MPI Helmholtz Equation

Contains serial and parallel (MPI) implementations of following algorithms:

• Helholtz equation solver (internal iterations using Jacobi method)
• Helholtz equation solver (internal iterations using Seidel method with black-red ordering)

Note that present implementations are intended for academic purposes, as such they are not meant to be used in any sort of high-performance production code.

Compilation

• Recommended compiler: Intel C++ Compiler
• Requires C++17 support
• Requires MPI implementation

Usage

Helmholtz equation:
$$-u_{xx} - u_{yy} + k^2 u(x, y) = f(x, y),$$
where
$k$ - wave_number,
$f$ - right_part,
defined on a 2D region $[0, L]\times[0, L]$ with $4$ fist-type boundary conditions

Adjust grid size $N$, area size $L$, wave number $k$, precision and boundary conditions in "main.cpp" to configure testing parameters. Parallel implementations assume $(N - 2)$ to be a multiple of MPI_Comm_size().

Version history

• 01.01

  • Reworked type 3 communication to utilize its' async nature and compute middle rows during sending of data
  • Refined comments, removed redundant dublicates

• 01.00

  • Changed table formatting
  • Added more error messages and safeguards
  • Changed type 1 and 2 MPI communications to guarantee downwards-upwards waves of data transfer

• 00.04

  • Added serial Seidel implementation
  • Implemented parallel Seidel nethod

• 00.03

  • Added serial Jacobi implementation
  • Added multiple types of MPI communication, that can be toggled as a module inside the method
  • Added proper output in form of a table
  • Parallelized Jacobi stop condition
  • Finalized Jacobi implementation and got proper speedup from parallelization

• 00.02

  • Included full method description in comments

• 00.01

  • Implemented parallel Jacobi method with MPI (stop condition is serial for now)
  • Implemented parallel calculation of relative error

License

This project is licensed under the MIT License - see the LICENSE.md file for details