This work considers multirate generalized-structure additively partitioned Runge-Kutta (MrGARK) methods for solving stiff systems of ordinary differential equations (ODEs) with multiple time scales. These treat different partitions the system timesteps a more targeted and efficient solution compared to monolithic single rate approaches. With implicit used across all partitions, must find balanc...

In this paper we propose a novel class of methods for high-order accurate integration multirate systems ordinary differential equation initial-value problems. The proposed construct schemes by approximating the action matrix $\varphi$ functions within explicit exponential Rosenbrock (ExpRB) methods, thereby called ExpRB (MERB) methods. They consist solution to sequence modified “fast” problems,...

In this paper we construct extrapolated multirate discretization methods that allows one to efficiently solve problems that have components with different dynamics. This approach is suited for the time integration of multiscale ordinary and partial differential equations and provides highly accurate discretizations. We analyze the linear stability properties of the multirate explicit and linear...

This paper contains a comparison of the asymptotic stability properties for two multirate strategies. For each strategy, the asymptotic stability regions are presented for a 2 x 2 test problem and the differences between the results are discussed. The considered multirate schemes use Rosenbrock type methods as the main time integration method and have one level of temporal local refinement. Som...

This paper contains a comparison of the asymptotic stability properties for two multirate strategies. For each strategy, the asymptotic stability regions are presented for a 2 x 2 test problem and the differences between the results are discussed. The considered multirate schemes use Rosenbrock type methods as the main time integration method and have one level of temporal local refinement. Som...

Multirate Data ow Graphs (MR-DFGs) are used for modelling iterative computations, allowing concurrency and arbitrary data rates at ports. This model is often used for signal processing algorithms. For static scheduling the iteration period bound represents the nal barrier for the computation speed, the approximation of which is often the goal of an implementation. For the singlerate case (SR-DF...

Multirate systems are abundant in industry. In this paper, the problem studied is designing a residual generator for fault detection based on multirate sampled data. The key new feature of such a residual generator is that it operates at a fast rate for prompt fault detection. The design is based on optimizing a performance index to obtain an optimal parity space based residual generator. The l...

A general multirate lter-bank system with multiple channels and nonuniform bands is studied with the reconstruction performance measured by the worst-case energy gain (H 1 norm) of the error system between the multirate system and a pure time-delay system. Using blocking and polyphase decomposition, we associate with the multirate system an equivalent linear time-invariant (LTI) system whose tr...