The Cuba library

Hahn, Thomas

doi:10.1016/j.nima.2005.11.150

Cited by 32 publications

(25 citation statements)

References 11 publications

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“…For the actual computations of fixed functions, eigenperturbations and critical exponents, we have implemented the procedures described above in a C++ program. The multidimensional numerical integrations were carried out using the Cuhre algorithm of the CUBA library [140][141][142][143] , which is a deterministic, high-precision integration scheme featuring globally adaptive subdivisions. As for the regularization, we mostly used an exponential regulator with shape function…”

Section: A Solution Strategymentioning

confidence: 99%

Momentum dependence of quantum critical Dirac systems

2019

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We analyze fermionic criticality in relativistic 2+1 dimensional fermion systems using the functional renormalization group (FRG), concentrating on the Gross-Neveu (chiral Ising) and the Thirring model. While a variety of methods, including the FRG, appear to reach quantitative consensus for the critical regime of the Gross-Neveu model, the situation seems more diverse for the Thirring model with different methods yielding vastly different results. We present a first exploratory FRG study of such fermion systems including momentum-dependent couplings using pseudo-spectral methods. Our results corroborate the stability of results in Gross-Neveu-type universality classes, but indicate that momentum dependencies become more important in Thirring-type models for small flavor numbers. For larger flavor numbers, we confirm the existence of a non-Gaussian fixed point and thus a physical continuum limit. In the large-N limit, we obtain an analytic solution for the momentum dependence of the fixed-point vertex.arXiv:1903.07388v2 [hep-th]

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Section: A Solution Strategymentioning

confidence: 99%

Momentum dependence of quantum critical Dirac systems

2019

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“…The region of integration for all the benchmark functions in our experiments is a unit hypercube [0, 1] n . For comparison, we use the sequential C-implementation of CUHRE from the CUBA package [4], [14] that was executed on the host machine. All the GPU kernels in our experiments are executed with a block size of 256 threads and H max is chosen to be 128 records.…”

Section: Performance/experimental Resultsmentioning

confidence: 99%

“…Thus, an efficient integration algorithm for use in higher dimensions should be adaptive in the entire n−D space. CUHRE is one such open source algorithm which is available as a part of CUBA library [4], [14]. Even though the CUHRE method uses much fewer points, in practice it compares fairly well with other adaptive integration methods in terms of accuracy [15].…”

Section: A Adaptive Multidimensional Integrationmentioning

confidence: 99%

A memory efficient algorithm for adaptive multidimensional integration with multiple GPUs

Arumugam

Godunov

Ranjan

et al. 2013

20th Annual International Conference on High Performance Computing

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Abstract-We present a memory-efficient algorithm and its implementation for solving multidimensional numerical integration on a cluster of compute nodes with multiple GPU devices per node. The effective use of shared memory is important for improving the performance on GPUs, because of the bandwidth limitation of the global memory. The best known sequential algorithm for multidimensional numerical integration CUHRE uses a large dynamic heap data structure which is accessed frequently. Devising a GPU algorithm that caches a part of this data structure in the shared memory so as to minimizes global memory access is a challenging task. The algorithm presented here addresses this problem. Furthermore we propose a technique to scale this algorithm to multiple GPU devices. The algorithm was implemented on a cluster of Intel R Xeon R CPU X5650 compute nodes with 4 Tesla M2090 GPU devices per node. We observed a speedup of up to 240 on a single GPU device as compared to a speedup of 70 when memory optimization was not used. On a cluster of 6 nodes (24 GPU devices) we were able to obtain a speedup of up to 3250. All speedups here are with reference to the sequential implementation running on the compute node.

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“…Three-dimensional simulations also offer the opportunity to evaluate the phase space acceptance of the different sequences, by calculating the six-dimensional phase space volume of the decelerated packets. To do so, we use a multi-dimensional numerical integration routine using Monte-Carlo methods (CUBA library) [61]. This is almost compulsory when the multi-dimensional volume exhibits complicated structures, as is indeed the case for packets decelerated with the standard sequence.…”

Section: Methodsmentioning

confidence: 99%

Advanced switching schemes in a Stark decelerator

2016

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We revisit the operation of the Stark decelerator and present a new, optimized operation scheme, which substantially improves the efficiency of the decelerator at both low and high final velocities, relevant for trapping experiments and collision experiments, respectively. Both experimental and simulation results show that this new mode of operation outperforms the schemes which have hitherto been in use. This new mode of operation could potentially be extended to other deceleration techniques.

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The Cuba library

Abstract: Concepts and implementation of the Cuba library for multidimensional numerical integration are elucidated.

Cited by 32 publications

References 11 publications

Momentum dependence of quantum critical Dirac systems

Momentum dependence of quantum critical Dirac systems

A memory efficient algorithm for adaptive multidimensional integration with multiple GPUs

Advanced switching schemes in a Stark decelerator

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