crazy_mesh_hybrid.py¶

In this script, we define a mesh in a unit cube,

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class crazy_mesh_hybrid.CrazyMeshHybrid(c, K)[source]¶

The hybrid version of class CrazyMesh.

surface_CT_of_element_index(surface_name, i, j, k)[source]¶

For the surface_name side of element $\Omega_{i,j,k}$ .

Parameters:

surface_name – ‘N’ ( $\xi^-$ ), ‘S’ ( $\xi^+$ ), ‘W’( $\eta^-$ ), ‘E’ ( $\eta^+$ ), ‘B’ ( $\varsigma^-$ ) or ‘F’ ( $\varsigma^+$ )?
i – Element index i.
j – Element index j.
k – Element index k.

Returns:

surface_CT_of_element_number(surface_name, m)[source]¶

For the surface_name side of element $\Omega_{m}$ .

Parameters:

surface_name – ‘N’ ( $\xi^-$ ), ‘S’ ( $\xi^+$ ), ‘W’( $\eta^-$ ), ‘E’ ( $\eta^+$ ), ‘B’ ( $\varsigma^-$ ) or ‘F’ ( $\varsigma^+$ )?
m – Element $\Omega_{m}$ .

Returns:

class crazy_mesh_hybrid.CrazyMeshHybridGlobalBoundaryDOFs(K, N)[source]¶

The hybrid version of class CrazyMeshGlobalBoundaryDOFs.

property TE¶

Find the dofs of an element in $\text{TE}_{N-1}(\partial\Omega)$ which are on boundary of the crazy mesh of $K^3$ elements.

Returns:: A dict whose keys are ‘x_minus’, ‘x_plus’, ‘y_minus’, ‘y_plus’, ‘z_minus’, ‘z_plus’, and whose values are the global numbering of the dofs on the boundaries indicated by the keys.

property TF¶

Find the dofs of an element in $\text{TF}_{N-1}(\partial\Omega)$ which are on boundary of the crazy mesh of $K^3$ elements.

Returns:: A dict whose keys are ‘x_minus’, ‘x_plus’, ‘y_minus’, ‘y_plus’, ‘z_minus’, ‘z_plus’, and whose values are the global numbering of the dofs on the boundaries indicated by the keys.

property TN¶

Find the dofs of an element in $\text{TN}_{N}(\partial\Omega)$ which are on boundary of the crazy mesh of $K^3$ elements.

Returns:: A dict whose keys are ‘x_minus’, ‘x_plus’, ‘y_minus’, ‘y_plus’, ‘z_minus’, ‘z_plus’, and whose values are the global numbering of the dofs on the boundaries indicated by the keys.

class crazy_mesh_hybrid.CrazyMeshHybridGlobalNumbering(K, N)[source]¶

The hybrid version of class CrazyMeshGlobalNumbering.

property EP¶: Generate a global numbering for the dofs of an element in $\text{EP}_{N-1}(\Omega)$ on a hybrid crazy mesh of $K^3$ elements.

property FP¶: Generate a global numbering for the dofs of an element in $\text{FP}_{N-1}(\Omega)$ on a hybrid crazy mesh of $K^3$ elements.

property NP¶: Generate a global numbering for the dofs of an element in $\text{NP}_{N}(\Omega)$ on a crazy mesh of $K^3$ elements.

property TE¶: Generate a global numbering for a discrete trace variable in $\text{TE}_{N-1}(\partial\Omega)$ on a hybrid crazy mesh of $K^3$ elements.

property TF¶: Generate a global numbering for a discrete trace variable in $\text{TF}_{N-1}(\partial\Omega)$ on a hybrid crazy mesh of $K^3$ elements.

property TN¶: Generate a global numbering for a discrete trace variable in $\text{TN}_{N}(\partial\Omega)$ on a hybrid crazy mesh of $K^3$ elements.

property VP¶

Generate a global numbering for the dofs of an element in $\text{VP}_{N-1}(\Omega)$ on a hybrid crazy mesh of $K^3$ elements.

Note that for $\text{VP}_{N-1}(\Omega)$ , we obviously can use the numbering for the non-hybrid crazy mesh such it is discontinuous any way.

class crazy_mesh_hybrid.CrazyMeshHybridLocalBoundaryDOFs(K, N)[source]¶

Like the CrazyMeshHybridGlobalBoundaryDOFs, but we now return the local numbering on each boundary.

Parameters:

K (int) – The crazy mesh is of $K^3$ elements.
N (int) – The degree $N$ . of the to be used mimetic polynomial basis functions.

property EP¶

Find the dofs of an element in $\text{EP}_{N-1}(\Omega)$ which are on boundary of the crazy mesh of $K^3$ elements.

Returns:: A dict whose keys are ‘x_minus’, ‘x_plus’, ‘y_minus’, ‘y_plus’, ‘z_minus’, ‘z_plus’, and whose values are the global numbering of the dofs on the boundaries indicated by the keys.

property FP¶

Find the dofs of an element in $\text{FP}_{N-1}(\Omega)$ which are on boundary of the crazy mesh of $K^3$ elements.

Returns:: A dict whose keys are ‘x_minus’, ‘x_plus’, ‘y_minus’, ‘y_plus’, ‘z_minus’, ‘z_plus’, and whose values are the global numbering of the dofs on the boundaries indicated by the keys.

property NP¶

Find the dofs of an element in $\text{NP}_{N}(\Omega)$ which are on boundary of the crazy mesh of $K^3$ elements.

Returns:: A dict whose keys are ‘x_minus’, ‘x_plus’, ‘y_minus’, ‘y_plus’, ‘z_minus’, ‘z_plus’, and whose values are the global numbering of the dofs on the boundaries indicated by the keys.

property TE¶

Find the dofs of an element in $\text{TE}_{N-1}(\partial\Omega)$ which are on boundary of the crazy mesh of $K^3$ elements.

Returns:: A dict whose keys are ‘x_minus’, ‘x_plus’, ‘y_minus’, ‘y_plus’, ‘z_minus’, ‘z_plus’, and whose values are the global numbering of the dofs on the boundaries indicated by the keys.

property TF¶

Find the dofs of an element in $\text{TF}_{N-1}(\partial\Omega)$ which are on boundary of the crazy mesh of $K^3$ elements.

Returns:: A dict whose keys are ‘x_minus’, ‘x_plus’, ‘y_minus’, ‘y_plus’, ‘z_minus’, ‘z_plus’, and whose values are the global numbering of the dofs on the boundaries indicated by the keys.

property TN¶

Find the dofs of an element in $\text{TN}_{N}(\partial\Omega)$ which are on boundary of the crazy mesh of $K^3$ elements.

Returns:: A dict whose keys are ‘x_minus’, ‘x_plus’, ‘y_minus’, ‘y_plus’, ‘z_minus’, ‘z_plus’, and whose values are the global numbering of the dofs on the boundaries indicated by the keys.

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crazy_mesh_hybrid.py¶

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