Library Usage¶

Using PyHOPE as a Python Library

PyHOPE can be included in other Python libraries. PyHOPE exposes its functionally via runtime contexts defined by Context Managers. The following Python code loads a HOPR HDF5 mesh and derived quantities.

from pyhope import Basis, Mesh
with Mesh('1-01-cartbox_mesh.h5') as m:
    elems = m.elems
    lobatto_nodes = Basis.legendre_gauss_lobatto_nodes(order=m.nGeo)

Currently implemented functions¶

Library functionally of PyHOPE is geared towards usage in post-processing tools which require mesh information to reconstruct meaningful quantities, for example, solution gradients for Schlieren visualization. Functions currently exposed through the Python interface are the following.

• Basis
  • legendre_gauss_nodes

    legendre_gauss_nodes(order: int) -> tuple[np.ndarray, np.ndarray]:
    """ Return Legendre-Gauss nodes and weights for a given order in 1D
    """
    

  • legendre_gauss_lobatto_nodes

    legendre_gauss_lobatto_nodes(order: int) -> tuple[np.ndarray, np.ndarray]:
    """ Return Legendre-Gauss-Lobatto nodes and weights for a given order in 1D
    """
    

  • barycentric_weights

    barycentric_weights(_: int, xGP: np.ndarray) -> np.ndarray:
    """ Compute the barycentric weights for a given node set
        > Algorithm 30, Kopriva (2009), Implementing Spectral Methods for Partial Differential Equations
    """
    

  • polynomial_derivative_matrix

    polynomial_derivative_matrix(order: int, xGP: np.ndarray) -> np.ndarray:
    """ Compute the polynomial derivative matrix for a given node set
        > Algorithm 37, Kopriva (2009), Implementing Spectral Methods for Partial Differential Equations
    """
    

  • lagrange_interpolation_polys

    lagrange_interpolation_polys(x: Union[float, np.ndarray], order: int, xGP: np.ndarray, wBary: np.ndarray) -> np.ndarray:
    """ Computes all Lagrange functions evaluated at position x in [-1;1]
        > Algorithm 34, Kopriva
    """
    

  • calc_vandermonde

    calc_vandermonde(n_In: int, n_Out: int, wBary_In: np.ndarray, xi_In: np.ndarray, xi_Out: np.ndarray) -> np.ndarray:
    """ Build a 1D Vandermonde matrix using the Lagrange basis functions of degree N_In,
        evaluated at the interpolation points xi_Out
    """
    

  • change_basis_3D

    change_basis_3D(Vdm: np.ndarray, x3D_In: np.ndarray) -> np.ndarray:
    """ Interpolate a 3D tensor product Lagrange basis defined by (N_in+1) 1D interpolation point positions xi_In(0:N_In)
        to another 3D tensor product node positions (number of nodes N_out+1)
        defined by (N_out+1) interpolation point  positions xi_Out(0:N_Out)
        xi is defined in the 1D reference element xi=[-1,1]
    """
    

  • change_basis_2D

    change_basis_2D(Vdm: np.ndarray, x2D_In: np.ndarray) -> np.ndarray:
    """ Interpolate a 2D tensor product Lagrange basis defined by (N_in+1) 1D interpolation point positions xi_In(0:N_In)
        to another 2D tensor product node positions (number of nodes N_out+1)
        defined by (N_out+1) interpolation point positions xi_Out(0:N_Out)
        xi is defined in the 1D reference element xi=[-1,1]
    """
    

  • evaluate_jacobian

    evaluate_jacobian(xGeo_In: np.ndarray, VdmGLtoAP: np.ndarray, D_EqToGL: np.ndarray) -> np.ndarray:
    """ Calculate the Jacobian of the mapping for a given element
    """
    

• Mesh
  • Context manager to generate a mesh from a given file

    Mesh(*args: str, stdout: bool = False, stderr: bool = True):
    """ Mesh context manager to generate a mesh from a given file
    
        Args:
            *args: The mesh file path(s) to be processed
            stdout (bool): If False, standard output is suppressed
            stderr (bool): If False, standard error  is suppressed
    
        Yields:
            Mesh: An object containing the generated mesh and its properties
    """