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A Survey on Continuous Time Computations
We provide an overview of theories of continuous time computation. These
theories allow us to understand both the hardness of questions related to
continuous time dynamical systems and the computational power of continuous
time analog models. We survey the existing models, summarizing results, and
point to relevant references in the literature
A short note on the nested-sweep polarized traces method for the 2D Helmholtz equation
We present a variant of the solver in Zepeda-N\'u\~nez and Demanet (2014),
for the 2D high-frequency Helmholtz equation in heterogeneous acoustic media.
By changing the domain decomposition from a layered to a grid-like partition,
this variant yields improved asymptotic online and offline runtimes and a lower
memory footprint. The solver has online parallel complexity that scales
\emph{sub linearly} as , where is
the number of volume unknowns, and is the number of processors, provided
that . The variant in Zepeda-N\'u\~nez and Demanet
(2014) only afforded . Algorithmic scalability is a
prime requirement for wave simulation in regimes of interest for geophysical
imaging.Comment: 5 pages, 5 figure
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