What parallel, distributed computational techniques can be used for Bitcoin mining? As far as I have read, I haven’t found a parallel algorithm to speed up Bitcoin mining. Are there any techniques that involve parallel or distributed algorithms, architectures that speed up Bitcoin mining ?
The atomic operation of Bitcoin mining is determining if a block candidate resolves to a hash that fulfils the required difficulty. This operation is so simple, that it is being performed about 700 quadrillion times per second. 

Since mining is a random process, there is no progress towards a block. It just succeeds whenever a block candidate turns out to be a valid block. Therefore, beyond making sure that every participant in a mining pool is checking different block candidates, there is no collaboration on mining.