265 research outputs found
A conservative implicit multirate method for hyperbolic problems
This work focuses on the development of a self adjusting multirate strategy
based on an implicit time discretization for the numerical solution of
hyperbolic equations, that could benefit from different time steps in different
areas of the spatial domain. We propose a novel mass conservative multirate
approach, that can be generalized to various implicit time discretization
methods. It is based on flux partitioning, so that flux exchanges between a
cell and its neighbors are balanced. A number of numerical experiments on both
non-linear scalar problems and systems of hyperbolic equations have been
carried out to test the efficiency and accuracy of the proposed approach
On Extrapolated Multirate Methods
In this manuscript we construct extrapolated multirate discretization methods that allow 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 linearly implicit extrapolated methods. Numerical results with multiscale ODEs illustrate the theoretical findings
Efficient simulation of DC-DC switch-mode power converters by multirate partial differential equations
In this paper, Multirate Partial Differential Equations (MPDEs) are used for
the efficient simulation of problems with 2-level pulsed excitations as they
often occur in power electronics, e.g., DC-DC switch-mode converters. The
differential equations describing the problem are reformulated as MPDEs which
are solved by a Galerkin approach and time discretization. For the solution
expansion two types of basis functions are proposed, namely classical Finite
Element (FE) nodal functions and the recently introduced excitation-specific
pulse width modulation (PWM) basis functions. The new method is applied to the
example of a buck converter. Convergence, accuracy of the solution and
computational efficiency of the method are numerically analyzed
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