VectorSTEM • Featured Research Project
Curved Contour Radiation
Radiation from a Curved Contour on a Plane via a Parabolic Equation Approach
This page collects the main article, theoretical notes, derivations, numerical verification files, code, data, and visual outputs for the curved-contour radiation project.
Project overview
Geometry, PDE reduction, Crank–Nicolson numerics, verification, algorithmic analysis, and supporting theory.
Geometry
PDE
Numerics
Verification
Plots
Research
Main article
Consolidated article version of the project and its current structure.
Verification
Circle benchmark, error analysis, runtime analysis, and convergence study.
Theory
Natural coordinates, Frenet–Serret geometry, PE theory, Tappert analysis, and wide-angle models.
Code
Python implementations, CSV results, and additional solver files.
Featured documents
dissertation_CD
Verification of the numerical scheme and computational algorithm (Sections C and D).
Theory and derivations
с (1).pdf
Practical applicability of parabolic wave models and links to existing methods
Анализ_статьи_Тапперта_о_методе_PE
Theoretical foundations and computational evolution of the PE method in hydroacoustics.
Метод_параболического_уравнения
PE theory from Tappert to applied engineering and naval-use models.
Волновые_уравнения
Wide-angle one-way wave equations, Padé approximations, and numerical strategies.
Code and data
Numerical plots
Relative L2 error vs N (Nt = 4000)
PNG preview of the fixed-time-step convergence plot.
Relative L2 error vs runtime (all runs)
PNG preview of runtime versus error for all tested grids.
Additional project figure
Supplementary visual from the project folder.
