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Cooking potatoes takes quite some time. You need to be patient. There are not many options to accelerate the process. One option is to use a pressure cooker which works well for boiling potatoes in their jacket (Boiled potatoes I recipe). It takes about 15 min. of boiling time, but of course at the end you'll have to let the pressure cooker cool down which itself takes 5 to 10 min. So in the end you save a few minutes by using a pressure cooker instead of a pot; in addition you save some water because a pressure cooker is filled only up to the inlay at the bottom, not to the top of the potatoes.
For fried potatoes and Rösti, using a larger pan accelerates cooking because a bigger surface means more pieces of potatoes are in direct contact with the hot pan surface at any given time.