Matrix Compression Research Articles

Experimental Study on the Effect of Gas Adsorption and Desorption on Ultrasonic Velocity and Elastic Mechanical Parameters of Coal

The rapid and accurate identification of the physical characteristics of coal by means of ultrasonic detection is of great significance to ensure safe mining of coal and efficient development of coal seam methane. In this paper, the ultrasonic velocity testing experiments of coal during gas adsorption and desorption were carried out, utilizing a low frequency petrophysical measurement device with primary and fractured coal as the research objects. The variations in the elastic mechanical parameters and ultrasonic velocity of coal samples were analyzed to elucidate the influence mechanism that gas adsorption and desorption have on them. During gas adsorption and desorption, the longitudinal wave velocity of the primary structure coal varies from 1990 m/s to 2200 m/s, and the transverse wave velocity varies from 1075 m/s to 1160 m/s, while the longitudinal wave velocity of the fractured structure coal varies from 1540 m/s to 1950 m/s, and the transverse wave velocity varies from 800 m/s to 1000 m/s. The elastic modulus and wave velocities, in both directions of the primary structural coal, were higher than those of the fractured structural coal. In comparison to the fractured structural coal, the main structural coal had a lower Poisson’s ratio. In addition, the spread of the elastic mechanical parameters and wave velocities, in both the longitudinal and transverse directions, was more pronounced in the fracture−structured coal than in the primary−structured coal. During gas adsorption and desorption, the speed of the coal’s longitudinal waves increased, and then decreased, due to the combined effect of gas adsorption expansion and pore gas pressure compression matrix effect. For this experiment, the maximum longitudinal wave velocity of the coal occurred at a gas pressure of 1.5 MPa. Primary structural coal has a longitudinal wave speed of 2103 m/s, whereas fragmented structural coal has a speed of 1925 m/s. The variation in the shear wave velocity of the coal is controlled only by the gas adsorption expansion effects. The shear wave velocity increases during gas adsorption and decreases during gas desorption. With the change of gas pressure, the longitudinal wave velocity can increase by 23.34%, and the shear wave velocity can increase by 17.97%. Coal undergoes changes to both its Poisson’s ratio and elastic modulus as a result of gas adsorption and desorption; these modifications are analogous to the velocity of longitudinal and shear waves, respectively.

Accelerating AI Applications with Sparse Matrix Compression in Halide

Accelerating AI Applications with Sparse Matrix Compression in Halide

3D inversion of vertical gravity gradient with multiple graphics processing units based on matrix compression

Among single-component inversions, vertical gravity gradient data have been proven to be sufficient to obtain reasonable density distribution. However, the increasing numbers of observations and model parameters inevitably produce a large-scale sensitivity matrix, causing problems such as large memory occupation and slow computations in the inversion. Aiming at solving these long-standing problems, we have introduced a matrix compression technique to reduce memory occupation and constructed a hybrid parallel algorithm for accelerating focusing inversion. We develop the source codes and the design pattern for the proposed algorithm using C language with open multiprocessing and compute unified device architecture for further improving algorithm feasibility and reusability. A graphical user interface and visualization tools also are developed using Python. In the tests with synthetic data produced by numerical simulation and real data from Vinton Dome, it is verified that the inversion can produce an accurate result of density values and object location. The performance analysis is conducted using different scales of data. The speedup increases with the increasing number of graphics processing units (GPUs) and model parameters, proving that the proposed parallel algorithm is scalable. We compare this algorithm with others without matrix compression to demonstrate how the compressed sensitivity matrix storing and accessing method influences inversion performance. More specifically, for an inversion with 100 × 100 × 20 cells, the average speed is approximately 6 s per iteration, with a maximum speedup of 36.94. Our algorithm has a short running time and high multiple-GPU parallel efficiency. Hence, the hybrid parallel algorithm is more powerful at implementing large-scale data calculations and could be used for solving computing problems in mass data inversions.

