Solvability Of System Research Articles

Theoretical kinetic study of key reactions between ammonia and fuel molecules, part I: Hydrogen atom abstraction from alkanes by ṄH2 radical

Cross reactions between ṄH2 radical and fuel molecules are essential in determining the reactivity for ammonia/fuel blends. A systematic theoretical chemical kinetic investigation of hydrogen atom abstraction by ṄH2 radical from C1–C6 alkanes, n-heptane, and isooctane has been performed in this study. The geometry optimization, frequency, and zero-point energy calculations for all species related to the title reactions were calculated at the M06-2X/6-311++G(d,p) level of theory. One-dimensional hindered rotor treatment has also been performed at the same level of theory to obtain the potential energy surface for the low frequency torsional modes. Single-point energy was obtained at the QCISD(T)/cc-pVDZ, QCISD(T)/cc-pVTZ, MP2/cc-pVDZ, MP2/cc-pVTZ and MP2/cc-pVQZ levels of theory and then extrapolated to the complete basis set. Benchmark calculations for single point energy have also been carried out at the CCSD(T)-F12/cc-pVTZ, CCSD(T)-F12/cc-pVQZ, CCSD(T)-F12/aug-cc-pVTZ and CCSD(T)-F12/aug-cc-pVQZ levels of theory based on the geometries obtained at the CCSD(T)/cc-pVDZ level of theory for the reaction systems of methane + ṄH2 and ethane + ṄH2. The rate constants of 41 reactions in the temperature range 298.15–2000 K were calculated by using the Master Equation System Solver (MESS) with conventional transition state theory. Good agreement has been gained between our calculated results and the available theoretical and experimental data in the literature. Rate rules for different reaction sites have also been derived, and the average rate constants for primary, secondary, and tertiary sites were also reported on a per hydrogen atom basis. The impact of calculation data for the ammonia/alkane blends model has also been investigated. The calculated rate constants are valuable for the combustion kinetic model development for ammonia blending fuels.

Normalized Newton method to solve generalized tensor eigenvalue problems

AbstractThe problem of generalized tensor eigenvalue is the focus of this paper. To solve the problem, we suggest using the normalized Newton generalized eigenproblem approach (NNGEM). Since the rate of convergence of the spectral gradient projection method (SGP), the generalized eigenproblem adaptive power (GEAP), and other approaches is only linear, they are significantly improved by our proposed method, which is demonstrated to be locally and cubically convergent. Additionally, the modified normalized Newton method (MNNM), which converges to symmetric tensors Z‐eigenpairs under the same ‐Newton stability requirement, is extended by the NNGEM technique. Using a Gröbner basis, a polynomial system solver (NSolve) generates all of the real eigenvalues for us. To illustrate the efficacy of our methodology, we present a few numerical findings.

Direct method for solving systems of second order ordinary differential equations

In the paper a direct solver for systems of structurally partitioned second order differential equations is proposed. a general scheme of the method algorithmically oriented towards the particular structure of the system is presented. With the last stage reuse (also known as FSAL approach) an embedded pair of sixth and fourth order methods with just six stages is constructed, which provides an easy step-size control. Numerical comparison is made with the well-known Dormand — Prince method 5(4)7F having the same computation cost, showing the advantage of the proposed method.

2D Beam Domain Statistical CSI Estimation for Massive MIMO Uplink

In this paper, we investigate the beam domain statistical channel state information (CSI) estimation for the two-dimensional (2D) beam-based statistical channel model (BSCM) in massive multi-input multi-output (MIMO) systems. The problem is to estimate the beam domain channel power matrices (BDCPMs) based on multiple received pilot signals. A received signal model showing the relation between the statistical properties of the received pilot signals and the BDCPMs is derived. On the basis of the received signal model, we formulate an optimization problem with the Kullback-Leibler (KL) divergence. By solving the optimization problem, a novel method to estimate the statistical CSI without the estimates of instantaneous CSI is proposed. We further reduce the complexity of the proposed method by utilizing the circulant structures of particular matrices in the algorithm. We also showed the generality of the proposed method by introducing another application, <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">i.e</i> ., estimation of the angle domain channel power matrix. Simulation results show that the proposed method has good convergence and can obtain sparse BDCPMs. Compared with the regularized multiple measurement vector focal underdetermined system solver (RM-FOCUSS) algorithm, the proposed algorithm obtains overall more accurate statistical CSI with much lower complexity and brings significant performance gains when used in channel estimation.

