Excerpts from the fourth rail, a milblog which is providing good analysis of the Fallujah battle:
Power has been cut off in the city, and all roads have been closed. The only people permitted to exit the city are women, children and boys under 15 and men over 50 years of age. The task force is using the full compliment of tools at its disposal: tanks, Bradley infantry vehicles, artillery, airstrikes, JDAMs, UAVs, robots, and the most effective tool in the U.S. military, the Infantryman and Marine trained in urban warfare (Military Operations on Urbanized Warfare - MOUT). The U.S. military seems to have perfected urban warfare and took historically low casualties in Fallujah last spring and in Najaf last summer. But the insurgents in Fallujah have had seven months to prepare the battlefield. Expect heavily fortified bunkers, roads littered with IEDs and buildings extensively booby-trapped.
A look at the map below [at the link] indicates that the city is effectively surrounded (blue boxes indicate suspected troop positions, keep in mind my assumptions on the Coalition forces both West and Southwest of the city). The neighborhood believed to be the stronghold of the insurgents is Jolan. Expect a box to form around this neighborhood as the Coalition forces segment and destroy all opposition in their area of operations; everything moving in this box will be fair game. The Marines and infantrymen will take buildings that will give then tactical superiority, then proceed to segment the Jolan neighborhood and clear the areas block by block, leveling any buildings deemed a threat to Coalition forces and clearing lanes of fire if needed. The railroad embankment to the North of Fallujah, the highway to the East (not pictured) and the Euphrates River to the West are effective man-made and natural boundaries that will help prevent the escape of insurgents fleeing the battlefield.
We haven't seen anything to suggest that there are simultaneous operations going on in Ramadi and other Sunni cities. Apparently, the commanders on the ground have decided that they would deal with these cities seriatim rather than all together as had been thought a possibility a couple of weeks ago.