Projective integrators are explicit methods that efficiently exploit the multiscale features that are characteristic of stiff systems. We will introduce projective versions of second-order accurate Runge-Kutta and Adams-Bashforth methods, and demonstrate their use as outer integrators in solving stiff initial value problems. An important outcome is that the new integrators, when combined with a telescopic projective inner integrator, can result in fully explicit methods with adaptive outer step size selection and solution accuracy comparable to those obtained by implicit methods.
This technical approach has significant benefits for high-performance computing because the integrators are explicit methods that scale well on massively parallel machines. It is also a cornerstone for enabling the Equation-Free and Heterogeneous Multiscale Method frameworks for solving atomistic-macroscopic problems.
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