These are my numerical simulations of Parareal Algorithms solving heat equation. The code is written by me in C++ using dealii library and the videos are generated using Paraview from the numerical solutions. The top 2 videos are the simulations using Parareal Algorithm derived from linear equation and nonlinear equations. The bottom video is the exact solution for the heat equation.
Use Parareal Algorithm derived from the linear equation to simulate the solution of heat equation with zero boundary. The video shows the first 4 iterations. The relative error is very small after the first iteration.
Use Parareal Algorithm derived from the nonlinear equation to simulate the solution of heat equation with zero boundary. The video shows the first 4 iterations. The relative error is very small after the first iteration.
This video shows the exact solution of heat equation with zero boundary.