FEA (was RE: [ODE] more c++, auto-enabling)

[Jeffrey Smith]

George Birbilis wrote:
> btw, I was told by some teacher that uses Interactive Physics that
> they say (Knowledge Revolution) that it uses a 5-order integrator
> instead of 1-order as ODE says it uses in its docs.

Interesting. It's generally accepted that (for RBD at any rate) a 4th
order Runge-Kutta solver gets you the most bang for your buck.  In
fact, I vaguely remember reading that higher order integrators can
actually cause more instability (as numerical errors mount) that a 3rd
or 4th order integrator.  I wish I could see what they're doing.

> they say something about a "FEA solver technology" there. Not sure
> what FEA means though.

FEA means "finite element analysis."  Briefly, FEA is the technique of
solving a complicated space (and sometimes time) dependent set of
nonlinear differntial equations over a discretized parameter space.
This reduces a problem which may have an infinite number of degrees of
freedom to one with a large (but finite) number.

For example, calculating the forces and torques acting on a propeller
as it cuts through the water might involve solving the Navier-Stokes
equations over a discretized set of voxels (for the water) and surface
patches (for the propller.)  Doing this, you can model 2nd and 3rd
order nonlinear physical effects, such as stress, strain, and the
physics of fracture.

-jeff