Coef

Descriptions of the contents of the Coef class, which cotntains matrices to perform operation on SEM data.

class pysemtools.datatypes.coef.Coef(msh, comm, get_area=False, apply_1d_operators=True, bckend='numpy')

Class that contains arrays like mass matrix, jacobian, jacobian inverse, etc.

This class can be used when mathematical operations such as derivation and integration is needed on the sem mesh.

Parameters:

mshMesh

Mesh object.

commComm

MPI comminicator object.

get_areabool, optional

If True, the area integration weight and normal vectors will be calculated. (Default value = True).

apply_1d_operatorsbool, optional

If True, the 1D operators will be applied instead of building 3D operators. (Default value = True).

Attributes:

drdxndarray

component [0,0] of the jacobian inverse tensor for each point. shape is (nelv, lz, ly, lx).

drdyndarray

component [0,1] of the jacobian inverse tensor for each point. shape is (nelv, lz, ly, lx).

drdzndarray

component [0,2] of the jacobian inverse tensor for each point. shape is (nelv, lz, ly, lx).

dsdxndarray

component [1,0] of the jacobian inverse tensor for each point. shape is (nelv, lz, ly, lx).

dsdyndarray

component [1,1] of the jacobian inverse tensor for each point. shape is (nelv, lz, ly, lx).

dsdzndarray

component [1,2] of the jacobian inverse tensor for each point. shape is (nelv, lz, ly, lx).

dtdxndarray

component [2,0] of the jacobian inverse tensor for each point. shape is (nelv, lz, ly, lx).

dtdyndarray

component [2,1] of the jacobian inverse tensor for each point. shape is (nelv, lz, ly, lx).

dtdzndarray

component [2,2] of the jacobian inverse tensor for each point. shape is (nelv, lz, ly, lx).

Bndarray

Mass matrix for each point. shape is (nelv, lz, ly, lx).

areandarray

Area integration weight for each point in the facets. shape is (nelv, 6, ly, lx).

nxndarray

x component of the normal vector for each point in the facets. shape is (nelv, 6, ly, lx).

nyndarray

y component of the normal vector for each point in the facets. shape is (nelv, 6, ly, lx).

nzndarray

z component of the normal vector for each point in the facets. shape is (nelv, 6, ly, lx).

Methods

dssum(field, msh)	Peform average of given field over shared points in each rank.
dudrst(field[, direction])	Perform derivative with respect to reference coordinate r/s/t.
dudrst_1d_operator(field, dr, ds[, dt])	Perform derivative applying the 1d operators provided as inputs.
dudrst_1d_operator_torch(field, dr, ds[, dt])	Perform derivative applying the 1D operators provided as inputs.
dudrst_3d_operator(field, dr)	Perform derivative with respect to reference coordinate r.
dudxyz(field, drdx, dsdx[, dtdx])	Perform derivative with respect to physical coordinate x,y,z.
glsum(a, comm[, dtype])	Peform global summatin of given qunaitity a using MPI.

Returns:

Examples

Assuming you have a mesh object and MPI communicator object, you can initialize the Coef object as follows:

>>> from pysemtools import Coef
>>> coef = Coef(msh, comm)

dssum(field, msh)

Peform average of given field over shared points in each rank.

This method averages the field over shared points in the same rank. It uses the connectivity data in the mesh object. dssum might be a missleading name.

Parameters:

fieldndarray

Field to average over shared points.

mshMesh

pySEMTools Mesh object.

Returns:

ndarray

Input field with shared points averaged with shared points in the SAME rank.

Examples

Assuming you have a Coef object and are working on a 3d field:

>>> dudx = coef.dssum(dudx, msh)

dudrst(field, direction='r')

Perform derivative with respect to reference coordinate r/s/t.

Used to perform the derivative in the reference coordinates

Parameters:

fieldndarray

Field to take derivative of. Shape should be (nelv, lz, ly, lx).

directionstr

Direction to take the derivative. Can be ‘r’, ‘s’, or ‘t’. (Default value = ‘r’).

