Module Scientific.Geometry.TensorAnalysis

Class TensorField: Tensor field of arbitrary rank

A tensor field is described by a tensor at each point of a three-dimensional rectangular grid. The grid spacing may be non-uniform. Tensor fields are implemented as a subclass of InterpolatingFunction from the module Scientific.Functions.Interpolation and thus share all methods defined in that class.

Constructor: TensorField(rank, axes, values, default=None)

rank

a non-negative integer indicating the tensor rank

axes

a sequence of three one-dimensional arrays, each of which specifies one coordinate (x, y, z) of the grid points

values

an array of rank+3 dimensions. Its first three dimensions correspond to the x, y, z directions and must have lengths compatible with the axis arrays. The remaining dimensions must have length 3.

default

the value of the field for points outside the grid. A value of None means that an exception will be raised for an attempt to evaluate the field outside the grid. Any other value must a tensor of the correct rank.

Evaluation:

• tensorfield(x, y, z) (three coordinates)

• tensorfield(coordinates) (any sequence containing three coordinates)

• zero()

  Returns a tensor of the correct rank with zero elements.

• derivative(variable)

  Returns the derivative with respect to variable, which must be one of 0, 1, or 2.

• allDerivatives()

  Returns all three derivatives (x, y, z).

Class ScalarField: Scalar field (tensor field of rank 0)

Constructor: ScalarField(axes, values, default=None)

A subclass of TensorField.

• gradient()

  Returns the gradient (a vector field).

• laplacian()

  Returns the laplacian (a scalar field).

Class VectorField: Vector field (tensor field of rank 1)

Constructor: VectorField(axes, values, default=None)

A subclass of TensorField.

• divergence()

  Returns the divergence (a scalar field).

• curl()

  Returns the curl (a vector field).

• strain()

  Returns the strain (a tensor field of rank 2).

• divergenceCurlAndStrain()

  Returns all derivative fields: divergence, curl, and strain.

• laplacian()

  Returns the laplacian (a vector field).

• length()

  Returns a scalar field corresponding to the length (norm) of the vector field.