Effect of sensing matrices on quality index parameters for block sparse bayesian learning-based EEG compressive sensing

Due to the ongoing research in the medical domain, we get lot of data for storage and transmission purposes. Real-time processing and reduction of medical data are tedious. Hence, an approach is required to compress the data and reconstruct it by using a few samples. We proposed a model with a remote Health Care Unit & Patient for EEG signals in this work. In this model, our prime concern is to reduce the number of samples to reconstruct a compressed EEG signal. So, to reduce the number of samples, we opt for compressive sensing approach. As it is a well-known concept, Compressive Sensing is the framework that mainly depends upon the Sensing matrix for compression and the Basis matrix for representation. By considering this fact, we demonstrate a technique, which is a combination of the Compressive Sensing and BSBL by employing different measurement matrices. Since BSBL has already been mentioned in the literature, we compared the results based on this demonstration with the previously mentioned approach and found a significant change in the parameters mentioned in the result and analysis section.

A Fast Singular Boundary Method for the Acoustic Design Sensitivity Analysis of Arbitrary Two- and Three-Dimensional Structures

This paper proposes a fast meshless scheme for acoustic sensitivity analysis by using the Burton–Miller-type singular boundary method (BM-SBM) and recursive skeletonization factorization (RSF). The Burton–Miller formulation was adopted to circumvent the fictitious frequency that occurs in external acoustic analysis, and then the direct differentiation method was used to obtain the sensitivity of sound pressure to design variables. More importantly, RSF was employed to solve the resultant linear system obtained by the BM-SBM. RSF is a fast direct factorization technique based on multilevel matrix compression, which allows fast factorization and application of the inverse in solving dense matrices. Firstly, the BM-SBM is a boundary-type collocation method that is a straightforward and accurate scheme owing to the use of the fundamental solution. Secondly, the introduction of the fast solver can effectively reduce the requirement of computer memory and increase the calculation scale compared to the conventional BM-SBM. Three numerical examples including two- and three-dimensional geometries indicate the precision and efficiency of the proposed fast numerical technique for acoustic design sensitivity analysis associated with large-scale and complicated structures.

Multiple hierarchical compression for deep neural network toward intelligent bearing fault diagnosis

Deep Neural Network (DNN) models have been extensively developed for intelligent bearing fault diagnosis. The superior performance of DNN-based fault diagnosis methods is attributed to the deepening network structure, which increases the complexity of the deep models and causes difficulties to deploy them in industrial environments with constrained resources. To address the problems, this paper proposes a multi-hierarchical compression to compact the deep neural network for intelligent fault diagnosis. It combines network pruning, parameter quantization, and matrix compression to process the deep model from different perspectives, which achieves a considerable reduction of parameter volume and acceleration of training and response. Firstly, structured pruning is employed to prune the inconsequential filters in the convolutional layer, and unstructured pruning is utilized to eliminate the trivial connections in the fully connected layer. Then, parameter quantization is applied to minimize the number of bits that are required for parameter representation. Finally, the matrix compression storage is taken advantage of to reduce the requirements of storage capacity and further alleviate the excessive demands for the monitoring system. Experimental results and comparisons on two bearing datasets validate the effectiveness of the proposed method. The results show that for two CNN networks with different depths, the integrated network compression method can achieve considerable reductions in the number of parameters and the floating-point operations while almost no decrease in recognition accuracy. The proposed method makes an inspiring exploration for the application of intelligent fault diagnosis in the practical industry.

