Efficient Acceleration Techniques Research Articles

An efficient acceleration technique of implicit schemes for quasi-linear parabolic problems

An efficient acceleration technique of implicit schemes for quasi-linear parabolic problems

NPTS-PK: A new point kernel code for fast calculation of 3D gamma radiation field

The point kernel integration method is commonly utilized for the analytical calculation of gamma radiation fields in the field of radiation protection and shielding design. This study introduces NPTS-PK, a program developed for rapid calculation of 3D gamma radiation fields based on the NPTS program and the point kernel integration method. Based on the geometric construction and input method of the NPTS program, NPTS-PK supports point kernel calculations for radiation sources and shielding structures of various complex shapes and materials. By calculating material attenuation coefficients using continuous energy cross-section parameters, combined with a more precise buildup factor calculation method, the accuracy of calculation results has been enhanced. Improvements in ray tracing processes and the implementation of the probability neighbor list method have accelerated geometric processing. To address the challenge of excessive computation time associated with large-scale grid counting in point kernel programs, NPTS-PK integrates several efficient acceleration techniques, elevating the speed of radiation field calculation by an order of magnitude. Tests on typical model and engineering scenario demonstrate that the deviation between NPTS-PK results and the reference values is within a few tens of percent, and the computational efficiency and accuracy are improved compared to the standard point kernel programs.

Challenges in high-fidelity thermal–hydraulic simulation of SFR cores: Insights and PACA-S4FR solutions

Numerical simulations in studying thermal–hydraulic behavior in sodium-cooled fast reactors (SFR) have gained attention for their safety and cost advantages. While low-fidelity numerical simulations commonly used in industry have the advantage of lower computational costs, they face challenges in accurately representing intricate flow phenomena. On the other hand, high-fidelity numerical simulations offer excellent characterization of turbulence but demand significant computational resources. The emergence of exascale supercomputers has provided opportunities and challenges for large-scale high-fidelity numerical simulations. In this paper, firstly, we review the research progress of thermal–hydraulic numerical simulations of SFR cores using both low-fidelity and high-fidelity methods. Secondly, we estimate the computational and storage requirements for high-fidelity numerical simulations of SFR core based on calculations performed on China Experimental Fast Reactor (CEFR). Subsequently, we analyze the challenges of conducting high-fidelity thermal–hydraulic simulations of the entire SFR core, including large-scale mesh generation, appropriate numerical discretization methods, efficient simulation acceleration techniques, coupled simulations, and the complexities of validation and verification processes. Finally, we present the research progress of PACA-S4FR, a high-fidelity thermal–hydraulic simulation software in the China Virtual Reactor (CVR1.0) project, along with the ongoing efforts to address challenges in high-fidelity simulations. This paper contributes to advancing the comprehension of SFR core thermal hydraulics, potentially aiding in safety and performance enhancements in SFR.

A novel guideline for the analysis of linear acceleration mechanics – outlining a conceptual framework of ‘shin roll’ motion

ABSTRACT Linear acceleration is a key performance determinant and major training component of many sports. Although extensive research about lower limb kinetics and kinematics is available, consistent definitions of distinctive key body positions, the underlying mechanisms and their related movement strategies are lacking. The aim of this ‘Method and Theoretical Perspective’ article is to introduce a conceptual framework which classifies the sagittal plane ‘shin roll’ motion during accelerated sprinting. By emphasising the importance of the shin segment’s orientation in space, four distinctive key positions are presented (‘shin block’, ‘touchdown’, ‘heel lock’ and ‘propulsion pose’), which are linked by a progressive ‘shin roll’ motion during swing-stance transition. The shin’s downward tilt is driven by three different movement strategies (‘shin alignment’, ‘horizontal ankle rocker’ and ‘shin drop’). The tilt’s optimal amount and timing will contribute to a mechanically efficient acceleration via timely staggered proximal-to-distal power output. Empirical data obtained from athletes of different performance levels and sporting backgrounds are required to verify the feasibility of this concept. The framework presented here should facilitate future biomechanical analyses and may enable coaches and practitioners to develop specific training programs and feedback strategies to provide athletes with a more efficient acceleration technique.

