In a sequence of major computational steps or in an iterative computation, a stencil amplifier can increase the number of data elements accessed from one or more data structures in a single major step or iteration, thereby decreasing the total number of computations and/or communication operations in the overall sequence or the iterative computation. Stencil amplification, which can be optimized according to a specified parameter such as compile time, run time, code size, etc., can improve the performance of a computing system executing the sequence or the iterative computation in terms of run time, memory load, energy consumption, etc. The stencil amplifier typically determines boundaries, to avoid erroneously accessing data elements not present in the one or more data structures.