DOA and polarization estimation for compressed EMVS array with arbitrary sensor geometry

Electromagnetic vector sensors (EMVS) are widely used in array signal processing because of their advantages in polarization diversity, which enables the estimation of the received polarization angle (RPA) in addition to the direction of arrival (DOA). However, these benefits are accompanied by a huge burden on hardware cost and computational complexity. Specifically, compared to scalar arrays, EMVS array signal processing requires more complex hardware devices, for instance, a larger number of front-end chains and higher computational complexity for multidimensional parameter estimation algorithms. We propose a novel compression framework to reduce the hardware cost while achieving high performance. Unlike the existing ones in the literature, the proposed compression network is a sparse network consisting of analog phase shifters; In addition, the proposed compression framework only works on spatial information except for polarization information; Further, for such a compressed EMVS array, we propose a two-step multi-parameter estimation algorithm. In detail, we firstly propose a compressed ESPRIT-like method to estimate the 2D-DOA coarsely. Then, we adopt a small-scale 2D search in the vicinity of the coarse estimate to obtain a high-accuracy estimate of 2D-DOA. After that, we obtain a high-accuracy estimate of 2D-RPA in a closed-form. Furthermore, to avoid any possible performance deterioration of the proposed estimators due to the randomly selected compression weights (a.k.a. compression matrix) from Gaussian distribution (as in literature) and thus cause loss of information, we propose an optimization algorithm to find the optimal solution for the compression matrix under the maximum signal-to-noise ratio (SNR) principle. In this way, we convert the intractable sparse complex matrix optimization problem into a quadratically constrained quadratic programming (QCQP); Then, we employ the semidefinite relaxation technique (SDR) to find the optimal compression matrix. Numerical simulations illustrate that the proposed algorithms could obtain high-accuracy multi-parameter estimates with reduced front-end chains and low computational complexity.

Pore‐Fracture Distribution Heterogeneity of Shale Reservoirs Determined by using HPMI and LPN2 GA Tests

AbstractThe compressibility of shale matrix reflects the effects of reservoir lithology, material composition, pore structure and tectonic deformation. It is important to understand the factors that influence shale matrix compressibility (SMC) and their effects on pore size distribution (PSD) heterogeneity in order to evaluate the properties of unconventional reservoirs. In this study, the volumes of pores whose diameters were in the range 6–100 nm were corrected for SMC for 17 shale samples from basins in China using high‐pressure mercury intrusion and low‐temperature nitrogen gas adsorption analyses, in order to investigate the factors influencing the SMC values. In addition, the variations in fractal dimensions before and after pore volume correction were determined, using single and multifractal models to explain the effects of SMC on PSD heterogeneity. In this process, the applicability of each fractal model for characterizing PSD heterogeneity was determined using statistical analyses. The Menger and Sierpinski single fractal models, the thermodynamic fractal model and a multi‐fractal model were all used in this study. The results showed the following. The matrix compression restricts the segmentation of the fractal dimension curves for the single fractal Menger and Sierpinski models, which leads to a uniformity of PSD heterogeneity for different pore diameters. However, matrix compression has only a weak influence on the results calculated using a thermodynamic model. The SMC clearly affects the multifractal value variations, showing that the fractal dimension values of shale samples under matrix compression are small. Overall PSD heterogeneity becomes small for pores with diameters below 100 nm and the SMC primarily affects the PSD heterogeneity of higher pore volume areas. The comparison of fractal curves before and after correction and the variance analysis indicate that the thermodynamic model is applicable to quantitatively characterize PSD heterogeneity of shale collected from this sampling area. The results show that PSD heterogeneity increases gradually as micro‐pore volumes increase.

Scalable Dry-Pressed Electrodes Based on Holey Graphene.

