firedrake.matrix_free package

Submodules

firedrake.matrix_free.operators module

class firedrake.matrix_free.operators.ImplicitMatrixContext(a, row_bcs=[], col_bcs=[], fc_params=None, appctx=None)

Bases: object

createSubMatrix(mat, row_is, col_is, target=None)

duplicate(mat, copy)

getDiagonal(mat, vec)

getInfo(mat, info=None)

missingDiagonal(mat)

mult(mat, X, Y)

multTranspose(mat, Y, X)

EquationBC makes multTranspose different from mult.

Decompose M^T into bundles of columns associated with the rows of M corresponding to cell, facet, edge, and vertice equations (if exist) and add up their contributions.

                   Domain
    a a a a 0 a a    |
    a a a a 0 a a    |
    a a a a 0 a a    |   EBC1
M = b b b b b b b    |    |   EBC2 DBC1
    0 0 0 0 1 0 0    |    |    |    |
    c c c c 0 c c    |         |
    c c c c 0 c c    |         |
                                             To avoid copys, use same _y, and update it
                                             from left (deepest ebc) to right (least deep ebc or domain)
Multiplication algorithm:                       _y         update ->     _y        update ->   _y

         a a a b 0 c c   _y0     0 0 0 0 c c c   *      0 0 0 b b 0 0    *     a a a a a a a   _y0          0
         a a a b 0 c c   _y1     0 0 0 0 c c c   *      0 0 0 b b 0 0    *     a a a a a a a   _y1          0
         a a a b 0 c c   _y2     0 0 0 0 c c c   *      0 0 0 b b 0 0    *     a a a a a a a   _y2          0
M^T _y = a a a b 0 c c   _y3  =  0 0 0 0 c c c   *    + 0 0 0 b b 0 0   _y3  + a a a a a a a    0      +    0
         0 0 0 0 1 0 0   _y4     0 0 0 0 c c c   0      0 0 0 b b 0 0    0     a a a a a a a    0          _y4 (replace at the end)
         a a a b 0 c c   _y5     0 0 0 0 c c c   _y5    0 0 0 b b 0 0    *     a a a a a a a    0           0
         a a a b 0 c c   _y6     0 0 0 0 c c c   _y6    0 0 0 b b 0 0    *     a a a a a a a    0           0
                                     (uniform on           (uniform          (uniform on domain)
                                      on facet2)            on facet1)

* = can be any number

on_diag = True

This class gives the Python context for a PETSc Python matrix.

Parameters:

• a – The bilinear form defining the matrix

• row_bcs – An iterable of the :class.`.DirichletBC`s that are imposed on the test space. We distinguish between row and column boundary conditions in the case of submatrices off of the diagonal.

• col_bcs – An iterable of the :class.`.DirichletBC`s that are imposed on the trial space.

• fcparams – A dictionary of parameters to pass on to the form compiler.

• appctx – Any extra user-supplied context, available to preconditioners and the like.

view(mat, viewer=None)

Module contents