An efficient GPU acceleration technique for CBCT based on memory aware optimization scheme

Among many of the image reconstruction techniques; the Feldkamp-Davis-Kress (FDK) is considered the most practical algorithm that used in clinical cone-beam Computed Tomography (CT) technology. In this paper, we present a full memory-aware management optimization scheme to reconstruct high-resolution volumes for a large number of X-Ray images as projections based on an efficient GPU acceleration technique. The proposed optimization technique is a scheme for FDK acceleration, that sheds new light on 4 new strategies: (1) Overcome limited device memory by evaluating different four configurations to migrate input and output data in the CPU/GPU system, (2) Reduce data transfer time during the FDK execution by using a Unified Memory (UM) model with data prefetching feature during reconstruction for data migration between host and device, (3) Accelerate the bottleneck algorithm back-projection as a result of computation mitigation, and (4) Optimize projection data layout that led to better device memory access and overcomes memory latency problem before processing and computing on GPU. The experimental results based on the proposed method show that it took 21.17 sec and 101.76 sec to reconstruct high-resolution 1024 3 , 2048 3 - voxel volume from 1800 projection of 1024 2 and 2048 2 -pixel respectively. The performance resulted from our optimization technique considered on-the-fly reconstruction (real-time), which means it can process 85 projections per second for high-resolution volumes from a large number of projections to achieve accuracy and resolution for reconstructed volume. In the term of speedup, the proposed method can achieve 1.72 speedup to reconstruct the low-resolution volume 512 3 , 1.82 speedup for 1024 3 volume and 1.70 s p e e d u p f o r 2048 3 for highest resolution volumes over baseline implementation and optimized over previous reconstruction methods based on FDK.

High-fidelity approximation of grid- and shell-based sampling schemes from undersampled DSI using compressed sensing: Post mortem validation

While many useful microstructural indices, as well as orientation distribution functions, can be obtained from multi-shell dMRI data, there is growing interest in exploring the richer set of microstructural features that can be extracted from the full ensemble average propagator (EAP). The EAP can be readily computed from diffusion spectrum imaging (DSI) data, at the cost of a very lengthy acquisition. Compressed sensing (CS) has been used to make DSI more practical by reducing its acquisition time. CS applied to DSI (CS-DSI) attempts to reconstruct the EAP from significantly undersampled q-space data. We present a post mortem validation study where we evaluate the ability of CS-DSI to approximate not only fully sampled DSI but also multi-shell acquisitions with high fidelity. Human brain samples are imaged with high-resolution DSI at 9.4T and with polarization-sensitive optical coherence tomography (PSOCT). The latter provides direct measurements of axonal orientations at microscopic resolutions, allowing us to evaluate the mesoscopic orientation estimates obtained from diffusion MRI, in terms of their angular error and the presence of spurious peaks. We test two fast, dictionary-based, L2-regularized algorithms for CS-DSI reconstruction. We find that, for a CS acceleration factor of R=3, i.e., an acquisition with 171 gradient directions, one of these methods is able to achieve both low angular error and low number of spurious peaks. With a scan length similar to that of high angular resolution multi-shell acquisition schemes, this CS-DSI approach is able to approximate both fully sampled DSI and multi-shell data with high accuracy. Thus it is suitable for orientation reconstruction and microstructural modeling techniques that require either grid- or shell-based acquisitions. We find that the signal-to-noise ratio (SNR) of the training data used to construct the dictionary can have an impact on the accuracy of CS-DSI, but that there is substantial robustness to loss of SNR in the test data. Finally, we show that, as the CS acceleration factor increases beyond R=3, the accuracy of these reconstruction methods degrade, either in terms of the angular error, or in terms of the number of spurious peaks. Our results provide useful benchmarks for the future development of even more efficient q-space acceleration techniques.

