Parallel Implementation of the BiCGStab（2） Method in GPU Using CUDA and Matlab for Solution of Linear Systems

This paper presents a parallel implementation of the hybrid BiCGStab（2） （bi-conjugate gradient stabilized） iterative method in a GPU （graphics processing unit） for solution of large and sparse linear systems. This implementation uses the CUDA-Matlab integration, in which the method operations are performed in a GPU core using Matlab built-in functions. The goal is to show that the exploitation of parallelism by using this new technology can provide a significant computational performance. For the validation of the work, we compared the proposed implementation with a BiCGStab（2） sequential and parallelized implementation in the C and CUDA-C languages. The results showed that the proposed implementation is more efficient and can be viable for simulations being carried out with quality and in a timely manner. The gains in computational efficiency were 76x and 6x compared to the implementation in C and CUDA-C, respectively.     

Finite-region stability and boundedness for discrete 2D Fornasini–Marchesini second models

In this paper, the concepts of finite-region stability (FRS) and finite-region boundedness (FRB) are formulated for discrete two-dimensional (2D) Fornasini–Marchesini second (FMII) models, and then the analysis methods for FRS and FRB are proposed to investigate the transient behaviour of such discrete 2D FMII models. First, by building special recursive formulas, we develop a sufficient condition which guarantees the FRS of the system under solvable linear matrix inequalities (LMIs) conditions. Next, the FRB problem is addressed for the FMII model with exogenous disturbances and the corresponding criteria and LMIs conditions are reported. Finally, we apply the proposed FRS analysis method to consider the finite-region stabilisation problem of a chemical reactor thermal process, as well as some other numerical examples, to illustrate the validity of the proposed methods.     

Criteria of robust stability for time-varying 2D Wang–Mitchel differential systems: integral funnel method

Two-dimensional nonlinear systems with parametrical interval uncertainty are studied. Differential geometric extremal deviations method is developed. Its basic elements are integral funnels (IFs) and their boundaries. Extreme matrix-valued functions determining the branches of the boundaries of IFs are synthesised. Typical phase portraits of considered uncertain systems with different oscillatory properties are presented. Analytical criteria of robust stability for different oscillatory classes of uncertain systems are formulated.     

Optimal Paths for Variants of the 2D and 3D Reeds–Shepp Car with Applications in Image Analysis

We present a PDE-based approach for finding optimal paths for the Reeds–Shepp car. In our model we minimize a (data-driven) functional involving both curvature and length penalization, with several generalizations. Our approach encompasses the two- and three-dimensional variants of this model, state-dependent costs, and moreover, the possibility of removing the reverse gear of the vehicle. We prove both global and local controllability results of the models. Via eikonal equations on the manifold \(\mathbb {R}^d \times {\mathbb {S}}^{d-1}\) we compute distance maps w.r.t. highly anisotropic Finsler metrics, which approximate the singular (quasi)-distances underlying the model. This is achieved using a fast-marching (FM) method, building on Mirebeau (Numer Math 126(3):515–557, 2013; SIAM J Numer Anal 52(4):1573–1599, 2014). The FM method is based on specific discretization stencils which are adapted to the preferred directions of the Finsler metric and obey a generalized acuteness property. The shortest paths can be found with a gradient descent method on the distance map, which we formalize in a theorem. We justify the use of our approximating metrics by proving convergence results. Our curve optimization model in \(\mathbb {R}^{d} \times \mathbb {S}^{d-1}\) with data-driven cost allows to extract complex tubular structures from medical images, e.g., crossings, and incomplete data due to occlusions or low contrast. Our work extends the results of Sanguinetti et al. (Progress in Pattern Recognition, Image Analysis, Computer Vision, and Applications LNCS 9423, 2015) on numerical sub-Riemannian eikonal equations and the Reeds–Shepp car to 3D, with comparisons to exact solutions by Duits et al. (J Dyn Control Syst 22(4):771–805, 2016). Numerical experiments show the high potential of our method in two applications: vessel tracking in retinal images for the case \(d=2\) and brain connectivity measures from diffusion-weighted MRI data for the case \(d=3\), extending the work of Bekkers et al. (SIAM J Imaging Sci 8(4):2740–2770, 2015). We demonstrate how the new model without reverse gear better handles bifurcations.     

A cost-optimal parallel algorithm for the 0–1 knapsack problem and its performance on multicore CPU and GPU implementations

The 0–1 knapsack problem has been extensively studied in the past years due to its immediate applications in industry and financial management, such as cargo loading, stock cutting, and budget control. Many algorithms have been proposed to solve this problem, most of which are heuristic, as the problem is well-known to be NP-hard. Only a few optimal algorithms have been designed to solve this problem but with high time complexity. This paper proposes the cost-optimal parallel algorithm (COPA) on an EREW PRAM model with shared memory to solve this problem. COPA is scalable and yields optimal solutions consuming less computational time. Furthermore, this paper implements COPA on two scenarios – multicore CPU based architectures using Open MP and GPU based configurations using CUDA. A series of experiments are conducted to examine the performance of COPA under two different test platforms. The experimental results show that COPA could reduce a significant amount of execution time. Our approach achieves the speedups of up to 10.26 on multicore CPU implementations and 17.53 on GPU implementations when the sequential dynamic programming algorithm for KP01 is considered as a baseline. Importantly, GPU implementations outstand themselves in the experimental results.     

