HYPRE.jl

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Julia interface to HYPRE ("high performance preconditioners and solvers featuring multigrid methods for the solution of large, sparse linear systems of equations on massively parallel computers").

While the main purpose of HYPRE is to solve problems on multiple cores, it can also be used for single core problems. HYPRE.jl aims to make it easy to use both modes of operation, with an interface that should be familiar to Julia programmers. This README includes some basic examples -- refer to the documentation for more details, and for information about the included solvers and preconditioners and how to configure them.

Example: Single-core solve with standard sparse matrices

It is possible to use Julia's standard sparse arrays (SparseMatrixCSC from the SparseArrays.jl standard library, and SparseMatrixCSR from the SparseMatricesCSR.jl package) directly in HYPRE.jl. For example, to solve Ax = b with conjugate gradients:

# Initialize linear system
A = SparseMatrixCSC(...)
b = Vector(...)

# Create a conjugate gradients solver
cg = HYPRE.PCG()

# Compute the solution
x = HYPRE.solve(cg, A, b)

Example: Multi-core solve using PartitionedArrays.jl

For multi-core problems it is possible to use PartitionedArrays.jl directly with HYPRE.jl. Once the linear system is setup the solver interface is identical. For example, to solve Ax = b with bi-conjugate gradients and an algebraic multigrid preconditioner:

# Initialize linear system
A = PSparseMatrix(...)
b = PVector(...)

# Create preconditioner
precond = BoomerAMG()

# Create a bi-conjugate gradients solver
bicg = HYPRE.BiCGSTAB(; Precond = precond)

# Compute the solution
x = HYPRE.solve(bicg, A, b)