Adaptive cross approximation of tensors arising in the discretization of boundary integral operator shape derivatives

The shape derivative of a dense N × N BEM matrix is a sparse three-way tensor with O ( N 2 ) non-zero entries, to which standard BEM acceleration techniques such as the adaptive cross approximation (ACA) and FMM cannot be directly applied. The tensor can be used to compute shape sensitivities, or via adjoint equations, the gradient of an objective function. Although for many PDEs, calculation of the tensor can be avoided by expressing the shape derivative of the solution as the solution of a related PDE, this approach is not always easily amenable to BEM. Therefore, the computation of shape derivatives via the sparse three-way tensor is a valuable alternative, provided that efficient acceleration techniques exist. We propose a new algorithm for the approximation of BEM shape derivative tensors based on ACA that achieves the same complexity and error bounds as ACA for the BEM matrix itself. Numerical examples show that despite the much larger amount of data involved, the tensor approximation is only moderately slower than the matrix approximation. We also demonstrate the method on a shape optimization problem from the literature.

Fast perspective volume ray casting method using GPU-based acceleration techniques for translucency rendering in 3D endoluminal CT colonography

Recent advances in graphics processing unit (GPU) have enabled direct volume rendering at interactive rates. However, although perspective volume rendering for opaque isosurface is rapidly performed using conventional GPU-based method, perspective volume rendering for non-opaque volume such as translucency rendering is still slow. In this paper, we propose an efficient GPU-based acceleration technique of fast perspective volume ray casting for translucency rendering in computed tomography (CT) colonography. The empty space searching step is separated from the shading and compositing steps, and they are divided into separate processing passes in the GPU. Using this multi-pass acceleration, empty space leaping is performed exactly at the voxel level rather than at the block level, so that the efficiency of empty space leaping is maximized for colon data set, which has many curved or narrow regions. In addition, the numbers of shading and compositing steps are fixed, and additional empty space leapings between colon walls are performed to increase computational efficiency further near the haustral folds. Experiments were performed to illustrate the efficiency of the proposed scheme compared with the conventional GPU-based method, which has been known to be the fastest algorithm. The experimental results showed that the rendering speed of our method was 7.72 fps for translucency rendering of 1024×1024 colonoscopy image, which was about 3.54 times faster than that of the conventional method. Since our method performed the fully optimized empty space leaping for any kind of colon inner shapes, the frame-rate variations of our method were about two times smaller than that of the conventional method to guarantee smooth navigation. The proposed method could be successfully applied to help diagnose colon cancer using translucency rendering in virtual colonoscopy.

Development and verification of an MOC code employing assembly modular ray tracing and efficient acceleration techniques

In this paper, we report the development and verification of a method of characteristics (MOC) code, PEACH, at Shanghai Jiao Tong University. Both the usual flat-source step characteristics (SC) scheme and the linear source (LS) approximation scheme are adopted for the tracking calculation along the neutron trajectory. The assembly-based modular ray tracing (AMRT) technique that possesses a good geometric flexibility and high efficiency is employed, which makes PEACH able to deal with practical LWR assembly and core problems. Moreover, in order to reduce the computational time of the MOC iteration process, both the multi/few-group two-level cell-based coarse mesh finite difference (CMFD) acceleration and the exponential function interpolation technique are used. This results in a significant acceleration. Numerical results for the OECD NEA C5G7 MOX benchmark problem and a 69-group BWR mini-core problem demonstrate that PEACH is accurate and efficient. Numerical results also demonstrate that the LS scheme is more efficient than the SC scheme, taking less time and system memory to generate results of comparable accuracy. In addition, we find that MOC with CMFD acceleration always converges with almost the same number of outer iterations regardless of the physical problem size and the discretization parameters used. This shows an ideal linear relationship between the run time and the geometric size of the problem.

Mean-Flow-Multigrid for Implicit Reynolds-Stress-Model Computations

The purpose of this work is to develop an efficient and robust multigrid acceleration technique for the computation of the compressible Favre-Reynolds-averaged Navier-Stokes equations with seven-equation Reynolds-stress-model turbulence closures. The basic monogrid algorithm uses an upwind-biased O(Δx 3 ) flux-vector-split space discretization with implicit time integration. The discrete system of nonlinear equations is solved by a subiterative procedure, based on a local dual-time-stepping technique, which includes quasi-Newton iteration in the limit Δt → ∞. Full-approximation scheme sawtooth cycle multigrid is applied on the mean-flow variables only, while turbulence variables are simply injected into coarser grids. Characteristic-based multigrid is used for the restriction operator. The straightforward extension of the method to lower-level two-equation k-e closures is described. Computational examples for various two- and three-dimensional complex flows, including large separation and/or shock-wave/boundary-layer interactions using different turbulence models, demonstrate that speed-ups of 3 to 4 are obtained, using three levels of multigrid (fine + two coarser grids).

