burst (up)on (one)
To occur to one suddenly. After that idea burst upon me, I was able to alter the experiment and finally achieve some success.
See also: burst
burst (up)on someone
Fig. [for an idea] to strike someone suddenly. (As if an idea had burst forth. Upon is formal and less commonly used than on.) After thinking all morning long, this really tremendous idea burst upon me. It burst on me like a bolt of lightning.