Analysis of variable inductor employing vegetable-based transformer oil with magnetic nanoparticles

Variable inductors using magnetorheological fluids have recently been successfully applied to power-conversion devices; however, the thermal properties of Vegetable oil-based Magnetic Nanofluids (VMNFs) have not been investigated. In this study, the temperature characteristics of a variable inductor embedded with a VMNF were analyzed by developing a multiphysics analysis method and verified experimentally. To analyze the temperature distribution efficiently, a coupled analysis of the Magnetoquasistatic (MQS) field and steady-state heat transfer field based on the finite-element method was performed. The B-H curves of the VMNF and ferrite core were obtained via magnetic property measurement experiments, and the input waveforms were measured from the current and high-frequency pulse voltages applied to the variable inductor of the DC–DC converter. To predict the temperature rise of the VMNF-gap variable inductor, the power dissipation was determined using the Steinmetz experimental equation modified by the Bertotti model in the electronic system solver and input as a heat source in the steady-state heat-transfer analysis. The temperature increase predicted by the multiphysics analysis method agreed well with the experimental data, and an increasing the concentration of magnetic nanoparticles had a cooling effect. The developed MQS–thermal field coupled analytical method and the cooling properties of VMNFs can be applied to the design of power-conversion devices operating with high-frequency power sources.

A study of concurrent multi-frontal solvers for modern massively parallel architectures

Leveraging Trace Theory, we investigate the efficient parallelization of direct solvers for large linear equation systems. Our focus lies on a multi-frontal algorithm, and we present a methodology for achieving near-optimal scheduling on modern massively parallel machines. By employing trace theory with Diekert Graphs and Foata Normal Form, we rigorously validate the correctness of our proposed solution. To establish a strong link between the mesh and elimination tree of the multi-frontal solver, we conduct extensive testing on matrices derived from the Finite Element Method (FEM). Furthermore, we assess the performance of computations on both GPU and CPU platforms, employing practical implementation strategies.

A comparison of numerical schemes for the GPU-accelerated simulation of variably-saturated groundwater flow

The optimal strategy to numerically solve the Richards equation is problem-dependent, especially on GPUs because an efficient numerical scheme on CPU might not scale well on GPU. In this work, four numerical schemes are coded to investigate their parallel performance on CPU and GPU. The results indicate that the scaling of Richards solvers on GPU is affected by the numerical scheme, the linear system solver, the soil constitutive model, the code structure, the problem size and the adaptive time stepping strategies. Compared with CPU, parallel simulations on GPU exhibit stronger variance in the scaling of different code sections. The poorly-scaled components could deteriorate the overall scaling. Under all circumstances, using a GPU significantly enhances computational speed, especially for large problems. Clearly, GPU computing have significant potential in accelerating large-scale hydrological simulations, but care must be taken on the design and implementation of the model structure.

Second-order Rosenbrock-exponential (ROSEXP) methods for partitioned differential equations

In this paper, we introduce a new framework for deriving partitioned implicit-exponential integrators for stiff systems of ordinary differential equations and construct several time integrators of this type. The new approach is suited for solving systems of equations where the forcing term is comprised of several additive nonlinear terms. We analyze the stability, convergence, and efficiency of the new integrators and compare their performance with existing schemes for such systems using several numerical examples. We also propose a novel approach to visualizing the linear stability of the partitioned schemes, which provides a more intuitive way to understand and compare the stability properties of various schemes. Our new integrators are A-stable, second-order methods that require only one call to the linear system solver and one exponential-like matrix function evaluation per time step.

