Scientific Computing Exercise Set #1

Vibrating string (1D wave equation) and time-dependent diffusion (2D diffusion + steady-state Laplace solvers).

This repository contains the notebooks used to generate the results and figures for the report.

Repository contents

• 1.1.ipynb – Tasks A–C: 1D wave equation (snapshots + animation)
• 1.2.ipynb – Tasks D–G: 2D diffusion (heatmaps + transient profiles vs analytic)
• methods.ipynb – Tasks H–L: steady-state solvers (Jacobi/GS/SOR) + internal objects (sink/insulator)

Quickstart (Conda)

# clone
git clone https://github.com/TimonJasarevic/SC_Assignments
cd SC_Assignments

# create and activate environment
conda env create -f environment.yml
conda activate sc-

# run notebooks
jupyter lab

Reproducing results (notebooks)

Open the notebooks in the order below and run Restart Kernel & Run All:

1. 1.1.ipynb (Tasks A–C)
2. 1.2.ipynb (Tasks D–G)
3. methods.ipynb (Tasks H–L)

Figure mapping (report)

The exact figure filenames in the LaTeX report are produced by exporting the corresponding notebook outputs:

• Wave snapshots: 1.1.ipynb (Tasks A–B)
• Wave animation: 1.1.ipynb (Task C)
• Diffusion transient profiles vs analytic: 1.2.ipynb (Task E)
• Diffusion heatmap snapshots: 1.2.ipynb (Task F)
• Convergence comparison (Jacobi vs GS vs SOR): methods.ipynb (Tasks H–I)
• SOR omega sweep / optimal omega: methods.ipynb (Task J)
• Internal objects (sink / insulator): methods.ipynb (Tasks K–L)

Note: The notebooks currently display figures inline. If you want the repo to auto-save PNGs with fixed names (for LaTeX), add plt.savefig("...png", dpi=300, bbox_inches="tight") in the plotting cells.

Determinism

No random components are used in the simulations. Results are deterministic given the package versions in environment.yml.

Environment

The conda environment is specified in environment.yml (Python, NumPy, SciPy, Matplotlib, Numba, and Jupyter).

Hardware

All experiments run on a standard CPU, no GPU required.

Scientific Computing Exercise Set #2

Dielectric Breakdown Model (DBM), Monte Carlo Diffusion-Limited Aggregation (DLA), and Gray-Scott reaction-diffusion.

This repository contains the notebooks used to generate the results and figures for the report.

Repository contents

• GM_DLA.ipynb - Tasks A-B: Laplacian growth / DBM, SOR optimization, and vectorized Red-Black SOR benchmarking
• MC_DLA.ipynb - Tasks C-D: Monte Carlo DLA and sticking probability experiments
• GS_DLA.ipynb - Task E: Gray-Scott reaction-diffusion parameter sweep

Quickstart (Conda)

# clone
git clone https://github.com/TimonJasarevic/SC_Assignments
cd SC_Assignments

# create and activate environment
conda env create -f environment.yml
conda activate sc-assignments

# run notebooks
jupyter lab

Reproducing results (notebooks)

Open the notebooks in the order below and run Restart Kernel & Run All:

1. GM_DLA.ipynb (Tasks A-B)
2. MC_DLA.ipynb (Tasks C-D)
3. GS_DLA.ipynb (Task E)

Figure mapping (report)

The exact figures in the LaTeX report are produced by the following notebooks:

• Laplacian growth clusters for different eta: GM_DLA.ipynb (Task A)
• SOR performance vs omega: GM_DLA.ipynb (Task A)
• Sequential vs vectorized Red-Black SOR timing comparison: GM_DLA.ipynb (Task B)
• Monte Carlo DLA cluster snapshot: MC_DLA.ipynb (Task C)
• Sticking probability p_s vs particles needed to reach the top: MC_DLA.ipynb (Task D)
• Gray-Scott final V-concentration plots for several (f, k) values: GS_DLA.ipynb (Task E)

Note: The notebooks currently display figures inline. If you want the repo to auto-save PNGs with fixed names for LaTeX, add plt.savefig("...png", dpi=300, bbox_inches="tight") in the plotting cells.

Determinism

The DBM and Monte Carlo DLA notebooks contain stochastic components. Fixed random seeds are used in the reported experiments so results are reproducible for the package versions listed in environment.yml. The Gray-Scott simulations also use a fixed seed for the added initial noise.

Environment

The conda environment is specified in environment.yml and includes Python, NumPy, SciPy, Matplotlib, tqdm, and Jupyter.

Hardware

All experiments run on a standard CPU, no GPU required.