Partitioned Multirate Time Integration for Coupled Systems of Ordinary Differential Equations
Abstract: In this thesis a new method for the numerical solution of coupled systems of ordinary differential equations is investigated. To understand this new method, the workings of existing Waveform iteration methods, in particular the Jacobi and Gauß-Seidel methods were explored first. These methods were introduced to be able to exploit multirate behaviour in systems and use an iterative procedure to successively approximate the solution of the problem. The new multirate time integration method is similar to these methods, but introduces a new way of parallelising the time integration, thereby improving performance over the existing methods. In this work an analysis of the performance of the Jacobi and Gauß-Seidel method when applied to linear systems is done, both for a singlerate setting as well as a multirate setting. This analysis is then compared to numerical simulations of the waveform iteration methods, as well as the new multirate time integration method. The results look promising for the new method, having a superior performance compared to the waveform iteration methods for almost all test cases when applied to the heat equation.
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