Comparison between a local and a nonlocal transparent boundary condition applied to the tropospheric ducting propagation problem

Brief review on PE method application to propagation channel modeling in sea environment

“…Close to the sea surface, Fig. 4 (b), the Ament t identical results for the PF for the used scenario; the difference between putation is carried out using the FE-based solution to (1) [61], with computational steps chosen afterwards [62]. The LTBC presents results relatively close to those given by the NTBC (for details and more examples see [86]).…”

“…Three main numerical techniques to solve (1) have become popular: the SSF-based algorithms [34,[44][45][46][47][48]58], finite difference (FD) based algorithms [19,33,59,60] and algorithms using the finite element (FE) method [41][42][43][61][62][63][64][65]. The choice of the PE solution method depends strongly on the specific propagation scenario.…”

“…To provide operational solution, some compromises in accuracy could be made applying simpler or more complex local TBCs (LTBCs) [85]. The simpler LTBC [85], firstly proposed and used in integrated optics, is validated for FE-based solution of (1) and tropospheric surface duct case in Sirkova [61] and later compared to the NTBC [83] for elevated ducts, evaporation ducts and cascades in Sirkova [62] and Sirkova [86]. The start of the computation procedure for the PE requires knowledge of the initial field U(0 ).…”

Applying the Parabolic Equation to Tropospheric Groundwave Propagation: A review of recent achievements and significant milestones

“…Over the past ten years, FEM has rapidly developed, and numerous scholars have published articles describing the derivation of the solution process and the verification of results. Moreover, the development of boundary conditions, such as perfectly matching layers (PML) transparent boundary conditions (TBCs) [35]- [37], Padé approximation, and Claerbout approximation, which are used to establish WAPE and cannot be solved by SSFT, has made FDM and FEM viable alternatives to SSFT. In 2010, Apaydin and Sevgi [20] performed systematic comparisons of FEM and SSFT using software called LINPE at a frequency of 300 MHz.…”