MultiGridBarrierPETSc.jl 0.1.7

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

Overview

MultiGridBarrierPETSc.jl extends the MultiGridBarrier.jl package to work with PETSc's distributed Mat and Vec types through SafePETSc.jl. This enables efficient parallel computation of multigrid barrier methods across multiple MPI ranks.

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
• Distributed Computing: Leverage PETSc's distributed linear algebra for large-scale problems
• Type Conversion: Easy conversion between native Julia arrays and PETSc distributed types
• MPI-Aware: All operations correctly handle MPI collective requirements
• MUMPS Solver: Automatically configures MUMPS direct solver for accurate Newton iterations

Quick Example

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

using MPI
using MultiGridBarrierPETSc
using MultiGridBarrier
using PyPlot
MultiGridBarrierPETSc.Init()

# Solve with PETSc distributed types (L=3 refinement levels)
sol_petsc = fem2d_petsc_solve(Float64; L=3, p=1.0, verbose=false)

# Convert to native types for visualization
sol_native = petsc_to_native(sol_petsc)

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

Run with 4 MPI ranks using Julia's MPI launcher:

julia -e 'using MPI; run(`$(MPI.mpiexec()) -n 4 $(Base.julia_cmd()) example.jl`)'

This command uses MPI.mpiexec() to get the correct MPI launcher configured for your Julia installation, avoiding compatibility issues with system mpiexec. Add --project or other Julia options as needed for your environment.

The plot above shows the solution to a 2D p-Laplace problem computed using distributed PETSc matrices across 4 MPI ranks, then converted back to native Julia types for visualization.

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
  • Common Patterns
  • 1D Problems
  • 3D Problems
  • Time-Dependent (Parabolic) Problems
  • Next Steps
• API Reference
• • Initialization
  • High-Level API
  • Type Conversion API
  • Type Mappings Reference
  • Geometry Structure
  • Solution Structure
  • MPI and IO Utilities
  • PETSc Configuration
  • 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)
• SafePETSc.jl: Safe PETSc bindings with automatic memory management
• MPI.jl: Julia MPI bindings for distributed computing

Requirements

• Julia 1.10 or later (LTS version)
• MPI installation (OpenMPI, MPICH, or Intel MPI)
• PETSc with MUMPS support (automatically configured)
• At least 4 MPI ranks recommended for testing

Citation

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

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

License

This package is licensed under the MIT License.