MultiGridBarrierMPI.jl 0.1.1

A Julia package that bridges MultiGridBarrier.jl and LinearAlgebraMPI.jl for distributed multigrid barrier computations.

Overview

MultiGridBarrierMPI.jl extends the MultiGridBarrier.jl package to work with LinearAlgebraMPI.jl's distributed matrix and vector types. This enables efficient parallel computation of multigrid barrier methods across multiple MPI ranks using pure Julia distributed types (no PETSc required).

Key Features

• 1D, 2D, and 3D Support: Full support for 1D elements, 2D triangular, and 3D hexahedral finite elements
• Seamless Integration: Drop-in replacement for MultiGridBarrier's native types
• Pure Julia MPI: Uses LinearAlgebraMPI.jl for distributed linear algebra
• Type Conversion: Easy conversion between native Julia arrays and MPI distributed types
• MPI-Aware: All operations correctly handle MPI collective requirements
• MUMPS Solver: Uses MUMPS direct solver for accurate Newton iterations

Quick Example

Solve a 2D p-Laplace problem with distributed MPI types. Save this code to example.jl:

using MPI
MPI.Init()

using MultiGridBarrierMPI
using LinearAlgebraMPI
using MultiGridBarrier

# Solve with MPI distributed types (L=3 refinement levels)
sol_mpi = fem2d_mpi_solve(Float64; L=3, p=1.0, verbose=false)

# Convert to native types for visualization
sol_native = mpi_to_native(sol_mpi)

# Only rank 0 creates the plot
rank = MPI.Comm_rank(MPI.COMM_WORLD)
if rank == 0
    using PyPlot
    plot(sol_native)
    savefig("solution.png")
    println("Plot saved to solution.png")
end

Run with MPI:

mpiexec -n 4 julia --project example.jl

Documentation Contents

• Installation
• • Prerequisites
  • Package Installation
  • Verification
  • Initialization Pattern
  • Running MPI Programs
  • Troubleshooting
  • Next Steps
• User Guide
• • Initialization
  • Basic Workflow
  • Understanding MPI Collective Operations
  • Type Conversions
  • Advanced Usage
  • IO and Output
  • Performance Considerations
  • 1D Problems
  • 2D Problems
  • 3D Problems
  • Time-Dependent (Parabolic) Problems
  • Common Patterns
  • Next Steps
• API Reference
• • High-Level API
  • Type Conversion API
  • Type Mappings Reference
  • Geometry Structure
  • Solution Structure
  • MPI and IO Utilities
  • Examples
  • Integration with MultiGridBarrier

Package Ecosystem

This package is part of a larger ecosystem:

• MultiGridBarrier.jl: Core multigrid barrier method implementation (1D, 2D, and 3D)
• LinearAlgebraMPI.jl: Pure Julia distributed linear algebra with MPI
• MPI.jl: Julia MPI bindings for distributed computing

Requirements

• Julia 1.10 or later (LTS version)
• MPI installation (OpenMPI, MPICH, or Intel MPI)
• MUMPS for sparse direct solves
• At least 2 MPI ranks recommended for testing

Citation

If you use this package in your research, please cite:

@software{multigridbarriermpi,
  author = {Loisel, Sebastien},
  title = {MultiGridBarrierMPI.jl: Distributed Multigrid Barrier Methods with MPI},
  year = {2024},
  url = {https://github.com/sloisel/MultiGridBarrierMPI.jl}
}

License

This package is licensed under the MIT License.