The draw function in Processing is like the loop function on the Arduino, except that loop() is called over and over as fast as possible, while draw() is called over and over, so many times per second, with pauses in between, if needed.
You can change how many times per second draw() is called. Look for information about frame rate.
That might be all that is needed to speed things up. Bear in mind that serial data transmission, even at 115200 is not terribly fast.