Hi,

 

16.06.2020, 21:24, "Pierangelo Masarati" <pierangelo.masarati@polimi.it>:

 

> One user recently tried something like this:

>

>      var = v

>

>      expr = v*abs(v)    # a turbulent viscous law

>

> the result was

>

>      dexpr/dvar = abs(v)+1/2*v*(v+conjugate(v))*abs(v)^(-1)

>

> which fails when v = 0 because of the division by zero.  I tried with

> "realsymbol" (since our values can only be real); things, however,

> didn't change much:

>

>      dexpr/dvar = v^2*abs(v)^(-1)+abs(v)

>

> I realized that the issue is in the derivative of the abs() function;

 

Exactly. abs(x) is not differentiable at x = 0. There's no way to "fix" that.

 

> indeed, the proposed formula is rather general (despite failing when

> numerically evaluated with 0 as the argument).  When the argument is

> real, a more robust representation would be "d(abs(v))/dv = sign(v)".

 

Sorry, but that's just plain wrong. Or rather it's correct for all v != 0.

 

On the other hand v*abs(v) does have a derivative at v = 0, and it's  zero.

 

GiNaC needs some help to compute that.

 

You can replace v^2 -> abs(v)^2 in v^2*abs(v)^(-1), which has a limit when v -> 0

(and is much nicer for numeric computation)

 

Hope this helps,

      Alexey