ConspectusHoley graphene (hG) is a structural derivative of graphene with arrays of through-thickness holes of a few to tens of nanometers in diameter, randomly distributed across the nanosheet surfaces. In most bulk preparation methods, the holes on hG sheets are preferentially generated from the pre-existing defects on graphene. Therefore, contrary to intuitive belief, hG is not necessarily more defective than the intact graphene. Instead, it retains essential parent properties, including high electrical conductivity, high surface area, mechanical robustness, and chemical inertness. Furthermore, the added holey structural motif imparts unique properties that are not present in unmodified graphene, making hG advantageous in numerous applications such as sensing, membranes, reinforcements, and electrochemical energy storage. In particular, the presence of holes enhances the mass transport through the nanosheet plane and thus significantly reduces tortuosity. This difference is a key advantage for using hG in energy storage applications where the transport of ions through the thickness becomes more hindered as the electrode thickness increases to meet practical energy density requirements.An unexpected discovery is that the holes of the hG sheets enable the dry hG powder to be directly compressed into robust monoliths. hG not only can be pressed into monoliths by itself but also can host other electrochemically active materials as a compressible matrix. This important yet unique property, which is not available for other carbon materials including intact graphene, significantly broadens the application horizon in energy storage applications. With the dry compressibility, electrodes with ultrahigh mass loading and thus ultrahigh areal capacity may be conveniently fabricated without toxic solvents or parasitic binders, which are required in conventional slurry-based approaches for electrode fabrication. The dry-press electrode preparation process can be completed within minutes regardless of mass loading. In comparison, high-mass-loading electrodes for advanced battery chemistries using conventional fabrication methods often need stringent and time-consuming process control. hG can also be combined with electrochemically active battery materials while maintaining dry compressibility. This has allowed the unprecedented, convenient manipulation of a wide variety of thick electrode compositions and architectures, which provides not only outstanding performance but also new physical insights for various battery chemistries.In this Account, we first present some basic observations on the dry compressibility of hG as well as the mechanistic investigations from atomistic modeling rationalizing this unique property. We then showcase the applications of neat and composite dry-pressed hG electrodes for various energy storage platforms including supercapacitors, lithium (Li) ion batteries, Li-O2 batteries, and Li-S/Se batteries. The preparation and performance of thick electrodes with practical mass loadings and unique electrode architecture manipulation, both enabled by the dry compressibility of hG, are highlighted and discussed.

A fully explicit staggered algorithm for near‐field wave propagation of fluid‐saturated porous media based on u‐p dynamic formulation

AbstractNear‐field wave propagation of the fluid‐saturated porous media (FSPM) is an important issue in soil dynamics and geotechnical earthquake engineering. In the current study, a fully explicit staggered algorithm for the near‐field wave propagation analysis of the FSPM in the time domain is developed based on the u‐p dynamic formulation. The decoupling of dynamic formulation is implemented by the diagonalization of the mass matrix and pore fluid compressibility matrix. The central difference method and Newmark constant average acceleration method are used for the solution of the displacement and velocity of solid skeleton, and the backward difference method is used for the solution of pore fluid pressure in the time domain. The effectiveness and feasibility of the matrix diagonalization are verified by the comparison with the classical numerical algorithm. The proposed algorithm is also validated by the comparison of the numerical results with the corresponding analytical solution results. Combing with the transmitting artificial boundary condition, the proposed algorithm is then applied to investigate the seismic response of a FSPM free field, and its applicability to the typical near‐field wave propagation problems of the FSPM is indicated. The stability analysis of the proposed algorithm is finally conducted, and the corresponding stability criterion is presented. For the proposed algorithm, all the dynamic variables of the FSPM are solved in an iterative way and the coupling dynamic equations need not to be solved at each time step. The computational effort can be reduced considerably, and the computational efficiency can be improved remarkably.

Distributed Satellite Relay Cooperative Communication with Optimized Signal Space Dimension

With the increasingly obvious trend of satellite communication and network integration, especially the emergence of inter satellite links, the interconnection between space nodes has become the development trend and inevitable requirement of future space communication. However, problems, such as long communication distance, large transmission delay and loss, limited network resources and frequent switching of transmission links, limit the ability of spatial information transmission. Firstly, based on the idea of ring planning and design, this paper uses the joint design of beamforming between nodes to design the physical layer network coding in the relay to realize the reliable transmission of information. Secondly, according to the diversity of relay signal space resources and network node information exchange, a joint design method of relay compression matrix and node precoding vector is studied, which breaks through the existing configuration constraints. In this scheme, the computational complexity is reduced by compressing and precoding the matrix to ensure reliable decoding while obtaining spatial alignment gain and degrees of freedom. Simulated and real data results demonstrate the superiority and effectiveness of the proposed method.

