The only artificial, large-scale desalting processes inherently either use lots of energy or much space for collecting solar energy, or haven't been sufficiently developed as yet. If we were able to re-purify water, recover and separate dissolved minerals cheaply, the Earth might support a considerably larger biosphere.
Salt water is composed of ions, electrically charged atoms, suspended in relatively un-ionized water. This major difference leads to a potentially easy way to separate ions from non-ions (in any fluid).
The first stage of mining valuable salts from seawater would probably be to concentrate the brine. The above process obviously takes care of that while producing fresh water, but also goes further. Different degrees of ionization, solubility and other factors, would cause various salts to concentrate at different stages.
The amount of energy required for my method is probably insignificant. It is in effect an electrostatic filter. The only significant energy load would be in the form of increased pump pressure.
My (alleged) method has been called impossible, but the only good reasons given have since been disproved. A successful version of it would literally change the world, by making fresh water, and all the minerals in salt water, much more available. It would also be useful throughout the chemical industry for separating ionized chemicals from non-ionized chemical in a fluid.