Rethrowing exception just as an information
Especially if you expect these exceptions to occur (relatively) often, I think that using exceptions is a bad idea here. Exceptions should not be used for regular flow of control, this applies to Java as well. Creating and throwing exceptions is among the most costly operations there is in many programming languages.

One comment especially that caught my attention was: "Now I have to make some specific calculations, but sth wrong happend and I do know what to do with it in this place..." If you know what to do with it, then why are you throwing an exception? If you look in the dictionary an exception is:


  special case, departure, freak, anomaly, inconsistency, deviation, quirk, oddity, peculiarity, irregularity" (+ exclusion, omission, objection).


Is your case really an anomaly? (Doesn't sound like it but I can't make this decision for you)

Instead, consider creating a CalculationResult class, which can be returned from your methods. The class can contain your solved variable (possibly among other things). Then when a method has returned a CalculationResult to it's caller, you can read the CalculationResult and decide what to do with it.