EVALUATION OF ORO-DISPERSIBLE TABLETS (ARTEMETHER- LUMEFANTRINE AND AMOXICILLIN TRIHYDRATE) USED FOR SOME COMMON CHILDHOOD DISEASES (MALARIA AND PHEUMONIA)

Background: Generic substitution of a brand of medicine for others, with the hope that they have the same therapeutic effect is difficult for health care providers and consumers.
 Aim: This study was able to evaluate the authenticity of label claim of eight samples of artemether-lumefantrine and two samples of amoxicillin trihydrate tablets available at Ogige market Nsukka and Ogbete main market, Enugu.
 Method: The following tests were carried out; hardness, friability, modified disintegration time, wetting time, water absorption ratio and weight uniformity. The compliance of each sample to the United States Pharmacopoeia (USP) requirements were recorded.
 Results: The friability test showed that all the tablets passed the test with less than 1% friability loss. The mean hardness ranged from 1.65±0.47 to 5.35±0.67 kgf for artemether-lumefantrine tablets, while that of amoxicillin trihydrate tablets ranged from 4.00±0.93 to 6.10±0.91 kgf respectively. The tablet diameter and mean thickness of artemether-lumefantrine tablets ranged from 9.00±1.53 to 11.00±1.0 mm and 2.00±1.15 to 4.00±1.53 mm respectively, while that of amoxicillin trihydrate ranged from 8.00± 0.9 to 10.00±1.0mm and 3.00±2.08 to 4.00±1.53mm respectively. The disintegration time of artemether-lumefantrine tablets ranged from 1.50±0.1 to 3.52±0.01 min and 2.06±0.02 to 3.30±0.03 min for amoxicillin trihydrate respectively. The study discovered that several generic brands of artemether-lumefantrine and amoxicillin trihydrate tablets in Nigeria could be sub-standard products.
 
 Peer Review History: 
 Received: 28 June 2022; Revised: 1 August; Accepted: 5 September, Available online: 15 September 2022
 Academic Editor: Prof. Dr. Gorkem Dulger, Duzce University, Turkey, gorkemdulger@yandex.com
 UJPR follows the most transparent and toughest ‘Advanced OPEN peer review’ system. The identity of the authors and, reviewers will be known to each other. This transparent process will help to eradicate any possible malicious/purposeful interference by any person (publishing staff, reviewer, editor, author, etc) during peer review. As a result of this unique system, all reviewers will get their due recognition and respect, once their names are published in the papers. We expect that, by publishing peer review reports with published papers, will be helpful to many authors for drafting their article according to the specifications. Auhors will remove any error of their article and they will improve their article(s) according to the previous reports displayed with published article(s). The main purpose of it is ‘to improve the quality of a candidate manuscript’. Our reviewers check the ‘strength and weakness of a manuscript honestly’. There will increase in the perfection, and transparency. 
 Received file: Reviewer's Comments:
 Average Peer review marks at initial stage: 5.5/10
 Average Peer review marks at publication stage: 7.0/10
 Reviewers:
 Dr. Mohammad Bayan, Faculty of Pharmacy, Philadelphia University, P.O. Box: 1 Philadelphia University 19392 Jordan, mbayan01@qub.ac
 Dr. Sally A. El-Zahaby, Pharos University in Alexandria, Egypt, sally.elzahaby@yahoo.com
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A novel method for identification of synchronous resonance frequency of blades based on random arrangement of tip-timing probes

Blade tip-timing (BTT) signal suffers from the undersampling feature, which causes the high-frequency information to be aliased to the low-frequency band, especially the aliasing problem of the synchronous resonance frequency more serious. In order to realize the frequency identification of undersampled signals in synchronous resonance, a novel multiscale cyclic-reverse optimized arrangement (MC-ROA) method based on the random arrangement of tip-timing probes is proposed in this paper. Firstly, a sparse model for frequency recovery is built based on the link between the known undersampled signals and the unknown original signals in the frequency domain, and the subspace pursuit (SP) algorithm of compressive sensing (CS) is used for frequency recovery. Then, under the random arrangement of probes, the number of ideal probes is adjusted at multiple scales and the datum probes are selected cyclically to obtain multiple sets of solutions. Finally, the target frequency weights are used to overcome the limitations of the restricted isometry property (RIP) of the parameterized compression matrix to determine the optimal recovery frequency. The BTT experiments are given to verify the effectiveness of the proposed method.

