Exercises in scientific computing

These are various exercises in scientific computing.

Sequential (`seq`)

basics
- ieee754
  - doubles_density: Relative density of double floating-point numbers
  - info: Extracting information from IEEE 754 floating-point numbers
  - ulps: Number of full floating-point intervals between two numbers
- summation
  - exp_taylor_series: Exponent calculation via Taylor series summation
  - kahan_summation: Kahan summation algorithm
- shift_and_subtract_division: Shift-and-subtract division division algorithm
lin
- laplace_2d_fdm
  - relaxation: Laplace BVP solution using finite-difference discretization and the Jacobi, the Gauss-Seidel, and the SOR iterative methods
- poisson_2d_fem: Poisson BVP solution using mixed finite-element P0+P1 method
- given_qr_factorization: QR factorization using Givens rotation
eigen
- jacobi: Matrix diagonalization using the Jacobi eigenvalue algorithm
random
- ising_model: 2D Ising model simulation with Metropolis Monte-Carlo algorithm
- uniform_distr_on_sphere: Uniform distribution on sphere
wavelet
- multiresolution_analysis: Wavelets, discrete wavelet transform

MPI (`mpi`)

mat_mat_multiplication.cpp: Matrix-matrix multiplication

Results

Generated images can be found in the corresponding directories inside the figs directory. Video animations can be found on the following YouTube channel.

How to build

Set MKLROOT environment variable to point to the MKL installation directory,
and be sure that your CMake version is >= 3.13. Then:

git clone --recursive https://github.com/eugnsp/sci_comp_exercises.git
cd sci_comp_exercises
mkdir build && cd build
cmake -DCMAKE_BUILD_TYPE=RELEASE .. && make

C++17/C++20 compiler is required. Tested with GCC 8.3.0.

External dependencies

License

This code is distributed under GNU General Public License v3.0.