Channel Estimation for LEO Satellite Massive MIMO OFDM Communications

In this paper, we investigate the massive multiple-input multiple-output orthogonal frequency division multiplexing channel estimation for low-earth-orbit satellite communication systems. First, we use the angle-delay domain channel to characterize the space-frequency domain channel. Then, we show that the asymptotic minimum mean square error (MMSE) of the channel estimation can be minimized if the array response vectors of the user terminals (UTs) that use the same pilot are orthogonal. Inspired by this, we design an efficient graph-based pilot allocation strategy to enhance the channel estimation performance. In addition, we devise a novel two-stage channel estimation (TSCE) approach, in which the received signals at the satellite are manipulated with per-subcarrier space domain processing followed by per-user frequency domain processing. Moreover, the space domain processing of each UT is shown to be identical for all the subcarriers, and an asymptotically optimal vector for the per-subcarrier space domain linear processing is derived. The frequency domain processing can be efficiently implemented by means of the fast Toeplitz system solver. Simulation results show that the proposed TSCE approach can achieve a near performance to the MMSE estimation with much lower complexity.

AI‐enhanced iterative solvers for accelerating the solution of large‐scale parametrized systems

SummaryRecent advances in the field of machine learning open a new era in high performance computing for challenging computational science and engineering applications. In this framework, the use of advanced machine learning algorithms for the development of accurate and cost‐efficient surrogate models of complex physical processes has already attracted major attention from scientists. However, despite their powerful approximation capabilities, surrogate model predictions are still far from being near to the ‘exact’ solution of the problem. To address this issue, the present work proposes the use of up‐to‐date machine learning tools in order to equip a new generation of iterative solvers of linear equation systems, capable of very efficiently solving large‐scale parametrized problems at any desired level of accuracy. The proposed approach consists of the following two steps. At first, a reduced set of model evaluations is performed using a standard finite element methodology and the corresponding solutions are used to establish an approximate mapping from the problem's parametric space to its solution space using a combination of deep feedforward neural networks and convolutional autoencoders. This mapping serves as a means of obtaining very accurate initial predictions of the system's response to new query points at negligible computational cost. Subsequently, an iterative solver inspired by the Algebraic Multigrid method in combination with Proper Orthogonal Decomposition, termed POD‐2G, is developed that successively refines the initial predictions of the surrogate model towards the exact solution. The application of POD‐2G as a standalone solver or as preconditioner in the context of preconditioned conjugate gradient methods is demonstrated on several numerical examples of large scale systems, with the results indicating its strong superiority over conventional iterative solution schemes.

Multi-target Localization Based on an Improved FOCUSS Algorithm with Missing Information

The situation where the observation stations or the sensors cannot fully detect the targets is called missing information, which makes it difficult to locate targets. Due to its sparsity, Compressed Sensing (CS) can be applied to multi-target localization with missing information. An improved Focal Undetermined System Solver (IFOCUSS) algorithm is proposed, by dynamically updating the regularized factor that has a significant impact on the convergence of iteration processes. What’s more, a re-weighting method is adopted for the weighting matrix to improve convergence property and accelerate convergence, and a new method of choosing correct items from a sparse estimation vector is proposed to improve the positioning accuracy. Several simulations corroborate its notable reconstruction performance, which is illustrated by correctly estimating five targets with only 11 sensors on a moving station, achieving better convergence at lower signal-to-noise ratios (such as 12 dB) with about half the run time of Regularized FOCUSS (RFOCUSS) and being able to estimate two targets even with missing information up to 60%. Under the same conditions of missing information, IFOCUSS can estimate more targets with smaller positioning errors than RFOCUSS, achieving better convergence performance by eliminating almost all interference terms.

