Simulation Methods in Biomedical Engineering

This repository contains MATLAB code and scripts for various laboratory assignments in the course Simulation Methods in Biomedical Engineering. The course covers a range of numerical methods used in biomedical engineering, including solving partial differential equations (PDEs), boundary value problems, molecular dynamics, and the finite element method (FEM).

Contents

• Boundary Value Problems

  • Boundary_Value_Problem_Heat_Conduction.m
    Solves and visualizes a 1D heat conduction boundary value problem using finite difference methods for different step sizes and convection velocities.

• Finite Element Method

  • 1D_FEM_of_2LinearElementSystem.m
    Solves a 1D FEM problem using two linear elements and plots the displacement solution.
  • Finite_Element_Problem_Fishing_Rod.m
    Models a fishing rod using the finite element method, assembling global stiffness matrices and plotting the rod's deformation.

• Molecular Dynamics

  • Molecular_Simulation_Verlets_Algorithm.m
    Simulates the van der Waals interaction between two Argon atoms using the Lennard-Jones potential and the Velocity Verlet algorithm. Compares results for different time steps.

How to Use

1. Open the desired .m script in MATLAB.
2. Run the script to reproduce the results and plots for each numerical method.
3. Modify parameters within the scripts to experiment with different scenarios.

Requirements

• MATLAB (R2018b or newer recommended)
• No additional toolboxes are strictly required, but the scripts use standard MATLAB functions for matrix operations and plotting.

File Overview

• Boundary_Value_Problem_Heat_Conduction.m
  Approximates temperature distribution in a rod for varying mesh sizes and convection velocities.
• 1D_FEM_of_2LinearElementSystem.m
  Demonstrates assembling and solving a simple 1D FEM system.
• Finite_Element_Problem_Fishing_Rod.m
  Assembles global stiffness matrices for a multi-segment rod and visualizes its deformation.
• Molecular_Simulation_Verlets_Algorithm.m
  Implements the Velocity Verlet algorithm for molecular dynamics simulation.

Notes

• Each script is self-contained and includes comments explaining the steps and parameters.
• Example problems are chosen for clarity and educational value; you can adapt the scripts for more complex systems.
• Plots are generated automatically to visualize the results of each simulation.

License

MIT License

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Maintained by David Dashti. For questions or suggestions, please open an issue or contact me.