Projection gradient method for energy functional minimization with a constraint and its application to computing the ground state of spin–orbit-coupled Bose–Einstein condensates

In this study, we propose a projection gradient method for energy functional minimization with a constraint, which we use to compute the ground state of spin–orbit-coupled Bose–Einstein condensates at extremely low temperatures. The method has the advantage that it maintains the constraint when evolving a gradient flow to find the energy functional minimization under a constraint. The original gradient projection method for energy functional minimization under a constraint only considers an energy functional with real functions as variables. Thus, we extend it to consider complex functions as independent variables. We apply the newly proposed method to study the ground state solution of spin–orbit-coupled pseudo-spin 1/2 Bose–Einstein condensates. Detailed numerical results demonstrate the effectiveness of our method. Using this method, we found various types of ground state structures of spin–orbit coupled Bose–Einstein condensates.     

Probabilistic odd–even: an adaptive wormhole routing algorithm for 2D mesh network-on-chip

Wormhole routing is a popular routing technique used in network-on-chip. It is efficient but susceptible to deadlock, while deadlock will significantly degrade the network performance of NoC. Most existing adaptive wormhole routings avoid deadlock by reducing the degree of adaptiveness and thus sacrificing network performance. In this paper, we address both deadlock and network performance issues jointly, and propose a probabilistic odd–even (POE) routing algorithm that achieves the minimum packet delivery delay. The proposed POE dynamically adjusts the probabilities of constrained turns that may lead to deadlocks according to the current network conditions, and uses an efficient deadlock detection and recovery scheme when a deadlock happens. By adopting constrained turns adaptively to the network status, it not only reduces the frequency of deadlock and allows the network to be swiftly recovered when it occurs, but also greatly improves the degree of adaptiveness to obtain high network performance. Experimental results show that our method achieves a significant performance improvement both in terms of network throughput and average packet latency compared with the existing methods such as XY, odd–even, abacus turn model and fully adaptive routing algorithm while it only has moderate energy consumption.     

A heterogeneous parallel implementation of the Markov clustering algorithm for large-scale biological networks on distributed CPU–GPU clusters

The Journal of Supercomputing - Biological interaction databases accommodate information about interacted proteins or genes. Clustering on the networks formed by the interaction information for...     

Experimental determination and thermodynamic optimization of the CuCl–ZnCl2, ZnCl2–FeCl3, CuCl–FeCl3, CuCl–CuCl2, FeCl2–FeCl3, FeCl2–CuCl2 and CuCl–PbCl2 phase equilibria

In copper flash smelting, flue dust causes corrosion problems in the heat recovery boiler of the gas train due to formation of dust accretions on the boiler walls. Within these, presence of heavy metal chlorides results in formation of molten salt deposits causing rapid corrosion. CuCl–ZnCl₂, FeCl₃–ZnCl₂ and CuCl–FeCl₃ systems were studied experimentally by equilibration-quenching, scanning electron microscopy and energy-dispersive X-ray spectroscopy in order to evaluate melting behaviour of these chlorides, typically present in the corrosive dust deposits. In addition, CuCl–PbCl₂, CuCl–CuCl₂, FeCl₂–FeCl₃ and CuCl₂–FeCl₂ phase diagrams were optimized incorporating and evaluating all available phase diagram and thermodynamic data on the systems. The modified quasi-chemical model was used to describe the thermodynamic properties of molten phases and compound energy formalism was used to model the terminal solid solutions. The calculated phase diagrams are presented and compared with experimental observations as well as with all available phase diagram data from existing literature.     

Topological optimization of continuum structures with design-dependent surface loading – Part II: algorithm and examples for 3D problems

The problem of topology optimization of 3D structures with design-dependent loading is considered. An algorithm for generating the valid loading surface of the 3D structure is presented, constituting an extension of the algorithm for 2D structures developed in Part I of this paper on the basis of a modified isoline technique. In this way the complicated calculation of the fit of the loading surface of a 3D structure may be avoided. Since the finite element mesh is fixed in the admissible 3D design domain during the period of topology evolution, the design-dependent loading surface may intersect the elements as the design changes. Independent interpolation functions are introduced along the loading surface so that the surface integral for generating the loading on the surface of the 3D structure can be performed more efficiently and simply. The bilinear 4-node serendipity surface element is constructed to describe the variable loading surface, and this matches well with the 8-node isoparametric 3D elements which have been used for the discretization of the 3D design domain. The validity of the algorithm is verified by numerical examples for 3D problems. Results of designing with design-dependent loads and with corresponding fixed loads are presented, and some important features of the computational results are discussed.     

On reference solutions and the sensitivity of the 2D Kelvin–Helmholtz instability problem

Two-dimensional Kelvin–Helmholtz instability problems are popular examples for assessing discretizations for incompressible flows at high Reynolds number. Unfortunately, the results in the literature differ considerably. This paper presents computational studies of a Kelvin–Helmholtz instability problem with high order divergence-free finite element methods. Reference results in several quantities of interest are obtained for three different Reynolds numbers up to the beginning of the final vortex pairing. A mesh-independent prediction of the final pairing is not achieved due to the sensitivity of the considered problem with respect to small perturbations. A theoretical explanation of this sensitivity to small perturbations is provided based on the theory of self-organization of 2D turbulence. Possible sources of perturbations that arise in almost any numerical simulation are discussed.     

A hybrid 2D–3D tangible interface combining a smartphone and controller for virtual reality

Virtual Reality - Virtual reality (VR) controllers are widely used for 3D virtual object selection and manipulation in immersive virtual worlds, while touchscreen-based devices like smartphones or...