The Triangle Method for Saving Startup Time in Parallel Computers

We present a new parallel implementation of explicit time stepping methods for time dependent equations in one or two spatial dimensions. The aim is to minimize the number of data transfers, to get faster algorthms. In one spatial dimension, z explicit time steps on p processors using a grid of size n need O i t n / p ) arithmetical operations and O( z ) startup operations The triangle method also requires Oi t n / p 1 arithmetical operations but only O! z p / n ) startup operations. In two spatial dimensions, using a grid of size n n and given the same algorithm, the startup time of OCTI operations using the conventional approach is considerably reduced to O( T 6 / n 1 startup operations. All constants regarding the 0-notation are less than 5