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.

Scientific Computing Exercise Set #3

Open challenge assignment: Kármán vortex street with three numerical methods, and WiFi router placement using the Helmholtz equation.

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

Repository contents

• Challenge_A.ipynb - Challenge A: Kármán vortex street using three methods:

  • Finite Difference Method (FDM)
  • Finite Element Method (FEM, using NGSolve)
  • Lattice Boltzmann Method (LBM)

• Challange_B.py - Challenge B: WiFi router optimization in a 2D floor plan using a Helmholtz solver with coarse-to-fine search and signal-strength evaluation at the prescribed measurement points

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 notebook / script
jupyter lab
python Challange_B.py

Reproducing results

Challenge A

Open Challenge_A.ipynb and run Restart Kernel & Run All.

The notebook contains three sections:

1. Finite Difference
2. Finite Element Method
3. LBM

These correspond directly to the three methods requested in Assignment Set 3 for the Kármán vortex street challenge.

Challenge B

Run:

python Challenge_B.py

This script:

• builds the room and wall masks
• solves the Helmholtz equation on a Cartesian grid
• evaluates signal strength by averaging in a small disk around the four measurement points
• performs a coarse-to-fine search over router locations
• prints the best router position and per-room scores
• plots the final signal-strength field

Figure mapping (report)

The main report figures are produced by the following files:

• Challenge A stability comparison and method experiments: Challenge_A.ipynb
• WiFi signal strength heatmap / best router location: Challange_B.py
• Per-room signal strengths and total score: Challange_B.py console output / report tables

Assignment-specific notes

Challenge A

Assignment Set 3 asks for the same flow problem to be solved with:

1. finite difference,
2. finite element using NGSolve,
3. lattice Boltzmann,

and compares how high the Reynolds number can go while remaining stable.

Challenge B

The router optimization challenge uses the scalar Helmholtz equation with:

• Gaussian source amplitude (A = 10^4)
• source width (\sigma = 0.2) m
• air refractive index (1.0)
• wall refractive index (2.5 + 0.5j)
• signal evaluation by averaging in a disk of radius (5) cm around the four measurement locations

The current implementation uses:

• optimization frequency: 0.8 GHz
• coarse grid spacing: 0.05 m
• refined grid spacing: 0.0125 m
• coarse-to-fine router search with local refinement

Determinism

Challenge A and Challenge B are deterministic for fixed parameter settings. No random components are used in the current WiFi optimization script.

Environment

The conda environment should include at least:

• Python
• NumPy
• SciPy
• Matplotlib
• Jupyter
• NGSolve / Netgen

Hardware

All experiments were run on a standard CPU. The WiFi optimization problem becomes computationally expensive at physically realistic WiFi frequencies, which is why motivated approximations and scaled visualization settings are used.