Sparse Approximate Multifrontal Factorization with Composite Compression Methods

This article presents a fast and approximate multifrontal solver for large sparse linear systems. In a recent work by Liu et al., we showed the efficiency of a multifrontal solver leveraging the butterfly algorithm and its hierarchical matrix extension, HODBF (hierarchical off-diagonal butterfly) compression to compress large frontal matrices. The resulting multifrontal solver can attain quasi-linear computation and memory complexity when applied to sparse linear systems arising from spatial discretization of high-frequency wave equations. To further reduce the overall number of operations and especially the factorization memory usage to scale to larger problem sizes, in this article we develop a composite multifrontal solver that employs the HODBF format for large-sized fronts, a reduced-memory version of the nonhierarchical block low-rank format for medium-sized fronts, and a lossy compression format for small-sized fronts. This allows us to solve sparse linear systems of dimension up to 2.7 × larger than before and leads to a memory consumption that is reduced by 70% while ensuring the same execution time. The code is made publicly available in GitHub.

Randomized Block Adaptive Linear System Solvers

Randomized Block Adaptive Linear System Solvers

Investigation of the energetic, exergetic performance, environmental, economic, and hydrogen production analyses of PV-T for increasing surface areas and mass flow rates compared to PV

This study investigated the energetic and exergetic efficiencies and environmental and economical, electricity and hydrogen production analyses of water-cooled photovoltaic thermal (PV-T) solar collectors and PV. For this purpose, simulations were made with Engineering Equation Solver (EES) for PV-T and PV systems with 3 different areas (A1 = 1 m2, A2 = 3 m2, and A3 = 5 m2). Also, PV-T was cooled with three mass flow rates (m˙1=0.01 kg/s, m˙2=0.03 kg/s and m˙3=0.05 kg/s). Simulations were made for each hour from 7 a.m. to 7 p.m. for a day in July. As a result, the maximum daily electricity production of the PV-T for the A1, A2, and A3 were found for m˙3=0.05 kg/s as 3.791 MJ, 11.227 MJ, and 18.49 MJ. The maximum daily electricity production PV for the A1, A2, and A3 were found as 3.305 MJ, 9.916 MJ, and 16.527 MJ. The highest energetic efficiency of the PV-T was found for m˙3=0.05 kg/s as 60.52%, 58.87%, and 57.19%. The highest exergetic efficiency of the PV-T was found for m˙1=0.01 kg/s as 16.77%, 16.89%, and 16.61% for A1, A2, and A3. The highest energetic and exergy efficiency of the PV was found as 14.40% and 15.44%. When PV-T cooled with a maximum of m˙3=0.05 kg/s, the system saved a total of 0.8475 kg 2.4799 kg, and 4.0368 kg CO2 for A1, A2, and A3. The daily carbon savings of the PV were found as 0.3709 kg, 1.1128 kg, and 1.8545 kg for the same areas. The highest hydrogen production of the system with PV-T was found for m˙3=0.05 kg/s as 18.5677 g 54.9966 g and 90.566 g for A1, A2, and A3. The daily hydrogen production of the system with the PV were found as 16.1884 g, 48.5637 g and 80.9418 g for A1, A2, and A3. The highest monthly economic contribution of the system with PV-T was found for m˙3=0.05 kg/s as 360.22 TL, 1047.22 TL and 1693.65 TL for A1, A2, and A3. Also, daily economic contribution of the system with PV was found 73.67 TL, 221.01 TL and 368.35 TL for same areas. It was found that the production performance of the system increased as the cooling flow rate increased and the PV-T area decreased. Also, the thermodynamic efficiency, the electricity and hydrogen production, economic contribution and carbon savings of the system with PV-T are found higher than the system with PV in all combinations.

Real-Valued Deep Unfolded Networks for Off-Grid DOA Estimation via Nested Array

Recently, deep unfolded networks have been widely utilized in direction of arrival (DOA) estimation due to the reduced computational complexity and improved estimation accuracy. However, few consider the nested array for off-grid DOA estimation, where the estimated DOAs are not on the prespecified grids. In this paper, we propose a deep unfolded FOCal Underdetermined System Solver (FOCUSS) network and a deep unfolded Alternating Direction Method of Multiplies (ADMM) to address the problem, which respectively aim to improve estimation accuracy and further reduce computational complexity. We first apply first-order Taylor expansion and vectorize the covariance matrix into a real-valued single snapshot for network input. We then train the proposed networks to obtain on-grid DOA spatial spectrum and off-grid values, where the off-grid DOA estimation is calculated by the peaks of on-grid DOA spatial spectrum and corresponding off-grid values. We demonstrate that the proposed networks with interpretable parameters can accelerate the convergence rate and achieve better generalization. Simulations verify the performance of proposed networks in comparison with the existing methods.

