[aragilar]

Which differential equations are you talking about? Linear ones have standard solutions and are definitely parallelisable (though you can basically just write the solution down by hand). Non-linear ones vary from can basically be approximated by a linear solution with corrections to needing to use relaxation methods (which are obviously not parallelisable).

Mechanics is generally linear, and for game physics engines fast is more valuable than correct (fast inverse square root being the obvious poster child). Add viscosity and you're in for a bad time.

[ted_dunning]

To be specific, a linear solver can be (as in I have done) written in a week.

A serious non-linear solver that handles legacy Spice models is another beast entirely. And if you want to integrate modern advances in algebraic-differential systems you take that to a higher level.

These are not partial differential equations such as you find in Navier-Stokes. These are sparse non-linear differential equations that do not parallelize nearly as simply.

Another example of related problems that parallelize poorly even though they are linear are the FDTD formulations for Maxwell's equations. These are relatively simple systems, but the bottleneck is almost always the memory bandwidth because it is so hard to parallelize.

[ycui7]

The type of people who need spice is dead serious about accuracy. 1ppm error sometimes is not tolerable. So, an optimization in a game engine is definitely not suitable for engineering simulation.

[NavinF]

Dude these are incredibly oversimplified models of real components. How are you getting 1ppm when basic shit like tempco and self heating are missing from pretty much every vendor provided spice model?