The standard iterative methods for solving linear and nonlinear systems of equations are all synchronous, meaning that in the parallel execution of these methods where some processors may complete an iteration before other processors (for example, due to load imbalance), the fastest processors must wait for the slowest processors before continuing to the next iteration. This talk will discuss parallel iterative methods that operate asynchronously, meaning that the processors never wait for each other, but instead proceed using whatever iterate values are already available from other processors. Processor idle time is thus eliminated, but questions arise about the convergence of these methods. Asynchronous iterative methods will be introduced using simple fixed-point iterative methods for linear systems, before discussing asynchronous versions of rapidly converging methods, in particular, optimized Schwarz and multigrid methods.
