A full-vectorial finite element method is developed to analyze the surface waves propagating at the interface between two media which could be dissipative particularly. The dissipative wave possessing a complex-valued propagation constant can be determined precisely for any given propagation direction and thus the property of losses could be thoroughly analyzed. Besides, by applying a special characteristic of the implicit circular block matrix, we reduce the computational consumptions in the analysis. By utilizing this method, the Dyakonov surface wave (DSW) at the interface between a dielectric and a metal-dielectric multilayered (MDM) structure which serves as a hyperbolic medium is discussed. Its propagation loss is smaller for larger period of the MDM structure but its field becomes less confined to the interface.
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