Projects of the numerical part of the course Computational Techniques for Molecular Modeling @ PoliMi - First Edition, Spring 2021
- Luca Caivano (Mathematical Engineering)
- Andrea Della Libera (Chemical Engineering)
- Manfred Nesti (Mathematical Engineering)
- Valeria Pajola (Chemical Engineering)
- Alessandro Pegurri (Chemical Engineering)
- Bruno Ursino (Mathematical Engineering)
- Chiara Vitale (Chemical Engineering)
- Implement a simulator of the conservative double pendulum using the Velocity-Verlet method as symplecting integrator and study the accuracy of trajectories and total energy with respect to time step.
- Reformulate the model so that the contraints are accounted for, simulating in cartesian coordinates using the SHAKE method.
- Apply the Velocity-Verlet method to the Frozen Argon Crystal example as in Hairer, Lubich, Wanner - Geometric Numerical Integration - Section I.4.
Reproduce the example in Gabriel, Knapek, Zumbusch - Numerical Simulation in Molecular Dynamics - Section 3.6.1 using periodic boundary conditions.
Reproduce the example of Rayleigh-Taylor instability with Coulomb potential in Gabriel, Knapek, Zumbusch - Numerical Simulation in Molecular Dynamics - Section 7.4.1.
For the C2H6 molecule
- Compute the equilibrium using GAUSSIAN
- Compute forces by invoking GAUSSIAN and parse output via Octave / Bash script
- Implement a descent method in Octave to perform the optimization using for example Gradient, BFG and Nonlinear Conjugate Gradien as descent directions
- Apply box constraints via orthogonal projection with feasible Projected Gradient or Projected quasi-Newton
- Apply Reduced Rank Extrapolation
Implement also the Quadratic Line Search (video reference)