3.5 KiB
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:
Pages = ["hypre-matrix-vector.md"]
MinDepth = 2
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.