BIRS Workshop Lecture Videos

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BIRS Workshop Lecture Videos

Implementation and application of explicit SSP multi-rate time integration methods in PETSc Zhang, Hong


Multirate time integration methods allow for adaptation of local time step size, are thus particularly efficient for multi-scale systems that have widely different time scale characteristics. However, classic multi-rate schemes designed for ODEs are typically difficult to be extended for PDEs because of additional stability requirements. For example, hyperbolic conservation laws require the numerical schemes to be positivity-preserving and total variation diminishing. While multi-rate partitioned Runge-Kutta methods were proposed to use different time steps on different grid cells to overcome the global CFL constraint, buffer regions have to be introduced in order to accommodate the transition between subdomains. Implementation of these methods are tricky and highly application-dependent, and especially challenging for general-purpose libraries. In this talk, we will present our recent development of multi-rate time integrators in PETSc, which is one of the most popular software library for the scalable solution of scientific applications modeled by PDEs. We will introduce the new data structure support for componentwise partitioned systems that arise naturally from mesh refinement, and show how the serial and parallel efficiency is achieved. To illustrate the capability of the PETSc multi-rate integrators for hyperbolic conservation laws, we will focus on the advection equation solved using conservative finite volume methods with consistent slope limiters.

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