id	summary	reporter	owner	description	type	status	priority	milestone	component	version	resolution	keywords	cc
6236	Solve simple linear systems in closed form if that leads to simple solution	Francesco Casella	Karim Adbdelhak	"Consider the following linear system, which is obtained when building object-oriented 1D, 2D, and 3D thermal models because of pairs of conductances being series connected:
{{{
Q = 2*g*(Tb - T2);
Q = 2*g*(T1 - Tb);
}}}
with unknowns {{{Q}}} and {{{Tb}}} ({{{T1}}} and {{{T2}}} are states).
This system has a simple closed-form solution:
{{{
Q := g*(T1 - T2);
Tb := (T1 + T2)/2;
}}}
that can be computed with a lot less overhead than it is needed to use a numerical linear solver such as LAPACK's {{{dgesv}}}.

We could consider trying to solve 2x2 (and possibly 3x3) systems by gaussian elimination using a variant of the ASSC algorithm. If the outcome is simple assignments, we could put them in the generated code, otherwise we should discard it and continue using the numerical solution instead."	enhancement	new	high		Backend	1.16.0			federico.terraneo@… Philip Hannebohm Andreas Heuermann Vitalij Ruge