Microstructural damage and response of stiffened composite submersible pressure hull subjected to underwater explosion

ABSTRACT Submerged structures in naval applications are susceptible to underwater explosion and predicting the transient response and damage is a prime concern for the designer. Coupled Arbitrary Lagrangian-Eulerian (ALE) based numerical investigation using LS-DYNA for the inelastic dynamic response and microstructure failures of composite hull subjected to UNDEX is presented. As a prelude to the study, shock pressure in fluid domain and strain values obtained on the composite pressure hull is compared with that available in literature. The numerical study is extended to predict the large deformation, puncture and microstructural behaviours of the hull by varying the charge weight of the explosive. The results of the predicted large deformation, puncture of the hull and the microstructural failures such as fibre tension, fibre compression, matrix shear, matrix tension, and matrix compression based on the Chang- Chang composite failure model, Tsai-Wu failure theory and maximum stress theory are presented.

Matrix compression along isogenic blocks

A matrix-compression algorithm is derived from a novel isogenicblock decomposition for square matrices. The resulting compression andinflation operations possess strong functorial and spectral-permanenceproperties. The basic observation that Hadamard entrywise functionalcalculus preserves isogenic blocks has already proved to be of paramountimportance for thresholding large correlation matrices. The proposedisogenic stratification of the set of complex matrices bears similarities tothe Schubert cell stratification of a homogeneous algebraic manifold. Anarray of potential applications to current investigations in computationalmatrix analysis is briefly mentioned, touching concepts such as symmetricstatistical models, hierarchical matrices and coherent matrix organizationinduced by partition trees.

Walsh–Hadamard Kernel Feature-Based Image Compression Using DCT with Bi-Level Quantization

To meet the high bit rate requirements in many multimedia applications, a lossy image compression algorithm based on Walsh–Hadamard kernel-based feature extraction, discrete cosine transform (DCT), and bi-level quantization is proposed in this paper. The selection of the quantization matrix of the block is made based on a weighted combination of the block feature strength (BFS) of the block extracted by projecting the selected Walsh–Hadamard basis kernels on an image block. The BFS is compared with an automatically generated threshold for applying the specific quantization matrix for compression. In this paper, higher BFS blocks are processed via DCT and high Q matrix, and blocks with lower feature strength are processed via DCT and low Q matrix. So, blocks with higher feature strength are less compressed and vice versa. The proposed algorithm is compared to different DCT and block truncation coding (BTC)-based approaches based on the quality parameters, such as peak signal-to-noise ratio (PSNR) and structural similarity (SSIM) at constant bits per pixel (bpp). The proposed method shows significant improvements in performance over standard JPEG and recent approaches at lower bpp. It achieved an average PSNR of 35.61 dB and an average SSIM of 0.90 at a bpp of 0.5 and better perceptual quality with lower visual artifacts.

Exploiting compressed sensing (CS) and RNA operations for effective content-adaptive image compression and encryption

Compressed sensing (CS) has been applied for image compression and encryption, for it may compress and encrypt images simultaneously. However, some CS-based image encryption algorithms still suffer from low security and compression performance. To solve these problems, a content-adaptive compression-encryption based on CS and RiboNucleic Acid (RNA) is proposed in this paper. Firstly, the 4D laser chaos system was used to construct a measurement matrix for image compression. Secondly, an Improved Fractal Sorting Matrix (IFSM) and its iterative approach are introduced based on the Fractal Sorting Matrix (FSM) for permutation. It has the same characteristics as FSM, but with a greater permutation effect and a broader range of applications. Finally, an adaptive RNA diffusion is designed based on the unique codon of RNA, which includes codon substitution and calculation operations. This adaptive operations make the algorithm more difficult to crack. Additionally, chaotic sequences driven by the hash value of plain image are utilized in the whole encryption, which enhances the correlation between the algorithm and plain image and improves the ability to resist known-plaintext and chosen-plaintext attacks. Experimental results and performance analyses demonstrate that the proposed scheme has excellent security and compression property.

