  Studies of ultra-fast laser-matter interaction are important for many
applications. Such interaction triggers extreme physical processes which are
localized in the range from $\sim 10$ nanometers to micron spatial scales and
developing within picosecond$-$nanosecond time range. Thus the experimental
observations are difficult and methods of applied mathematics are necessary to
understand these processes. Here we describe our simulation approaches and
present solutions for a laser problem significant for applications. Namely, the
processes of melting, a liquid jet formation, and its rupture are considered.
Motion with the jet is caused by a short $\sim 0.1-1$ ps pulse illuminating a
small spot on a surface of a thin $\sim 10-100$ nm film deposited onto
substrate.
