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This article is mainly devoted to the research of dielectric breakdown phenomenon during high power microwave propagation. Under the force of the high-intensity fields, bound charges break free and a part of an insulator becomes electrically conductive, which may lead to electrical breakdown and thermal breakdown in high power microwave (HPM) devices or on the output window. A three-dimensional (3D) multi-physics electromagnetic-thermal model is developed and solved by spectral-element time-domain (SETD) method. The nonlinear conductivity caused by HPM is introduced into Maxwell's equations, which makes its nonlinear. The heat flux from transient power loss is utilized to construct the heat source for solving the thermal conduction equation. In the SETD process, the Galerkin's method and central difference scheme are employed for the space discretization and temporal discretization, respectively. The numerical results show that physical mechanism of electrical breakdown, thermal effect and nonlinear effect can be captured accurately during high power microwave propagation. Once the strength of the electric field exceeds the critical value experienced by the dielectric, the current increases rapidly, along with the temperature change is very severe. The validity and accuracy of the proposed method are demonstrated, and our research is beneficial for the HPM devices protection. [ABSTRACT FROM AUTHOR]