On Krylov methods for large-scale CBCT reconstruction.

Krylov subspace methods are a powerful family of iterative solvers for linear systems of equations, which are commonly used for inverse problems due to their intrinsic regularization properties. Moreover, these methods are naturally suited to solve large-scale problems, as they only require matrix-vector products with the system matrix (and its adjoint) to compute approximate solutions, and they display a very fast convergence. Even if this class of methods has been widely researched and studied in the numerical linear algebra community, its use in applied medical physics and applied engineering is still very limited. e.g. in realistic large-scale computed tomography (CT) problems, and more specifically in cone beam CT (CBCT). This work attempts to breach this gap by providing a general framework for the most relevant Krylov subspace methods applied to 3D CT problems, including the most well-known Krylov solvers for non-square systems (CGLS, LSQR, LSMR), possibly in combination with Tikhonov regularization, and methods that incorporate total variation regularization. This is provided within an open source framework: the tomographic iterative GPU-based reconstruction toolbox, with the idea of promoting accessibility and reproducibility of the results for the algorithms presented. Finally, numerical results in synthetic and real-world 3D CT applications (medical CBCT andμ-CT datasets) are provided to showcase and compare the different Krylov subspace methods presented in the paper, as well as their suitability for different kinds of problems.

An Adaptive Two-Grid Solver for DPG Formulation of Compressible Navier–Stokes Equations in 3D

Abstract We present an overlapping domain decomposition iterative solver for linear systems resulting from the discretization of compressible viscous flows with the Discontinuous Petrov–Galerkin (DPG) method in three dimensions. It is a two-grid solver utilizing the solution on the auxiliary coarse grid and the standard block-Jacobi iteration on patches of elements defined by supports of the coarse mesh base shape functions. The simple iteration defined in this way is used as a preconditioner for the conjugate gradient procedure. Theoretical analysis indicates that the condition number of the preconditioned system should be independent of the actual finite element mesh and the auxiliary coarse mesh, provided that they are quasiuniform. Numerical tests confirm this result. Moreover, they show that presence of strongly flattened or elongated elements does not slow the convergence. The finite element mesh is subject to adaptivity, i.e. dividing the elements with large errors until a required accuracy is reached. The auxiliary coarse mesh is adjusting to the nonuniform actual mesh.

Machine learning rate constants of hydrogen abstraction reactions between ester and H atom

The rate constants of hydrogen abstraction reactions of alkyl ester by H atom are crucial for optimizing combustion reaction network and improving combustion efficiency of biodiesel. Due to the lack of experimental and theoretical rate coefficients data for some reactions - such as hydrogen abstraction of large biodiesel molecules by free radicals - machine learning provides a viable alternative to predict rate constants. In this study, three different machine learning (ML) methods - feedforward neural network (FNN), extreme gradient boosting (XGB) and XGB-FNN hybrid model - were used to predict rate constants of the reactions between alkyl ester and H atom. The rate constants of 41 reactions between H + CnH2n+1COOCmH2m+1 (n = 0–5, m = 1, 2) were calculated by the Master Equation System Solver (MESS) program over a temperature range of 300–2000 K for model training. The results showed that the XGB-FNN model with 8 descriptors has better overall performance than the other two ML methods. The average deviation of XGB-FNN model on the test set is 33.56% by performing leave one out (LOO) cross validations. The rate constants of the H + methyl decanoate (MD) reactions over a temperature range of 300∼2000 K were predicted by the XGB-FNN model, which follow well the modified three-parameter Arrhenius equation and agree well with theoretical values, indicating that the hybrid XGB-FNN model is robust in predicting the rate constants of alkyl ester and H atom in the temperature range of combustion. The present ML method in this study is supposed to be able to provide accurate and affordable rate constants prediction of larger systems, the molecular sizes of which are comparable to those of the dominant components of real biodiesel. That is important for the development of biodiesel kinetic models.

