Systems and methods for stencil amplification

A system for amplifying a stencil, the system comprising:

• a first processor;
• and
• a first memory in electrical communication with the first processor, the first memory comprising instructions which, when executed by a processing unit comprising at least one of the first processor and a second processor, and in electronic communication with a memory module comprising at least one of the first memory and a second memory, program the processing unit to:
• identify, in a computation sequence comprising a plurality of sequence steps, a computation using a stencil comprising a set of stencil points, each stencil point corresponding to a value of a respective element of a data structure in a current sequence step;
• and
• modify the computation by replacing a stencil point with a first-level substencil comprising a set of first-level substencil points, each first-level substencil point corresponding to a value of a respective element of the data structure from a first previous sequence step, at least one first-level substencil point being associated with a data-structure element that is different from data-structure elements associated with all stencil points.