Number Of Fast Fourier Transforms Research Articles

An Efficient Algorithm Based on Spectrum Migration for High Frame Rate Ultrasound Imaging

The high frame rate (HFR) imaging technique requires only one emission event for imaging. Therefore, it can achieve ultrafast imaging with frame rates up to the kHz regime, which satisfies the frame rate requirements for imaging moving tissues in scientific research and clinics. Lu’s Fourier migration method is based on a non-diffraction beam to obtain HFR images and can improve computational speed and efficiency. However, in order to obtain high-quality images, Fourier migration needs to make full use of the spectrum of echo signals for imaging, which requires a large number of Fast Fourier Transform (FFT) points and increases the complexity of the hardware when the echo frequency is high. Here, an efficient algorithm using the spectrum migration technique based on the spectrum’s distribution characteristics is proposed to improve the imaging efficiency in HFR imaging. Since the actual echo signal spectrum is of limited bandwidth, low-frequency and high-frequency parts with low-energy have little contribution to the imaging spectrum. We transform the effective part that provides the main energy in the signal spectrum to the imaging spectrum while the ineffective spectrum components are not utilized for imaging. This can significantly reduce the number of Fourier transform points, improve Fourier imaging efficiency, and ensure the imaging quality. The proposed method is evaluated on simulated and experimental datasets. Results demonstrated that the proposed method could achieve equivalent image quality with a reduced point number for FFT compared to the complete spectrum migration. In this paper, it only requires a quarter of the FFT points used in the complete spectrum migration, which can improve the computational efficiency; thus, it is more suitable for real-time data processing. The proposed spectrum migration method has a specific significance for the study and clinical application of HFR imaging.

Real-time multi-threaded reflectometry density profile reconstructions on COMPASS Tokamak

In COMPASS tokamak, the ordinary mode (O-mode) microwave reflectometry diagnostic has been equipped with an upgraded acquisition system and dedicated computational node running the Multi-Threaded Application Real-Time executor (MARTe). This upgrade aims at the deployment of a real-time (RT) plasma position reflectometry (PPR) diagnostic system for future application in closed-loop plasma position control experiments. The system is synchronized with COMPASS MARTe main controller slow cycle, running at 500 μs, and allows a maximum measurement delivery latency of 450 μs. The RT signal processing algorithms, used to reconstruct the O-mode density profiles are the most time consuming step in the control cycle. This is due to the computation of a large number of Fast Fourier Transforms (FFT) over long data arrays, produced for each reflectometry profile measurement. MARTe is a software control framework that allows the integration of external C/C++ libraries and code such as the FFTW3 C library, a highly optimized and performant implementation of the FFT algorithm into the real-time designs. The framework also provides a set of tools to handle the execution of parallel threads, which can be used to expedite the execution of computationally demanding signal processing algorithms. Herein, we present the processing architecture implemented for the multi-threaded reflectometry density profile reconstruction on MARTe framework, using the FTTW3 library. Consistent systematic results have shown that the implemented solution satisfies COMPASS slow control cycle maximum data latency requirement. Moreover, the obtained reduced latency opens the possibility to either increase the number of processed measurements, leading to a more robust plasma position estimate or even to provide multiple position measurements during each control cycle.

Scalable GW software for quasiparticle properties using OpenAtom

The GW method, which can describe electronic excitations accurately, is a powerful ab initio electronic structure technique in molecular, condensed matter and materials physics. However, the applications of the GW method to large systems require supercomputers and efficient fine-grained parallel software to overcome the computational complexity and expense of the method which scales as O(N4). Here, we develop fine-grained parallel GW software for the plane-wave basis. We proceed by revisiting the standard GW formulae in order to discern the optimal approaches for each phase of the GW calculation on present day supercomputers and to take into account recent methodological advances to inform our choices. These best numerical practices are implemented in the OpenAtom software which is written on top of the Charm++ parallel framework. We then evaluate the performance of the new software for a wide range of system sizes. Our GW software shows significantly improved parallel scaling compared to publicly available GW software on the Mira and Blue Waters supercomputers, two of most powerful computing platforms in the world. Program summaryProgram title: OpenAtom-GWProgram files doi:http://dx.doi.org/10.17632/pvj723crcx.1Licensing provisions: BSD 3-clauseProgramming language: C++Nature of problem: The GW method describes electronic excitations in materials: the energetics and quantum wave behavior when electrons are added or removed from a material. The GW method scales as O(N4) where N is the number of atoms in the simulation cell. The input variables for GW method are single-particle electronic states computed from mean-field calculations such as Density Functional Theory (DFT). The GW method, which is a proper quasiparticle approach, provides corrections to the mean-field electronic state information that include physics beyond DFT to treat excitations. We employ a plane-wave basis set as is common in condensed matter and materials physics.Solution method: The first step is to construct the static polarizability matrix (P) which represents the response of the electronic density with respect to changes in the electronic potential, and whose construction is the most expensive part of a GW computation. The P matrix calculation requires a large dense spatial grid (real space) and has a double summation over filled and empty electronic states requiring outer product operations. A large number of Fast Fourier Transforms (FFTs) must also be performed. Next, the polarizability is employed to compute the self-energy which represents the dynamic potential acting upon moving electrons. We employ a real-space representation of static polarizability matrix because the real-space method reduces the number of FFTs and the size of the real-space grids compared to working solely in the Fourier (g-space) representation. Parallelization is carried out using the Charm++ parallel middleware which through overdecomposition and virtualization, supports and enables highly scalable fine-grained parallel applications.Additional comments including restrictions and unusual features: Users need to run a DFT calculation using, e.g., the Quantum Espresso software or OpenAtom itself, to obtain the input electronic states (i.e., single particle wavefunctions and energies). Since the OpenAtom-GW software is written on top of Charm++ parallel middleware, the user must install Charm++; however, Charm++ is an increasingly widely used framework in scientific computing and this requirement does not present a bottleneck to usage.