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Matrix/vector representation

HYPRE.jl defines the structs HYPREMatrix and HYPREVector representing HYPREs datastructures. Specifically it uses the IJ System Interface which can be used for general sparse matrices.

HYPRE.jl defines conversion methods from standard Julia datastructures to HYPREMatrix and HYPREVector, respectively. See the following sections for details:

PartitionedArrays.jl (multi-process)

HYPRE.jl integrates seemlessly with PSparseMatrix and PVector from the PartitionedArrays.jl package. These can be passed directly to solve and solve!. Internally this will construct a HYPREMatrix and HYPREVectors and then convert the solution back to a PVector.

The HYPREMatrix constructor support both SparseMatrixCSC and SparseMatrixCSR as storage backends for the PSparseMatrix. However, since HYPREs internal storage is also CSR based it can be slightly more resource efficient to use SparseMatrixCSR.

The constructors also support both PartitionedArrays.jl backends: When using the MPI backend the communicator of the PSparseMatrix/PVector is used also for the HYPREMatrix/HYPREVector, and when using the Sequential backend it is assumed to be a single-process setup, and the global communicator MPI.COMM_WORLD is used.

Example pseudocode

# Assemble linear system (see documentation for PartitionedArrays)
A = PSparseMatrix(...)
b = PVector(...)

# Solve with zero initial guess
x = solve(solver, A, b)

# Inplace solve with x as initial guess
x = PVector(...)
solve!(solver, x, A, b)

It is also possible to construct the arrays explicitly. This can save some resources when performing multiple consecutive solves (multiple time steps, Newton iterations, etc). To copy data back and forth between PSparseMatrix/PVector and HYPREMatrix/HYPREVector use the copy! function.

Example pseudocode

A = PSparseMatrix(...)
x = PVector(...)
b = PVector(...)

# Construct the HYPRE arrays
A_h = HYPREMatrix(A)
x_h = HYPREVector(x)
b_h = HYPREVector(b)

# Solve
solve!(solver, x_h, A_h, b_h)

# Copy solution back to x
copy!(x, x_h)

SparseMatrixCSC / SparseMatrixCSR (single-process)

HYPRE.jl also support working directly with SparseMatrixCSC (from the SparseArrays.jl standard library) and SparseMatrixCSR (from the SparseMatricesCSR.jl package). This makes it possible to use solvers and preconditioners even for single-process problems. When using these type of spars matrices it is assumed that the right hand side and solution vectors are regular Julia Vectors.

Just like when using the PartitionedArrays.jl package, it is possible to pass sparse matrices directly to solve and solve!, but it is also possible to create HYPREMatrix and HYPREVector explicitly, possibly saving some resources when doing multiple consecutive linear solves (see previous section).

Example pseudocode

A = SparseMatrixCSC(...)
x = Vector(...)
b = Vector(...)

# Solve with zero initial guess
x = solve(solver, A, b)

# Inplace solve with x as initial guess
x = zeros(length(b))
solve!(solver, x, A, b)

SparseMatrixCSC / SparseMatrixCSR (multi-process)

Warning

This interface isn't finalized yet and is therefore not documented since it is subject to change.