IntelliJ IDEA: the first compilation takes a lot of time

You can use the Eclipse compiler from IntelliJ IDEA.

Enable the Eclipse compiler from Settings -> Compiler -> Java Compiler: "Use compiler:" (change from Javac to Eclipse).

update: Here's my compilation times for a full rebuild, using IntelliJ IDEA 13 on a fairly large project:

Using javac 1.7.0_45 to compile java sources
Compilation completed successfully with 60 warnings in 27 sec

Using eclipse compiler to compile java sources
Compilation completed successfully with 652 warnings in 26 sec

So there seems to be something strange with your setup.

Change the following setting (Build process heap size) to some large value

Answer from IntelliJ Support:

Try 13.0.2 from http://confluence.jetbrains.com/display/IDEADEV/IDEA+13+EAP .

Disable the option to clean output directories on rebuild in the compiler settings.