USA This seminar will describe parallel algorithms as a commutative diagram of linear operators among vector spaces.
Physical problems correspond to vectors in a vector space with dimension determined by the problem.
Linear operators from the original space to a set of other vector spaces describe decomposition of the problem into separate domains. They are related to each other through a transpose operator, which is an isomorphism under certain conditions on the operators. The operating system represents these images as threads, tasks, or processes, which it maps onto physical processors. The commutative diagram is independent of computer architecture and independent of programming language. Co-Array Fortran defines one description of the commutative diagram by exploiting an analogy with tensor notation.