Computation of an infinite integral using series acceleration

A numerical computation in crystallography involves an infinite integral depending on one parameter. In a recent article in this journal this computational problem is addressed using Romberg’s method and tools for error control. One observe numerical difficulties with the reported approach both near the parameter’s endpoints and near the parameter interval’s midpoint. In this short note we will present an alternative approach making use of a known infinite series formulation of the problem at hand and a simple and efficient series acceleration technique. If some care is taken to avoid cancellations the numerical results are excellent for all values of the parameter.

Fast Multipath Radiosity using Hierarchical Subscenes

AbstractThis paper presents an efficient acceleration technique for the global line radiosity Multipath method. In this approach, the scene is subdivided in a hierarchy of box bounded subscenes, the boxes subdivided in a grid of virtual patches which store angular information. A new recursive (according to the hierarchy of subscenes) function allows to execute the Multipath algorithm at different levels of the hierarchy. A speed up factor up to 3–4 has been obtained on some of the tested scenes.

Automatic Hybrid Hierarchy Creation: a Cost‐model Based Approach

Abstract While using hierarchical search structures has been proved as one of the most efficient acceleration techniques when rendering complex scenes, automatic creation of appropriate hierarchies is not solved yet. Well‐known algorithms for automatic creation of bounding volume hierarchies are not enough. Higher performance is achieved by introducing spatial uniform subdivision, although algorithms proposed up to now are not truly automatic, as they need some parameters to be adjusted. In this paper we present a full‐automatic hierarchy creation scheme that structures the scene in a hybrid way, combining bounding volumes and voxel grids in the same tree, selecting the search structure that best fits to each scene region. It uses no parameters at all. This efficient proposal relies on a new cost model that estimates the goodness of a hybrid hierarchy if used for rendering the scene. ACM CSS: I.3.7 Computer Graphics—Three‐Dimensional Graphics and Realism

Efficient ray-tracing acceleration techniques for radio propagation modeling

Ray-tracing and uniform theory of diffraction techniques are already widely applied to site-specific radio propagation modeling for wireless applications. Software tools using such techniques may take considerable computation time in the analysis of the propagation conditions in a given environment even for a short mobile terminal route. Efficient acceleration techniques are required to make such analysis tools practical for the design of modern radio systems. To reduce computation time, ray-tracing routines must be applied only to those areas where rays are likely to exist. This is achieved by using ray-path search algorithms prior to performing any actual ray tracing. An efficient ray-path search algorithm is presented. First, a two-dimensional version is described, which is valid for indoor and microcell studies. Then, an extension to the three-dimensional case is explained in detail. Finally, the software tool Radio Tracer using such techniques is briefly described, and some comparisons between experimental results and computed predictions for indoor and outdoor scenarios are shown.

Residual scaling techniques in multigrid, I: Equivalence proof

This paper addresses the residual scaling techniques (coarse-grid-correction optimization techniques) in multigrid methods. We surveyed recent developments in this area and prove the equivalence of the overweighted residual technique and the overcorrection technique. This leads to the proof of mathematical equivalence of the prescaling and postscaling acceleration techniques. Two theorems have been proved to unify the concept of the residual scaling techniques. These theoretical results clear the way for developing efficient prescaling acceleration techniques for practical applications. Those practical prescaling acceleration techniques are discussed in a companion paper: Residual scaling techniques, II: practical applications.

