How we change what others think, feel, believe and do
When the enemy has fortified positions that seem impossible to penetrate, first surround these positions so no-one can enter or leave.
Then try to wear them down so they surrender.
Where your enemy has many castles and you have superior military force, defeating them largely means laying siege to each castle. If you have sufficient forces, you can do this to several castles at once.
Siege war is the natural response to heavy fortification, which itself is a response to regular conflict and lawlessness and where a small force can hold a much larger one at bay.
Fortified castles are often designed to withstand sieges, with all angles covered, moats, reinforced doors and traps for the unwary invader. They may have bigger cannons than you, forcing you back beyond firing range. When expecting a siege they may lay in a large food supply, allowing them to be independent of external supplies for many months.
A circumvallation is a is circle of fortification facing towards the target that protects against sorties.
The greatest danger of laying siege is that you are in an exposed position and forces from elsewhere may come to the rescue, perhaps even sneaking up on an unprotected rear.
A contravallation matches the circumvallation in being an outer circle of fortification, facing outwards to protect against rescue attempts.
Fortified positions still continue to the present day, although the power and accuracy of bombs and artillery make them less relevant.
In 1993 the ATF and FBI laid siege to David Koresh' Branch Davidian sect in Mount Carmel, near Waco, Texas. Koresh' group were heavily armed and repelled an early attack, killing four agents. The siege included the use of loud music, tanks, helicopters and CS gas to wear them down. Eventually, after negotiations failed a tank incursion was followed by a fire in which many died.
More traditionally, the medieval castles were built as impregnable defensive positions and defeat was only possible through siege. This was a very common form of war up until around the mid-eighteenth century.
In negotiations, do not allow people any breaks. Attack the walls of their arguments. Do not let up until they concede.