Acceleration of option pricing technique on graphics processing units

This paper presents a review of the progress of smoothed particle hydrodynamics (SPH) towards high-order converged simulations. As a mesh-free Lagrangian method suitable for complex flows with interfaces and multiple phases, SPH has developed considerably in the past decade. While original applications were in astrophysics, early engineering applications showed the versatility and robustness of the method without emphasis on accuracy and convergence. The early method was of weakly compressible form resulting in noisy pressures due to spurious pressure waves. This was effectively removed in the incompressible (divergence-free) form which followed; since then the weakly compressible form has been advanced, reducing pressure noise. Now numerical convergence studies are standard. While the method is computationally demanding on conventional processors, it is well suited to parallel processing on massively parallel computing and graphics processing units. Applications are diverse and encompass wave–structure interaction, geophysical flows due to landslides, nuclear sludge flows, welding, gearbox flows and many others. In the state of the art, convergence is typically between the first- and second-order theoretical limits. Recent advances are improving convergence to fourth order (and higher) and these will also be outlined. This can be necessary to resolve multi-scale aspects of turbulent flow.

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Adaptive Precision Block-Jacobi for High Performance Preconditioning in the Ginkgo Linear Algebra Software

ACM Transactions on Mathematical Software ◽

10.1145/3441850 ◽

2021 ◽

Vol 47 (2) ◽

pp. 1-28

Author(s):

Goran Flegar ◽

Hartwig Anzt ◽

Terry Cojean ◽

Enrique S. Quintana-Ortí

Keyword(s):

Linear Algebra ◽

Graphics Processing Units ◽

High Performance ◽

Numerical Algorithms ◽

Mixed Precision ◽

Before And After ◽

Memory Accesses ◽

Specialized Hardware ◽

The Individual ◽

Graphics Processing

The use of mixed precision in numerical algorithms is a promising strategy for accelerating scientific applications. In particular, the adoption of specialized hardware and data formats for low-precision arithmetic in high-end GPUs (graphics processing units) has motivated numerous efforts aiming at carefully reducing the working precision in order to speed up the computations. For algorithms whose performance is bound by the memory bandwidth, the idea of compressing its data before (and after) memory accesses has received considerable attention. One idea is to store an approximate operator–like a preconditioner–in lower than working precision hopefully without impacting the algorithm output. We realize the first high-performance implementation of an adaptive precision block-Jacobi preconditioner which selects the precision format used to store the preconditioner data on-the-fly, taking into account the numerical properties of the individual preconditioner blocks. We implement the adaptive block-Jacobi preconditioner as production-ready functionality in the Ginkgo linear algebra library, considering not only the precision formats that are part of the IEEE standard, but also customized formats which optimize the length of the exponent and significand to the characteristics of the preconditioner blocks. Experiments run on a state-of-the-art GPU accelerator show that our implementation offers attractive runtime savings.

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DSPSR: Digital Signal Processing Software for Pulsar Astronomy

Publications of the Astronomical Society of Australia ◽

10.1071/as10021 ◽

2011 ◽

Vol 28 (1) ◽

pp. 1-14 ◽

Cited By ~ 172

Author(s):

W. van Straten ◽

M. Bailes

Keyword(s):

Signal Processing ◽

Digital Signal Processing ◽

Graphics Processing Units ◽

High Performance ◽

Digital Signal ◽

General Purpose ◽

Design Decisions ◽

Extensive Range ◽

Processing Software ◽

Graphics Processing

Abstractdspsr is a high-performance, open-source, object-oriented, digital signal processing software library and application suite for use in radio pulsar astronomy. Written primarily in C++, the library implements an extensive range of modular algorithms that can optionally exploit both multiple-core processors and general-purpose graphics processing units. After over a decade of research and development, dspsr is now stable and in widespread use in the community. This paper presents a detailed description of its functionality, justification of major design decisions, analysis of phase-coherent dispersion removal algorithms, and demonstration of performance on some contemporary microprocessor architectures.

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