elastodynamicsx.solvers.eigensolver

Module contents

class elastodynamicsx.solvers.eigensolver.EigenmodesSolver(comm: Comm, M: Mat, C: Mat, K: Mat, **kwargs)[source]

Bases: EPS

Convenience class inhereted from SLEPc.EPS, with methods and default parameters that are relevant for computing the resonances of an elastic component.

Parameters:

comm – The MPI communicator
M – The mass matrix
C – The damping matrix. C=None means no dissipation. C!=None is not supported yet.
K – The stiffness matrix

Keyword Arguments:

nev – The number of eigenvalues to be computed

Example

# ###
# Free resonances of an elastic cube
# ###
from mpi4py import MPI
from dolfinx import mesh, fem
from elastodynamicsx.solvers import EigenmodesSolver
from elastodynamicsx.pde import material, PDE

domain = mesh.create_box(MPI.COMM_WORLD, [[0,0,0], [1,1,1]], [10,10,10])
V      = dolfinx.fem.functionspace(domain, ("CG", 1, (3,)))

rho, lambda_, mu = 1, 2, 1
mat = material(V, rho, lambda_, mu)
pde = PDE(V, materials=[mat])
nev = 6 + 6  # the first 6 resonances are rigid body motion
eps = EigenmodesSolver(V.mesh.comm, pde.M(), None, pde.K(), nev=nev)
eps.solve()
eps.plot(V)
freqs = eps.getEigenfrequencies()
print('First resonance frequencies:', freqs)

getWn() → ndarray[source]: The eigen angular frequencies from the computed eigenvalues

getEigenfrequencies() → ndarray[source]: The eigenfrequencies from the computed eigenvalues

getEigenmodes(which='all') → List[Vec][source]

Returns the desired modeshapes

Parameters:: which – ‘all’, or an integer, or a list of integers, or a slice object

Example

getEigenmodes()   # returns all computed eigenmodes
getEigenmodes(3)  # returns mode number 4
getEigenmodes([3,5])  # returns modes number 4 and 6
getEigenmodes(slice(0,None,2))  # returns even modes

getModalBasis() → ModalBasis[source]

getErrors() → ndarray[source]: Returns the error estimate on the computed eigenvalues

plot(function_space: FunctionSpace, which='all', **kwargs) → None[source]

Plots the desired modeshapes

Parameters:

function_space – The underlying function space
which – ‘all’, or an integer, or a list of integers, or a slice object -> the same as for getEigenmodes

printEigenvalues() → None[source]: Prints the computed eigenvalues and error estimates