224,099 research outputs found
High-order, Dispersionless "Fast-Hybrid" Wave Equation Solver. Part I: Sampling Cost via Incident-Field Windowing and Recentering
This paper proposes a frequency/time hybrid integral-equation method for the
time dependent wave equation in two and three-dimensional spatial domains.
Relying on Fourier Transformation in time, the method utilizes a fixed
(time-independent) number of frequency-domain integral-equation solutions to
evaluate, with superalgebraically-small errors, time domain solutions for
arbitrarily long times. The approach relies on two main elements, namely, 1) A
smooth time-windowing methodology that enables accurate band-limited
representations for arbitrarily-long time signals, and 2) A novel Fourier
transform approach which, in a time-parallel manner and without causing
spurious periodicity effects, delivers numerically dispersionless
spectrally-accurate solutions. A similar hybrid technique can be obtained on
the basis of Laplace transforms instead of Fourier transforms, but we do not
consider the Laplace-based method in the present contribution. The algorithm
can handle dispersive media, it can tackle complex physical structures, it
enables parallelization in time in a straightforward manner, and it allows for
time leaping---that is, solution sampling at any given time at
-bounded sampling cost, for arbitrarily large values of ,
and without requirement of evaluation of the solution at intermediate times.
The proposed frequency-time hybridization strategy, which generalizes to any
linear partial differential equation in the time domain for which
frequency-domain solutions can be obtained (including e.g. the time-domain
Maxwell equations), and which is applicable in a wide range of scientific and
engineering contexts, provides significant advantages over other available
alternatives such as volumetric discretization, time-domain integral equations,
and convolution-quadrature approaches.Comment: 33 pages, 8 figures, revised and extended manuscript (and now
including direct comparisons to existing CQ and TDIE solver implementations)
(Part I of II
ArrayBridge: Interweaving declarative array processing with high-performance computing
Scientists are increasingly turning to datacenter-scale computers to produce
and analyze massive arrays. Despite decades of database research that extols
the virtues of declarative query processing, scientists still write, debug and
parallelize imperative HPC kernels even for the most mundane queries. This
impedance mismatch has been partly attributed to the cumbersome data loading
process; in response, the database community has proposed in situ mechanisms to
access data in scientific file formats. Scientists, however, desire more than a
passive access method that reads arrays from files.
This paper describes ArrayBridge, a bi-directional array view mechanism for
scientific file formats, that aims to make declarative array manipulations
interoperable with imperative file-centric analyses. Our prototype
implementation of ArrayBridge uses HDF5 as the underlying array storage library
and seamlessly integrates into the SciDB open-source array database system. In
addition to fast querying over external array objects, ArrayBridge produces
arrays in the HDF5 file format just as easily as it can read from it.
ArrayBridge also supports time travel queries from imperative kernels through
the unmodified HDF5 API, and automatically deduplicates between array versions
for space efficiency. Our extensive performance evaluation in NERSC, a
large-scale scientific computing facility, shows that ArrayBridge exhibits
statistically indistinguishable performance and I/O scalability to the native
SciDB storage engine.Comment: 12 pages, 13 figure
Generating Surface Geometry in Higher Dimensions using Local Cell Tilers
In two dimensions contour elements surround two dimensional objects, in three dimensions surfaces surround three dimensional objects and in four dimensions hypersurfaces surround hyperobjects. These surfaces can be represented by a collection of connected simplices, hence, continuous n dimensional surfaces can be represented by a lattice of connected n-1 dimensional simplices. The lattice of connected simplices can be calculated over a set of adjacent n-dimensional cubes, via for example the Marching Cubes Algorithm. These algorithms are often named local cell tilers. We propose that the local-cell tiling method can be usefully-applied to four dimensions and potentially to N-dimensions. We present an algorithm for the generation of major cases (cases that are topologically invariant under standard geometrical transformations) and introduce the notion of a sub-case which simplifies their representations. Each sub-case can be easily subdivided into simplices for rendering and we describe a backtracking tetrahedronization algorithm for the four dimensional case. An implementation for surfaces from the fourth dimension is presented and we describe and discuss ambiguities inherent within this and related algorithms
- …