Transparent boundary conditions for iterative high-order parabolic equations

Transparent nonlinear networks

“…The problem of transparent boundary conditions (TBC) for the linear partial differential equations (PDE) is well developed topic in mathematical and theoretical physics (see, e.g., [21][22][23][24][25][26][27][28][29][30][31][32][33][34][35][36] for review). However, despite such progress, for the nonlinear PDE, the topic is not well established, yet, due to certain complications of the problem in nonlinear case.…”

“…These latter conditions are well studied previously in detail in the Refs. [21][22][23][24][25][26][27][28][29][30][31][32][33][34][35][36].…”

Automated Selection of the Computational Parameters for the Higher-Order Parabolic Equation Numerical Methods

“…The PE method is well suitable for wave propagation modeling in inhomogeneous waveguides. PE method is used for tropospheric radio wave propagation [ 22 ], propagation of the acoustic waves in the underwater sound channel [ 18 , 29 ], acoustic and electromagnetic scattering [ 17 , 32 ], optics [ 14 ], quantum mechanics [ 11 , 26 ] and geophysics [ 35 ]. The main advantage of this method is the possibility of effective numerical implementation.…”

Transparent quantum graphs

“…To describe the regime, when there is no backscattering at the network branching points, we use the concept of transparent boundary conditions for the time-dependent Schrödinger equation studied earlier in detail in the Refs. [8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23]. Combining transparent boundary conditions concept with that of vertex boundary conditions for the linear Schrödinger equation on metric graphs, we derive the constraints, providing the regime of reflectionless transmission of the waves through the graph branching points (vertices).…”