NNSA, Nvidia to create an open-source Fortran compiler front-end for LLVM

Usually the strategy is to break the domain into chunks, with each chunk being multiple cells. Inside the chunk, the processor already has the data for adjacent cells so it can just read it. On the boundaries where some of the adjacent cells are in another chunk and on a different processor, it has to ask for the data... the vast majority of scientific codes here use OpenMP (not so bad, shared memory) or MPI (absolutely miserable to use IMO, but powerful distributed memory) to communicate. There's other tools for the job that are nicer than MPI, but they don't get much attention from HPC people (who tend to be very conservative with new technology, especially "high-level" abstractions).

Inter-processor communication is orders of magnitude slower than querying local memory (especially if that processor is say on another machine), so on top of that there's lots of clever methods of what is essentially figuring out how to slice up the problem domain; examples include Red-Black schemes, domain decomposition and Wavefront propagation.

To answer your question specifically on boundary conditions (and here I'm talking about the edges of the whole image where there's literally nothing in some cells nearby, not boundaries between partitioned regions like I was above)... you just have to choose something. There are three common approaches, which I'll illustrate by imagining you're doing a blur that decides how to blur a pixel by looking at the 8 pixels that surround it and that you're on the far right edge of the image (so the right three neighboring pixels would lie outside the image):

1. Zero - treat the three pixels as black/zero when calculating. Equivalently, treat them as whatever arbitrary value you find works best (e.g. white/1).

2. Reflective - treat the three pixels as whatever value the pixels on the left side at the appropriate positions would be. That is to say, wrap around to the other side.

3. Symmetric - treat the right three pixels as if they were the same as the left three (or the center three if you like).

This is a common problem also when solving something like a differential equation on a discretized spatial grid. In this case, the edge values are determined based on your boundary conditions- method 1 corresponds to vacuum boundaries, 2. corresponds to periodic boundaries and 3. is a specific type of extrapolated boundary.

They had a glass room overlooking the actual computer room where you'd go after handing one of the techs your cards to be entered. They brought the guy up there and he was waiting after handing off his cards and they had pre-arranged with the technician to trip and dump the cards everywhere. He said the Army guy turned white as a sheet of paper and looked like he was going to cry (this would have necessitated many hours putting the cards back in order). Then he told the guy that it was fine and they already had a copy loaded in on the drive.

It likely seems niche to most programmers, but array slicing is such a godsend to certain areas of software that there really is no more natural language to write a code in. There is Matlab, but its purpose is for prototyping. In fact it is a major credit to Matlab that the conversion is very natural.

This niche is why Fortran exists and has such a strong following. And the more modern features are like candy sprinkled on the core features. I could write a sonnet about modern fortran.