Analytical modeling of chip formation mechanism in cutting unidirectional carbon fiber reinforced polymer

Fiber orientation of the unidirectional carbon fiber reinforced polymer (UD CFRP) dominates the chip formation in the cutting process owing to its anisotropy. Existing analytical cutting models focus on cutting force prediction based on the pre-defined chip formation modes obtained from experimental analyses at different fiber orientation ranges. This paper presents the analytical prediction of CFRP chip formation modes, including fiber tension, fiber compression, matrix tension, and matrix compression, based on the stress state in the chip formation region in the fiber orientation range of [0°,180°]. The chip formation angle and the stresses activating the material failure on the chip formation plane are predicted with the minimum cutting energy principle. The transition of the chip formation mode as the fiber orientation increases, and the variations of the chip morphology and cutting forces owing to the change of chip formation mode are predicted and analyzed. The chip formation angle, chip morphology, and cutting forces are compared between the simulations and the measurements through orthogonal cutting experiments of UD CFRP at different uncut chip thicknesses and fiber orientations.

H2Opus: a distributed-memory multi-GPU software package for non-local operators

Hierarchical \({\mathscr{H}}^{2}\)-matrices are asymptotically optimal representations for the discretizations of non-local operators such as those arising in integral equations or from kernel functions. Their O(N) complexity in both memory and operator application makes them particularly suited for large-scale problems. As a result, there is a need for software that provides support for distributed operations on these matrices to allow large-scale problems to be represented. In this paper, we present high-performance, distributed-memory GPU-accelerated algorithms and implementations for matrix-vector multiplication and matrix recompression of hierarchical matrices in the \({\mathscr{H}}^{2}\) format. The algorithms are a new module of H2Opus, a performance-oriented package that supports a broad variety of \({\mathscr{H}}^{2}\) matrix operations on CPUs and GPUs. Performance in the distributed GPU setting is achieved by marshaling the tree data of the hierarchical matrix representation to allow batched kernels to be executed on the individual GPUs. MPI is used for inter-process communication. We optimize the communication data volume and hide much of the communication cost with local compute phases of the algorithms. Results show near-ideal scalability up to 1024 NVIDIA V100 GPUs on Summit, with performance exceeding 2.3 Tflop/s/GPU for the matrix-vector multiplication, and 670 Gflop/s/GPU for matrix compression, which involves batched QR and SVD operations. We illustrate the flexibility and efficiency of the library by solving a 2D variable diffusivity integral fractional diffusion problem with an algebraic multigrid-preconditioned Krylov solver and demonstrate scalability up to 16M degrees of freedom problems on 64 GPUs.

Simulation of High Frequency Twisted Pair Cable Using DDM-FEM Hybrid Algorithm

In this article, an efficient domain decomposition method finite element method (DDM-FEM) algorithm is presented for the lossy twisted pair cable. In harsh environment and anti-interface ability, cables need high toughness, noise immunity, and extraordinary strength. We, in this paper, simulate a physical model of twisted pair cable and apply a hybrid solver of DDM-FEM to analyze these problems by compression and approximation of matrix-vector product. The DDM-FEM solver along with matrix compression is used to compute the RLCG, propagation constant in the twisted pair cable, and to reduce the computational time and memory size. Therefore, in the proposed algorithm, the complexities of the system become linear. The study compares the calculated results with the existing standard to verify the effectiveness of the proposed algorithm.