Solvers
Parthenon does not yet provide an exhaustive set of solvers. Currently, a few basic building blocks are provided and we hope to develop more capability in the future.
Stencil
This class provides a very simple and efficient means of storing a
sparse matrix with the special form that every row has identical entries
relative to the matrix diagonal. A good example of this is in the
straightforward finite difference discretization of the Poisson equation
(see here for example
usage). The Stencil
object is extremely efficient at storing these
sparse matrices because it only has to store the matrix values and
offsets from the diagnonal for a single row. The Stencil
class
provides member functions to compute matrix vector products (MatVec
)
and Jacobi iterates (Jacobi
). Both are designed to be called from
within kernels and operate on a single matrix row at a time.
SparseMatrixAccessor
This is a helper class that allows one to store a more general sparse
matrix than Stencil
provides. Like Stencil
, the
SparseMatrixAccessor
class assumes that the location of the nonzero
matrix elements have fixed offsets from the diagonal in every row. Here,
though, the values of the matrix elements can be different from row to
row. The sparse matrix itself can be stored in a normal
CellVariable with the number of components
equal to the number of nonzero elements in a row of the matrix. The
SparseMatrixAccessor
class than associates each of these components
with a particular matrix element. Like Stencil
, the
SparseMatrixAccessor
class provides MatVec
and Jacobi
member
functions. A simple demonstration of usage can be found in the Poisson
example.