Performance enhancement of the simultaneous solvers for non-convex and ill-conditioned vapor compression systems utilizing gradient methods

Simultaneous solvers using gradient methods are desirable for solving complex vapor compression system (VCS) models due to their flexibility and computational efficiency; however, they often lack robustness. Recent research has contributed towards improving the robustness of the simultaneous solvers, but there is still a need to understand why these solvers lack robustness and how to improve their convergence as the solver variables are increased. Furthermore, for a thorough system analysis, it is important to decrease the computational cost while increasing prediction accuracy. In this study, the performance of simultaneous solvers in terms of robustness, accuracy, and computational cost is evaluated using the standard ejector cycle as a representative example of advanced VCS. To ensure the focus of the study is on the solver's performance, computationally efficient, and accurate component models are considered. Utilizing optimization theory and problem formulation with minimum variables, this study finds for the first time that the non-convex and ill-conditioned behavior of the residual equations causes the simultaneous solvers to be less robust. Non-convexity primarily comes from the enthalpy residual, while the ill-conditioned behavior comes from the pressure residuals and the difference in the order of magnitude of the residuals. A novel method of the failure grid is introduced for a fair comparison of different solvers’ robustness. A few methods to improve the solver’s performance using gradient methods are introduced. The robustness of unconstrained algorithms can be improved by almost four times using scaling factors in the residual equations. However, the improvement in convergence of constrained algorithms is found to be almost twice more than the unconstrained algorithms using the same scaling factors, proving that the constrained algorithms result in a more robust solver. The study also finds that the computational cost is reduced by almost half when using a problem formulation without nested loops. However, this results in a higher number of solver variables for which constrained algorithms are found to be more robust, indicating that robustness remains important in determining the most computationally efficient solver. The accuracy of all the solvers evaluated is found to be comparable. Overall, these findings can help in developing flexible, robust, and computationally efficient simultaneous solvers with a higher number of variables for advanced thermal systems that include both vapor compression systems and thermal power systems. The findings can also be extended to develop parallelized-finite-volume heat exchanger models to reduce their computational cost.

Singly TASE Operators for the Numerical Solution of Stiff Differential Equations by Explicit Runge–Kutta Schemes

In this paper new explicit integrators for numerical solution of stiff evolution equations are proposed. As shown by Bassenne, Fu and Mani in (J Comput Phys 424:109847, 2021), the action on the original vector field of the stiff equations of an appropriate time-accurate and highly-stable explicit (TASE) linear operator, allows us to use explicit Runge–Kutta (RK) schemes with these modified equations so that the resulting algorithm becomes stable for the original stiff equations. Here a new family of TASE operators is considered. The new operators, called Singly TASE, have the advantage over the TASE operators of Bassenne et al. that the action on the vector field depends on the powers of the inverse of only one matrix, which can be computationally more simple, without loosing stability properties. A complete study of the linear stability properties of k–stage, kth–order explicit RK schemes under the action of Singly TASE operators of the same order is carried out for k le 4. For orders two, three and four, particular schemes that are nearly strongly A–stable and therefore suitable for stiff problems are devised. Further, explicit RK schemes with orders three and four that can be implemented with only two storage locations under the action of Singly TASE operators of the same order are discussed. A particular implementation of the classical four–stage fourth–order RK scheme with two Singly TASE operators is presented. A set of numerical experiments has been conducted to demonstrate the performance of the new schemes by comparing with previous RKTASE and other established methods. The main conclusion is that the new integrators provide a very simple solver for stiff systems with good stability properties and avoids the difficulties of using implicit algorithms.