Superheated gas under pressures of millions of atmospheres, like at the center of Jupiter or inside a laser target, behaves in tricky ways. Electrons are ripped from atoms and form a shared cloud that continuously reshapes itself. To simulate such a state on a computer, one usually solves cumbersome equations for each electron. The authors of the new program Archē took a different route: they work not with individual particles but with the averaged density of this cloud.

The key trick is reuse. When you cook pancakes one after another, you don't need to guess from scratch how the batter will spread each time: just glance at the previous pancake and tweak the shape slightly. Archē does the same: it takes the electron distribution from the previous moment and shifts it to the new positions of the nuclei. This speeds up the calculation severalfold. The second trick is to mix the old and new densities in a ratio that gives the most stable picture.

The code was tested on aluminum — a metal familiar from kitchen foil, but here heated to the state of stellar interiors. The results matched much more complex calculations that track every electron. A small correction had to be added, related to how electrons interact with the atomic core. The final program runs on ordinary graphics cards and handles the task tens of times faster than hundreds of CPUs. The hotter the plasma, the easier it is to compute — unlike traditional methods, which only slow down with temperature.