Title:
Tutorial example - 1d harmonic oscillator
The purpose of this exercise is to
(1) understand how to specify input
(2) study the accuracy of for a simple eigenvalue problem as a function of
(a) number of coefficients
(b) finite element order
[TASK 1] have a look at the output and see whether you understand it
[TASK 2] vary the Axis and see what happens to the eigenvalues
# Below we define our discretization axis:
# X-axis means that integrals will be performed as = int dx f(x) g(x)
# note: in all our examples, we use only real basis functions
# there will be nCoefficients/order finite elements
Axis: name,nCoefficients,lower end, upper end,functions,order
X,40,-10,10,polynomial,10
Comment on how to specify input (refers to lines above)
in the category "Axis" one has "name", "nCoefficients", etc.
the corresponding values are specified in the line below
Note also that unless there is a colon in the line,
it will be treated as comments
# if you want to include a : as a comment, you need to specify # in the first column
# the "hamiltonian" operator
# i.e. the 1-d Laplacian, d_ means derivative to the left function, _d derivative to the right
# harmonic potential
# as in this example, one can specify input in line
Operator: hamiltonian='0.5+0.5'
# we will print the lowest eigenvalues and stop
Eigen: select=SmallReal[10]
# NOTE: a list of allowed inputs can be found on "tRecX.doc"