1,223 research outputs found
Pipeline Implementations of Neumann-Neumann and Dirichlet-Neumann Waveform Relaxation Methods
This paper is concerned with the reformulation of Neumann-Neumann Waveform
Relaxation (NNWR) methods and Dirichlet-Neumann Waveform Relaxation (DNWR)
methods, a family of parallel space-time approaches to solving time-dependent
PDEs. By changing the order of the operations, pipeline-parallel computation of
the waveform iterates are possible without changing the final solution. The
parallel efficiency and the increased communication cost of the pipeline
implementation is presented, along with weak scaling studies to show the
effectiveness of the pipeline NNWR and DNWR algorithms.Comment: 20 pages, 8 figure
An Asymptotic Preserving Maxwell Solver Resulting in the Darwin Limit of Electrodynamics
In plasma simulations, where the speed of light divided by a characteristic
length is at a much higher frequency than other relevant parameters in the
underlying system, such as the plasma frequency, implicit methods begin to play
an important role in generating efficient solutions in these multi-scale
problems. Under conditions of scale separation, one can rescale Maxwell's
equations in such a way as to give a magneto static limit known as the Darwin
approximation of electromagnetics. In this work, we present a new approach to
solve Maxwell's equations based on a Method of Lines Transpose (MOL)
formulation, combined with a fast summation method with computational
complexity , where is the number of grid points (particles).
Under appropriate scaling, we show that the proposed schemes result in
asymptotic preserving methods that can recover the Darwin limit of
electrodynamics
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