  Superconductors play a crucial role in the advancement of high-field
electromagnets. Unfortunately, their performance can be compromised by
thermomagnetic instabilities, wherein the interplay of rapid magnetic and slow
heat diffusion can result in catastrophic flux jumps eventually leading to
irreversible damage. This issue has long plagued high-$J_c$ Nb$_3$Sn wires at
the core of high-field magnets. In this study, we introduce a groundbreaking
large-scale GPU-optimized algorithm aimed at tackling the complex intertwined
effects of electromagnetism, heating, and strain acting concomitantly during
the quenching process of superconducting coils. We validate our model by
conducting comparisons with magnetization measurements obtained from short
multifilamentary Nb$_3$Sn wires and further experimental tests conducted on
solenoid coils while subject to ramping transport currents. Furthermore,
leveraging our developed numerical algorithm, we unveil the dynamic propagation
mechanisms underlying thermomagnetic instabilities (including flux jumps and
quenches) within the coils. Remarkably, our findings reveal that the velocity
field of flux jumps and quenches within the coil is correlated with the amount
of Joule heating experienced by each wire over a specific time interval, rather
than solely being dependent on instantaneous Joule heating or maximum
temperature. These insights have the potential to pave the way for optimizing
the design of next-generation superconducting magnets, thereby directly
influencing a wide array of technologically relevant and multidisciplinary
applications.
