tlm_adjoint.firedrake.interpolation

Interpolation operations with Firedrake.

Module Contents

class tlm_adjoint.firedrake.interpolation.ExprInterpolation(x, rhs)

Represents interpolation of rhs onto the space for x.

The forward residual \(\mathcal{F}\) is defined so that \(\partial \mathcal{F} / \partial x\) is the identity.

Parameters:

• x – The forward solution.

• rhs – A ufl.core.expr.Expr defining the expression to interpolate onto the space for x. Should not depend on x.

drop_references()

Drop references to variables which store values.

forward_solve(x, deps=None)

Compute the forward solution.

Can assume that the currently active EquationManager is paused.

Parameters:

• X – A variable or a Sequence of variables storing the solution. May define an initial guess, and should be set by this method.

• deps – A tuple of variables, defining values for dependencies. Only the elements corresponding to X may be modified. self.dependencies() should be used if not supplied.

adjoint_derivative_action(nl_deps, dep_index, adj_x)

Return the action of the adjoint of a derivative of the forward residual on the adjoint solution. This is the negative of an adjoint right-hand-side term.

Parameters:

• nl_deps – A Sequence of variables defining values for non-linear dependencies. Should not be modified.

• dep_index – An int. The derivative is defined by differentiation of the forward residual with respect to self.dependencies()[dep_index].

• adj_X – The adjoint solution. A variable or a Sequence of variables. Should not be modified.

Returns:

The action of the adjoint of a derivative on the adjoint solution. Will be passed to subtract_adjoint_derivative_action(), and valid types depend upon the adjoint variable type. Typically this will be a variable, or a two element tuple (alpha, F), where alpha is a numbers.Complex and F a variable, with the value defined by the product of alpha and F.

adjoint_jacobian_solve(adj_x, nl_deps, b)

Compute an adjoint solution.

Parameters:

• adj_X – Either None, or a variable or Sequence of variables defining the initial guess for an iterative solve. May be modified or returned.

• nl_deps – A Sequence of variables defining values for non-linear dependencies. Should not be modified.

• B – The right-hand-side. A variable or Sequence of variables storing the value of the right-hand-side. May be modified or returned.

Returns:

A variable or Sequence of variables storing the value of the adjoint solution. May return None to indicate a value of zero.

tangent_linear(tlm_map)

Derive an Equation corresponding to a tangent-linear operation.

Parameters:

tlm_map – A TangentLinearMap storing values for tangent-linear variables.

Returns:

An Equation, corresponding to the tangent-linear operation.