Hi,

I hope all are fine. I need help to solve the eigenvalue problem to compute critical load for the beam using Euler-Bernoulli beam equation and apply axial load. For this I solved 1D poisson equation by using Arnoldi method my computed value is similar to the analytical value. I also want to compute eigenvector of 1D poisson equation. Can anyone tell me how I can compute the eigenvector? Its only for benchmark. But I want to compute critical load for the beam.I used mixed saddle point method reduce power of derivative. I am using the same Arnoldi method but computed value did not matched with analytical value. Please tell me about my problem. I will be very thankful to you.

Best,

Rauf.

#Code for poisson equation:

from ngsolve import *

from ngsolve.webgui import Draw

from ngsolve.meshes import Make1DMesh

import math

mesh = Make1DMesh(100)

fes = H1(mesh, order=2, dirichlet=“left|right”)

u = fes.TrialFunction()

v = fes.TestFunction()

a = BilinearForm(fes)

a += grad(u)*grad(v)*dx

m = BilinearForm(fes)

m += u*v*dx

a.Assemble()

m.Assemble()

u = GridFunction(fes,multidim=3)

with TaskManager():

lam = ArnoldiSolver(a.mat, m.mat, fes.FreeDofs(),list(u.vecs), shift=1)

print ("lam: ", lam)

#Code for Beam

from ngsolve import *

from ngsolve.meshes import Make1DMesh

from ngsolve.la import EigenValues_Preconditioner

from ngsolve.webgui import Draw

import numpy as np

import math

import scipy.linalg

from scipy import random

import scipy.sparse as sp

mesh = Make1DMesh(100)

w = H1(mesh, order=2, dirichlet=“left|right”)

sigma = H1(mesh, order=2, dirichlet=" ")

fesm = w*sigma

w, sigma = fesm.TrialFunction()

v , tau = fesm.TestFunction()

a = BilinearForm(fesm,symmetric=True)

a += (grad(sigma)*grad(v) + sigma*tau + grad(w)*grad(tau))*dx

m = BilinearForm(fesm,symmetric=True)

m += grad(w)*grad(v)*dx

a.Assemble()

m.Assemble()

u = GridFunction(fesm)

with TaskManager():

lam = ArnoldiSolver(a.mat, m.mat, fesm.FreeDofs(),list(u.vecs), shift=1)

computed value is -262.11 but analytical value is 4pi^2