rc
commented
4 years ago The equation syntax, as it is, is the result of a design decision (not perfect), that allows solver access to the individual matrix blocks, i.e. the matrices M (mass), B (damping) and K (stiffness). Note that dv and ddv are not to be interpreted as derivatives of v, but simply as auxiliary variables - dv allows to define the damping block (with du) and ddv the inertia block (with ddu). In sfepy, each unknown variable has to have a corresponding test (virtual) variable. The elastodynamic solvers can then be abstract in a sense that they do not "see" the individual terms, and expect only the three blocks in the matrix/residual, defined by the three pairs of variables. Note that the equation in the example is not the equation that is actually solved - instead, each solver solves a set of equations corresponding to its time discretization scheme.
In retrospect, another definition might have been preferable:
equations = {
'M' :
"""dw_volume_dot.i.Omega(solid.rho, ddv, ddu)""",
'B' :
"""dw_zero.i.Omega(dv, du)""",
'K' :
"""dw_lin_elastic.i.Omega(solid.D, v, u)""",
}Does it help?
ashwmk
I tried running simple.py on elastodynamics.py in the examples/linear_elasticity folder, and everything went fine. I checked the solution with postproc.py and the result seemed sensible. My issue is that I don't understand the equation to be solved:
First of all, the first term doesn't seem to match the one shown in the documentation:
\int_{\Omega} \rho \ul{v} \pddiff{\ul{u}}{\ul{v}}Second of all, neither one of these is what I would have expected to pop out of the weak form of the wave equation:\int_{\Omega} \rho \ul{v} \ul{ddu}Finally, the equation definition doesn't even pass a unit analysis test.solid.rho,ddv,ddu,solid.D,v, anduhave SI units of kg/m3, m/s2, m/s2, N/m2 (or kg/m/s2), m, and m, respectively, so the integrand for the first term ends up with units of kg/m/s4 and the integrand for the third term ends up with units of kg*m/s2.Out of curiosity, I tried changing the first term in the equations definition to the one I thought made sense, and ran simple.py on it. The result was the following error message:
I guess it's possible that I needed to change something else in the code, but in any case I'm still mystified as to where the original equation definition comes from and how it even works. Can anyone provide an explanation?