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Efficient implementation of computationally intensive algorithms on parallel computing platforms

Csaba Nemes
Faculty of Information Technology And Bionics, Peter Pazmany Catholic University
Peter Pazmany Catholic University, 2014

@article{nemes2014efficient,

   title={Efficient implementation of computationally intensive algorithms on parallel computing platforms},

   author={Nemes, Csaba},

   year={2014}

}

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Two different types of computationally intensive problems have been researched to investigate the design methodology of the acceleration and to give a high-performance implementation on parallel architectures. Each problem was accelerated via a different architecture, and the results of the investigation were summarized in different thesis groups. The design methodology proposed in Thesis 1 can be applied during any type of complex AU design when the AU has a significant number of I/Os and the performance takes priority over the area requirements. In my research, the AU design was motivated by the numerical solution of different conservation laws via the FVM discretization, however, other applications require complex AU design as well, e.g. Monte Carlo experiments requiring the computation of an expression with a lot of input variables. Numerical solution of conservation laws was successfully demonstrated on FPGAs in case of simulation of CFD [1], electromagnetics [95] or seismic waves [96]. Areas profiting from the acceleration of these simulations include automotive, aircraft and wind power industries, circuit design and seismology. The idea to feedback the high-level floorplan information to high-level circuit design can also be generalized. In the proposed methodology, the partitioning of the FPUs can be altered freely to find a favorable floorplan, however, in theory, any free design parameter could be tuned in a similar way. The proposed methodology can be integrated into high-level synthesis tools at the AU generation step or at other parts of the compilation process where a free parameter shall be optimized for speed. The results of Thesis 2 were primarily applied in the GPU implementation of the DMRG algorithm, however, they can be used in further applications where similar challenges occur. The presented scheduling of matrix-matrix multiplications can be applied in Tensor Network (TN) methods [97], which compose a broader class of algorithms including DMRG as well, while the proposed kernel for asymmetric matrix-vector multiplication can be applied in Davidson implementations frequently used in quantum chemistry (e.g. [98]). As the DMRG algorithm is one of the leading tools to study the low energy physics of strongly correlated quantum systems exhibiting chain-like entanglement structure, it can be applied to simulate anisotropic materials (e.g. polymers [99]) or to describe accurately the electronic structure of open d shell molecules [100]. Furthermore, the interacting system of atoms trapped in an optical lattice, proposed as physical implementation of quantum computer, is also tractable via DMRG [79].
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