Returns:

ndarray

Derivative of the field with respect to r/s/t. Shape is the same as the input field.

dudrst_1d_operator(field, dr, ds, dt=None)

Perform derivative applying the 1d operators provided as inputs.

This method uses the 1D operators to apply the derivative. To apply derivative in r. you mush provide the 1d differenciation matrix in that direction and identity in the others.

Parameters:

fieldndarray

Field to take derivative of. Shape should be (nelv, lz, ly, lx).

drndarray

Derivative matrix in the r direction to apply to each element. Shape should be (lx, lx).

dsndarray

Derivative matrix in the s direction to apply to each element. Shape should be (ly, ly).

dtndarray

Derivative matrix in the t direction to apply to each element. Shape should be (lz, lz). This is optional. If none is passed, it is assumed that the field is 2D.

Returns:

ndarray

Derivative of the field with respect to r/s/t. Shape is the same as the input field.

Examples

Assuming you have a Coef object

>>> dxdr = coef.dudrst(x, coef.dr, np.eye(ly, dtype=coef.dtype), np.eye(lz, dtype=coef.dtype))

dudrst_1d_operator_torch(field, dr, ds, dt=None)

Perform derivative applying the 1D operators provided as inputs.

Parameters:

fieldtorch.Tensor

Field to take derivative of. Shape should be (nelv, lz, ly, lx).

drtorch.Tensor

Derivative matrix in the r direction to apply to each element. Shape should be (lx, lx).

dstorch.Tensor

Derivative matrix in the s direction to apply to each element. Shape should be (ly, ly).

dttorch.Tensor (optional)

Derivative matrix in the t direction. Shape should be (lz, lz).

Returns:

torch.Tensor

Derivative of the field with respect to r/s/t. Shape is the same as the input field.

dudrst_3d_operator(field, dr)

Perform derivative with respect to reference coordinate r.

This method uses derivation matrices from the lagrange polynomials at the GLL points.

Parameters:

fieldndarray

Field to take derivative of. Shape should be (nelv, lz, ly, lx).

drndarray

Derivative matrix in the r/s/t direction to apply to each element. Shape should be (lx*ly*lz, lx*ly*lz).

Returns:

ndarray

Derivative of the field with respect to r/s/t. Shape is the same as the input field.

Examples

Assuming you have a Coef object

>>> dxdr = coef.dudrst(x, coef.dr)

dudxyz(field, drdx, dsdx, dtdx=None)

Perform derivative with respect to physical coordinate x,y,z.

This method uses the chain rule, first evaluating derivatives with respect to rst, then multiplying by the inverse of the jacobian to map to xyz.

Parameters:

fieldndarray

Field to take derivative of. Shape should be (nelv, lz, ly, lx).

drdxndarray

Derivative of the reference coordinates with respect to x, i.e., first entry in the appropiate row of the jacobian inverse. Shape should be the same as the field.

dsdxndarray

Derivative of the reference coordinates with respect to y, i.e., second entry in the appropiate row of the jacobian inverse. Shape should be the same as the field.

dtdxndarray

Derivative of the reference coordinates with respect to z, i.e., third entry in the appropiate row of the jacobian inverse. Shape should be the same as the field. (Default value = None) Only valid for 3D fields.

Returns:

ndarray

Derivative of the field with respect to x,y,z. Shape is the same as the input field.

Examples

Assuming you have a Coef object and are working on a 3d field:

>>> dudx = coef.dudxyz(u, coef.drdx, coef.dsdx, coef.dtdx)

glsum(a, comm, dtype=<class 'numpy.float64'>)

Peform global summatin of given qunaitity a using MPI.

This method uses MPI to sum over all MPI ranks. It works with any numpy array shape and returns one value.

Parameters:

andarray

Quantity to sum over all mpiranks.

commComm

MPI communicator object.

datypenumpy.dtype

(Default value = np.double).

Returns:

float

Sum of the quantity a over all MPI ranks.

Examples

Assuming you have a Coef object and are working on a 3d field:

>>> volume = coef.glsum(coef.B, comm)