104 research outputs found
Geodesic distances in Liouville quantum gravity
In order to study the quantum geometry of random surfaces in Liouville
gravity, we propose a definition of geodesic distance associated to a Gaussian
free field on a regular lattice. This geodesic distance is used to numerically
determine the Hausdorff dimension associated to shortest cycles of 2d quantum
gravity on the torus coupled to conformal matter fields, showing agreement with
a conjectured formula by Y. Watabiki. Finally, the numerical tools are put to
test by quantitatively comparing the distribution of lengths of shortest cycles
to the corresponding distribution in large random triangulations.Comment: 21 pages, 8 figure
Generating optimized Fourier interpolation routines for density function theory using SPIRAL
© 2015 IEEE.Upsampling of a multi-dimensional data-set is an operation with wide application in image processing and quantum mechanical calculations using density functional theory. For small up sampling factors as seen in the quantum chemistry code ONETEP, a time-shift based implementation that shifts samples by a fraction of the original grid spacing to fill in the intermediate values using a frequency domain Fourier property can be a good choice. Readily available highly optimized multidimensional FFT implementations are leveraged at the expense of extra passes through the entire working set. In this paper we present an optimized variant of the time-shift based up sampling. Since ONETEP handles threading, we address the memory hierarchy and SIMD vectorization, and focus on problem dimensions relevant for ONETEP. We present a formalization of this operation within the SPIRAL framework and demonstrate auto-generated and auto-tuned interpolation libraries. We compare the performance of our generated code against the previous best implementations using highly optimized FFT libraries (FFTW and MKL). We demonstrate speed-ups in isolation averaging 3x and within ONETEP of up to 15%
Type-II/III DCT/DST algorithms with reduced number of arithmetic operations
We present algorithms for the discrete cosine transform (DCT) and discrete
sine transform (DST), of types II and III, that achieve a lower count of real
multiplications and additions than previously published algorithms, without
sacrificing numerical accuracy. Asymptotically, the operation count is reduced
from ~ 2N log_2 N to ~ (17/9) N log_2 N for a power-of-two transform size N.
Furthermore, we show that a further N multiplications may be saved by a certain
rescaling of the inputs or outputs, generalizing a well-known technique for N=8
by Arai et al. These results are derived by considering the DCT to be a special
case of a DFT of length 4N, with certain symmetries, and then pruning redundant
operations from a recent improved fast Fourier transform algorithm (based on a
recursive rescaling of the conjugate-pair split radix algorithm). The improved
algorithms for DCT-III, DST-II, and DST-III follow immediately from the
improved count for the DCT-II.Comment: 9 page
Fast calculation of thermodynamic and structural parameters of solutions using the 3DRISM model and the multi-grid method
In the paper a new method to solve the tree-dimensional reference interaction
site model (3DRISM) integral equations is proposed. The algorithm uses the
multi-grid technique which allows to decrease the computational expanses.
3DRISM calculations for aqueous solutions of four compounds (argon, water,
methane, methanol) on the different grids are performed in order to determine a
dependence of the computational error on the parameters of the grid. It is
shown that calculations on the grid with the step 0.05\Angstr and buffer
8\Angstr give the error of solvation free energy calculations less than 0.3
kcal/mol which is comparable to the accuracy of the experimental measurements.
The performance of the algorithm is tested. It is shown that the proposed
algorithm is in average more than 12 times faster than the standard Picard
direct iteration method.Comment: the information in this preprint is not up to date. Since the first
publication of the preprint (9 Nov 2011) the algorithm was modified which
allowed to achieve better results. For the new algorithm see the JCTC paper:
DOI: 10.1021/ct200815v, http://pubs.acs.org/doi/abs/10.1021/ct200815
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