The assemble Module

stat_fem.assemble.assemble(f, tensor=None, bcs=None, form_compiler_parameters=None, mat_type=None, sub_mat_type=None, appctx={}, options_prefix=None, **kwargs)

Overloaded assembly function to include assembly of stat-fem operators

This provides a functional interface to assemblying stat-fem objects in the same manner as other matrices and vectors in Firedrake. If the input object is a ForcingCovariance or InterpolationMatrix object, it calls the assemble method and returns. Otherwise, it passes the arguments along to Firedrake for assembly.

If f is a Form then this evaluates the corresponding integral(s) and returns a float for 0-forms, a Function for 1-forms and a Matrix or ImplicitMatrix for 2-forms.

If f is an expression other than a form, it will be evaluated pointwise on the Functions in the expression. This will only succeed if all the Functions are on the same FunctionSpace.

If f is a Slate tensor expression, then it will be compiled using Slate’s linear algebra compiler.

If tensor is supplied, the assembled result will be placed there, otherwise a new object of the appropriate type will be returned.

If bcs is supplied and f is a 2-form, the rows and columns of the resulting Matrix corresponding to boundary nodes will be set to 0 and the diagonal entries to 1. If f is a 1-form, the vector entries at boundary nodes are set to the boundary condition values.

Parameters:

• f – a ForcingCovariance, InterpolationMatrix, Form, Expr or TensorBase expression.
• tensor – an existing tensor object to place the result in (optional).
• bcs – a list of boundary conditions to apply (optional).
• form_compiler_parameters – (optional) dict of parameters to pass to the form compiler. Ignored if not assembling a Form. Any parameters provided here will be overridden by parameters set on the Measure in the form. For example, if a quadrature_degree of 4 is specified in this argument, but a degree of 3 is requested in the measure, the latter will be used.
• mat_type – (optional) string indicating how a 2-form (matrix) should be assembled – either as a monolithic matrix (‘aij’ or ‘baij’), a block matrix (‘nest’), or left as a ImplicitMatrix giving matrix-free actions (‘matfree’). If not supplied, the default value in parameters["default_matrix_type"] is used. BAIJ differs from AIJ in that only the block sparsity rather than the dof sparsity is constructed. This can result in some memory savings, but does not work with all PETSc preconditioners. BAIJ matrices only make sense for non-mixed matrices.
• sub_mat_type – (optional) string indicating the matrix type to use inside a nested block matrix. Only makes sense if mat_type is nest. May be one of ‘aij’ or ‘baij’. If not supplied, defaults to parameters["default_sub_matrix_type"].
• appctx – Additional information to hang on the assembled matrix if an implicit matrix is requested (mat_type “matfree”).
• options_prefix – PETSc options prefix to apply to matrices.