In Ubuntu 16.04
You should be able do this with CCSM (CompizConfig-Settings-Manager) in Ubuntu 16.04. Ubuntu 18.04 will be using Gnome 3 Shell instead of Unity, Wayland instead of Xorg, and Mutter instead of Compiz, which don't have an easy way to achieve a lot of the nice efficiency tweaks that Compiz brings.
- Install CCSM: sudo apt install compizconfig-settings-manager compiz-plugins-extra
- Go to the General plugin
- Click the Display Settings tab.
- Un-check the Detect Outputs check-box.
- Change the setting in the Outputs box to be four different areas, with offsets, that add up to the area of your extreme HD monitor. For example, 1920x1080+1920+0 would mean that "display" is 1920 wide, 1080 tall, and placed 1920 pixels to the right from the left edge, and 0 pixels down from the top.
For a 4K monitor, if you want to make it behave like four 1080p monitors, you would set it up like the screen-shot below: (Good luck in finding "display" edges with the mouse pointer!)
This was never intended to be used this way, so if you hit maximize on your window, the menu bar will be in the upper left display. If you want to keep the menu bar for the program in the current display, use the Ctrl+Alt+KeypadNumber to place the window on an edge, in a corner, or fullscreen(keypad 5) on the current display. You might also want to disable the screen edge aero-snap like options of the Grid plugin for CCSM.
Below is a link to another post from me, explaining how to set up the CCSM Display Settings for multiple monitors. Maybe you can find some useful, related info there also.
Multi-Monitor Issues in Ubuntu