VectorSTEM
VectorSTEM • Research Files

Curved Contour Radiation

Radiation from a Curved Contour on a Plane via a Parabolic Equation Approach

This page collects all theory PDFs, derivations, code, CSV results, and numerical plots for the curved-contour radiation project.

Project overview
Geometry, PDE reduction, Crank–Nicolson numerics, verification data, and visual outputs.
Geometry PDE Numerics Verification Plots Research
Theory
Natural coordinates, Frenet–Serret formulas, Helmholtz reduction, and detailed derivations.
Code
Python implementation for the circle test with Crank–Nicolson time stepping.
Data
CSV runs with N, Nt, relative error, and runtime diagnostics.
Plots
Error vs N, error vs Nt, and error vs runtime.
Back to Research Contact

Theory and derivations

метод_Кранка_Николсона.pdf
Crank–Nicolson note.
Open Download
frenet-serret-derivation.pdf
Frenet–Serret formulas and derivation notes.
Open Download
Получение_1_4_15.pdf
Detailed derivation of formula 1.4.15.
Open Download
Получение_1_4_19.pdf
Detailed derivation of formula 1.4.19.
Open Download
Разобрать_смысл_этих_координат.pdf
Interpretation of the coordinates and variables.
Open Download
pde-variable-substitution.pdf
Manual variable substitution in the PDE.
Open Download
A___D.pdf
Research structure / roadmap.
Open Download
ia1.pdf
Draft research material.
Open Download
ib1.pdf
Draft research material.
Open Download

Code and data

cn_circle.py
Python implementation of the circle benchmark.
Open Download
results_cn_circle.csv
Exported numerical results for all runs.
Open Download
README.txt
Short run description and project notes.
Open Download

Numerical plots

Relative L2 error vs N (Nt = 4000)
Relative L2 error vs N
Relative L2 error vs Nt (N = 1024)
Relative L2 error vs Nt
Relative L2 error vs runtime (all runs)
Relative L2 error vs runtime