Re: Acausal systems modelling and compilation

[Francesco Casella]

Hi Arquimedes,

I have read the Open Modelica Compiler Phases document and it gives a
very good high-level perspective on how the omc works. I have also
read some of the related papers on the omc compiler and this is where
things start getting fuzzy.

I'd suggest you to also read the books by Tiller and by Fritzson about 
Modelica :)

While I can see the benefit of ordering the dependency matrix in BLT
form for reducing the reaching definitions of variables for
parallelization, I don't fully understand why this step is necessary
for generating uniprocessor code. Is it to reduce the complexity of
the matrix manipulation algorithms ? How does the BLT form affect the
quality of the generated code, in the case of uniprocessor ?.

Even with a single thread, in general it is obviously easier to solve N 
smaller systems than one, single, bigger system.

Concerning the numerical solver selection, I have seen the ongoing
discussion about DAEs with index > 1. It seems that DAEs are passed to
the index reduction and if the resulting system has an index == 1 then
we can easily solve with fixed-step ODE solvers, Runge-Kutta methods
for example. However, if the index > 1, are we forced to use DASSL ?.

No, if the system has index > 1, symbolic index reduction is applied to 
reduce it to index = 1, no matter what solver is later used. BTW, DASSL 
cannot handle index>1 DAEs.

What criteria does openmodelica apply for the selection of DASSL or
Euler ?

DASSL is a high-order, variable step size BDF solver, with support for 
event handling. Euler is a simple one-step, first order solver, usually 
employed at fixed time step for real-time simulation.

An excellent source to know more about this is the book by Petzold and 
Ascher "Computer Methods for ordinary differential equations and 
differential-algebraic equations.

Note that OMC conceptually brings the DAE into ODE form before linking 
to a solver, so even if DASSL is used, it is used as an ode solver.

I know this is highly dependent on the problem itself, but how often
do you get systems with index >= 2 ?

In mechanical systems, every time you make a rigid connection, you get 
index = 3.

In electrical circuit, you get index=2 whenever connect condensers in 
parallel, or inductors in series.

How do you handle them ?

Pantelides' algorithm + dummy derivative algorithm.

, is it
possible to apply index reduction again and again until we reach our
target ?

Yes, if OMC can differentiate the constraint equations enough times.

Finally, I would like to ask about the meaning of 'acausality' inside
a Modelica compiler, openmodelica in this case. After deciding the
ordering of equations based on their data dependencies and scheduling
them, aren't we transforming the 'acausal' system into a 'causal' one

No, if there are algebraic loops (i.e. implicit algebraic equations) in 
the model.

Hope this helps

                                Francesco

--
Francesco Casella - Ph.D.
Dipartimento di Elettronica e Informazione
Politecnico di Milano
Via Ponzio 34/5
I-20133 MILANO - ITALY

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