Classes of Physical Simulations
Mathematical (Numerical) formulations of simulations fall into a few key classes which have their own distinctive algorithmic and parallelism issues
Most common formalism is that of a field theory where quantities of interest are represented by densities defined over a 1,2,3 or 4 dimensional space.
- Such a description could be “fundamental” as in electromagnetism or relativity for gravitational field or “approximate” as in CFD where a fluid density averages over a particle description.
- Our Laplace example is of this form where field ? could either be fundamental (as in electrostatics) or approximate if comes from Euler equations for CFD