analysis. Firstly, we developed the first derived equivalent circuit model of arbitrary shape graphene sheets. It is also a novel contribution to PEEC for handling dispersive and anisotropic medium. Graphene''s numerical modeling is extremely cost prohibitive due to the huge contrast between its thickness and other dimensions. In this work, for the first time, the electromagnetic features of graphene are characterized by a derived equivalent circuit model from the first principle. Physical properties of the material can be conveniently obtained, such as radiation, scattering and resistance properties. Secondly, we developed the equivalent circuit model for optical electronic devices. By developing a new generalized equivalent circuit model for nanoantennas derived from the wave equation, not only material properties such as dispersivity and loss of the permittivity can be handled conveniently and efficiently, but also more physical insight of the working mechanism can be developed from the derived mo