Higher-order and tuple-based massively-parallel prefix sums

2016 ◽  
Vol 51 (6) ◽  
pp. 539-552 ◽  
Author(s):  
Sepideh Maleki ◽  
Annie Yang ◽  
Martin Burtscher
Keyword(s):  
Higher Order ◽  
Massively Parallel ◽  
Parallel Prefix ◽  
Prefix Sums

ON PARALLEL PREFIX COMPUTATION

1994 ◽  
Vol 04 (04) ◽  
pp. 429-436 ◽  
Author(s):  
SANJEEV SAXENA ◽  
P.C.P. BHATT ◽  
V.C. PRASAD
Keyword(s):  
Linear Time ◽  
Time Algorithm ◽  
Optimal Time ◽  
Word Size ◽  
Parallel Prefix ◽  
Parallel Merge ◽  
Merge Sort ◽  
Sort Algorithm ◽  
Crcw Pram ◽  
Prefix Sums

We prove that prefix sums of n integers of at most b bits can be found on a COMMON CRCW PRAM in [Formula: see text] time with a linear time-processor product. The algorithm is optimally fast, for any polynomial number of processors. In particular, if [Formula: see text] the time taken is [Formula: see text]. This is a generalisation of previous result. The previous [Formula: see text] time algorithm was valid only for O(log n)-bit numbers. Application of this algorithm to r-way parallel merge sort algorithm is also considered. We also consider a more realistic PRAM variant, in which the word size, m, may be smaller than b (m≥log n). On this model, prefix sums can be found in [Formula: see text] optimal time.

Massively parallel structured direct solver for equations describing time-harmonic qP-polarized waves in TTI media

Geophysics ◽  
2012 ◽  
Vol 77 (3) ◽  
pp. T69-T82 ◽  
Author(s):  
Shen Wang ◽  
Jianlin Xia ◽  
Maarten V. de Hoop ◽  
Xiaoye S. Li
Keyword(s):  
Finite Difference ◽  
Higher Order ◽  
Difference Schemes ◽  
Massively Parallel ◽  
Finite Difference Schemes ◽  
Variable Order ◽  
Nested Dissection ◽  
Partial Differential ◽  
Polarized Waves ◽  
Time Harmonic

We considered the discretization and approximate solutions of equations describing time-harmonic qP-polarized waves in 3D inhomogeneous anisotropic media. The anisotropy comprises general (tilted) transversely isotropic symmetries. We are concerned with solving these equations for a large number of different sources. We considered higher-order partial differential equations and variable-order finite-difference schemes to accommodate anisotropy on the one hand and allow higher-order accuracy — to control sampling rates for relatively high frequencies — on the other hand. We made use of a nested dissection based domain decomposition in a massively parallel multifrontal solver combined with hierarchically semiseparable matrix compression techniques. The higher-order partial differential operators and the variable-order finite-difference schemes require the introduction of separators with variable thickness in the nested dissection; the development of these and their integration with the multifrontal solver is the main focus of our study. The algorithm that we developed is a powerful tool for anisotropic full-waveform inversion.

scholarly journals Faster optimal parallel prefix sums and list ranking

1989 ◽  
Vol 81 (3) ◽  
pp. 334-352 ◽  
Author(s):  
Richard Cole ◽  
Uzi Vishkin
Keyword(s):  
List Ranking ◽  
Parallel Prefix ◽  
Prefix Sums
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