Integration of Navier-Stokes equations using dual time stepping and a multigrid method

Efficient acceleration techniques typical of explicit steady-state solvers are extended to tune-accurate calcu- lations. Stability restrictions are greatly reduced by means of a fully implicit time discretization. A four-stage Runge-Kutta scheme with local tune stepping, residual smoothing, and multigridding is used instead of traditional computationally expensive factorizations. Two applications to natural unsteady viscous flows are presented to check for the capability of the procedure. ECENT progress in computational fluid dynamics along with the evolution of computer performance encourages scientists to look in to details of flow physics. There are practical applications where the unsteadiness of the problem can not be neglected (i.e., vortex shedding, natural unsteadiness, forced unsteadiness, aeroe- lasticity, turbomachinery rotor-stator interaction). Up to now, most of the analysis and designing tools are based on a steady or quasi- steady assumption, even if the flow is known to be unsteady. Today, due to the improvement in computer resources, there is a strong interest in developing methodologies for efficient and reliable sim- ulation of unsteady flow features. It is a common experience, while using time-accurate explicit schemes, to be forced to choose the time step on the basis of stability restrictions. As a consequence, unless the problem is a very high frequency one, the number of time steps to be performed is much higher than the one required for time accuracy. By means of some implicit factorization, stability restrictions can be relaxed, but the work required at each time step grows rapidly with grid dimension and complexity of the flow equations. In addition, application of boundary conditions in a fully implicit manner is difficult. In viscous flow calculations, the grid is clustered close to the shear layer and the characteristic time step varies several orders of mag- nitude inside the computational domain. Even if in several practical applications the characteristic time step of the core-flow region is comparable with the one required by time accuracy, close to the walls the time step restrictions become extremely severe. There- fore, highly vectorizable schemes with less stability restrictions on the allowable time step would be an interesting combination. Explicit schemes combined with acceleration techniques have proven to be very effective for solving steady problems.13 Unfortu- nately, the computational efficiency of those time-marching solvers is achieved by sacrificing the accuracy in time. In this paper, it is shown that the conventional steady-state acceleration techniques, specifically the multigrid techniques, can still be applied to unsteady viscous problems. The basic idea is to introduce a dual time stepping and to reformulate the governing equations so that they can be han- dled by an explicit accelerated scheme.4 If the time discretization is made implicit, stability restrictions are removed and accelera- tion techniques can be used instead of traditional time-consuming factorizations (i.e., alternate directional implicit and lower/upper).

A globally and quadratically convergent algorithm for solving nonlinear resistive networks

A globally convergent algorithm that is also quadratically convergent for solving bipolar transistor networks is proposed. The algorithm is based on the homotopy method using a rectangular subdivision. Since the algorithm uses rectangles, it is much more efficient than the conventional simplicial-type algorithms. It is shown that the algorithm is globally convergent for a general class of nonlinear resistive networks. Here, the term globally convergent means that a starting point which leads to the solution can be obtained easily. An efficient acceleration technique which improves the local convergence speed of the rectangular algorithm is proposed. By this technique, the sequence of the approximate solutions generated by the algorithm converges to the exact solution quadratically. Also, in this case the computational work involved in each iteration is almost identical to that of Newton's method. Therefore, the algorithm becomes as efficient as Newton's method when it arrives sufficiently close to the solution. It is also shown that sparse-matrix techniques can be introduced to the rectangular algorithm, and the partial linearity of the system of equations can be exploited to improve the computational efficiency. Some numerical examples are also given in order to demonstrate the effectiveness of the proposed algorithm. >

The summation of alternating and monotonic series

In previous papers the author has treated the question of convergence acceleration of alternating series, and of power series in x having positive coefficients. In the latter case it was assumed that 0 < x < 1, but even for x extremely close (but not equal) to 1, a powerful convergence acceleration was obtained. The present paper propounds an improved convergence acceleration method for alternating series, and also an efficient convergence acceleration technique which is valid for many monotonic series of importance in applied mathematics, i.e. the case x = 1 is now treated. In essence this technique obtains from the positive terms of the monotonic series an alternating sequence of convergents, which are then handled by the method for alternating series or sequences. It is assumed that the coefficients (or terms) of the series treated in this paper are moments of a function itf( u) over the interval 0 ⩽ u ⩽ 1, and the methods are based on properties of the shifted Legendre polynomials P ∗ n ( u), and on the author's earlier summation formula for power series having moment coefficients. The function itf( u) does not need to be known.