fastvpinns.FE.quad_affine module

The file quad_affine.py defines the Quad Affine transformation of the reference element. The implementation is referenced from the ParMooN project (File: QuadAffine.C).

Author: Thivin Anandh D

Changelog: 30/Aug/2023 - Initial version

Known issues: None

Dependencies: None specified

class fastvpinns.FE.quad_affine.QuadAffin(co_ordinates)[source]

Bases: FETransforamtion2D

Defines the Quad Affine transformation of the reference element.

Parameters:

co_ordinates (numpy.ndarray) – The coordinates of the reference element.

get_jacobian(xi, eta)[source]

Returns the Jacobian of the transformation.

Parameters:

  • xi (float) – The xi coordinate.

  • eta (float) – The eta coordinate.

Returns:

The Jacobian of the transformation.

Return type:

float

get_orig_from_ref_derivative(ref_gradx, ref_grady, xi, eta)[source]

Returns the derivatives of the original coordinates with respect to the reference coordinates.

Parameters:

  • ref_gradx (numpy.ndarray) – The reference gradient in the x-direction.

  • ref_grady (numpy.ndarray) – The reference gradient in the y-direction.

  • xi (float) – The xi coordinate.

  • eta (float) – The eta coordinate.

Returns:

The derivatives of the original coordinates with respect to the reference coordinates.

Return type:

tuple

get_orig_from_ref_second_derivative(grad_xx_ref, grad_xy_ref, grad_yy_ref, xi, eta)[source]

Returns the second derivatives (xx, xy, yy) of the original coordinates with respect to the reference coordinates.

Parameters:

  • grad_xx_ref (numpy.ndarray) – The reference second derivative in the xx-direction.

  • grad_xy_ref (numpy.ndarray) – The reference second derivative in the xy-direction.

  • grad_yy_ref (numpy.ndarray) – The reference second derivative in the yy-direction.

  • xi (float) – The xi coordinate.

  • eta (float) – The eta coordinate.

Returns:

The second derivatives (xx, xy, yy) of the original coordinates with respect to the reference coordinates.

Return type:

tuple

get_original_from_ref(xi, eta)[source]

Returns the original coordinates from the reference coordinates.

Parameters:

  • xi (float) – The xi coordinate.

  • eta (float) – The eta coordinate.

Returns:

numpy.ndarray The original coordinates.

set_cell()[source]

Set the cell coordinates, which will be used to calculate the Jacobian and actual values.

Parameters:

None – There are no parameters for this method.

Returns None:

This method does not return anything.