Sparse Approximations of the Schur Complement for Parallel Algebraic Hybrid Solvers in 3D

In this paper we study the computational performance of variants of an algebraic additive Schwarz preconditioner for the Schur complement for the solution of large sparse linear systems.In earlier works,the local Schur complements were computed exactly using a sparse direct solver.The robustness of the preconditioner comes at the price of this memory and time intensive computation that is the main bottleneck of the approach for tackling huge problems.In this work we investigate the use of sparse approximation of the dense local Schur complements.These approximations are computed using a partial incomplete LU factorization.Such a numerical calculation is the core of the multi-level incomplete factorization such as the one implemented in pARMS. The numerical and computing performance of the new numerical scheme is illustrated on a set of large 3D convection-diffusion problems;preliminary experiments on linear systems arising from structural mechanics are also reported.

THE SCHWARZ CHAOTIC RELAXATION METHOD WITH INEXACT SOLVERS ON THE SUBDOMAINS

In this paper, a S-CR method with inexact solvers on the subdomains is presented, and then its convergence property is proved under very general conditions. This result is important because it guarantees the effectiveness of the Schwarz alternating method when executed on message-passing distributed memory multiprocessor system.

Implementation of a particle-in-cell method for the energy solver in 3D spherical geodynamic modeling

The thermal evolution of the Earth’s interior and its dynamic effects are the focus of Earth sciences.However,the commonly adopted grid-based temperature solver is usually prone to numerical oscillations,especially in the presence of sharp thermal gradients,such as when modeling subducting slabs and rising plumes.This phenomenon prohibits the correct representation of thermal evolution and may cause incorrect implications of geodynamic processes.After examining several approaches for removing these numerical oscillations,we show that the Lagrangian method provides an ideal way to solve this problem.In this study,we propose a particle-in-cell method as a strategy for improving the solution to the energy equation and demonstrate its effectiveness in both one-dimensional and three-dimensional thermal problems,as well as in a global spherical simulation with data assimilation.We have implemented this method in the open-source finite-element code CitcomS,which features a spherical coordinate system,distributed memory parallel computing,and data assimilation algorithms.

ChemNODE: A neural ordinary differential equations framework for efficient chemical kinetic solvers

Solving for detailed chemical kinetics remains one of the major bottlenecks for computational fluid dynamics simulations of reacting flows using a finite-rate-chemistry approach.This has motivated the use of neural networks to predict stiff chemical source terms as functions of the thermochemical state of the combustion system.However,due to the nonlinearities and multi-scale nature of combustion,the predicted solution often diverges from the true solution when these machine learning models are coupled with a computational fluid dynamics solver.This is because these approaches minimize the error during training without guaranteeing successful integration with ordinary differential equation solvers.In the present work,a novel neural ordinary differential equations approach to modeling chemical kinetics,termed as ChemNODE,is developed.In this machine learning framework,the chemical source terms predicted by the neural networks are integrated during training,and by computing the required derivatives,the neural network weights are adjusted accordingly to minimize the difference between the predicted and ground-truth solution.A proof-of-concept study is performed with ChemNODE for homogeneous autoignition of hydrogen-air mixture over a range of composition and thermodynamic conditions.It is shown that ChemNODE accurately captures the chemical kinetic behavior and reproduces the results obtained using the detailed kinetic mechanism at a fraction of the computational cost.

浊度补偿紫外光谱法测定市政污水厂进水COD

为解决市政污水厂进水预警问题,采用紫外光谱法对某市政污水厂进水样本进行了跟踪测定,拟合出COD-A模型以及浊度-A模型。实验排除了共价化合物、其他紫外区弱吸收的化合物以及浊度对检测结果的影响。实验结果表明,在波长254 nm处,具有稳定组成的样品其COD和吸光度A存在良好线性关系,皮尔逊相关系数r=0.941 475;利用SOLVER拟合出模型最小期望值∑θ^(2)=0.011 679,只要将254 nm及546 nm处的吸光度值带入浊度补偿模型就可以快速计算出COD值。

Spectral Elliptic Solvers in a Finite Cylinder

New direct spectral solvers for the 3D Helmholtz equation in a finite cylindrical region are presented.A purely variational(no collocation)formulation of the problem is adopted,based on Fourier series expansion of the angular dependence and Legendre polynomials for the axial dependence.A new Jacobi basis is proposed for the radial direction overcoming the main disadvantages of previously developed bases for the Dirichlet problem.Nonhomogeneous Dirichlet boundary conditions are enforced by a discrete lifting and the vector problem is solved by means of a classical uncoupling technique.In the considered formulation,boundary conditions on the axis of the cylindrical domain are never mentioned,by construction.The solution algorithms for the scalar equations are based on double diagonalization along the radial and axial directions.The spectral accuracy of the proposed algorithms is verified by numerical tests.

Parallel Iterative FEM Solver with Initial Guess for Frequency Domain Electromagnetic Analysis

The finite element method is a key player in computational electromag-netics for designing RF(Radio Frequency)components such as waveguides.The frequency-domain analysis is fundamental to identify the characteristics of the components.For the conventional frequency-domain electromagnetic analysis using FEM(Finite Element Method),the system matrix is complex-numbered as well as indefinite.The iterative solvers can be faster than the direct solver when the solver convergence is guaranteed and done in a few steps.However,such complex-numbered and indefinite systems are hard to exploit the merit of the iterative solver.It is also hard to benefit from matrix factorization techniques due to varying system matrix parts according to frequency.Overall,it is hard to adopt conventional iterative solvers even though the system matrix is sparse.A new parallel iterative FEM solver for frequency domain analysis is implemented for inhomogeneous waveguide structures in this paper.In this implementation,the previous solution of the iterative solver of Matlab(Matrix Laboratory)employ-ing the preconditioner is used for the initial guess for the next step’s solution process.The overlapped parallel stage using Matlab’s Parallel Computing Toolbox is also proposed to alleviate the cold starting,which ruins the convergence of early steps in each parallel stage.Numerical experiments based on waveguide structures have demonstrated the accuracy and efficiency of the proposed scheme.

Energy-Efficient UAVs Coverage Path Planning Approach

Unmanned aerial vehicles(UAVs),commonly known as drones,have drawn significant consideration thanks to their agility,mobility,and flexibility features.They play a crucial role in modern reconnaissance,inspection,intelligence,and surveillance missions.Coverage path planning(CPP)which is one of the crucial aspects that determines an intelligent system’s quality seeks an optimal trajectory to fully cover the region of interest(ROI).However,the flight time of the UAV is limited due to a battery limitation and may not cover the whole region,especially in large region.Therefore,energy consumption is one of the most challenging issues that need to be optimized.In this paper,we propose an energy-efficient coverage path planning algorithm to solve the CPP problem.The objective is to generate a collision-free coverage path that minimizes the overall energy consumption and guarantees covering the whole region.To do so,the flight path is optimized and the number of turns is reduced to minimize the energy consumption.The proposed approach first decomposes the ROI into a set of cells depending on a UAV camera footprint.Then,the coverage path planning problem is formulated,where the exact solution is determined using the CPLEX solver.For small-scale problems,the CPLEX shows a better solution in a reasonable time.However,the CPLEX solver fails to generate the solution within a reasonable time for large-scale problems.Thus,to solve the model for large-scale problems,simulated annealing forCPP is developed.The results show that heuristic approaches yield a better solution for large-scale problems within amuch shorter execution time than the CPLEX solver.Finally,we compare the simulated annealing against the greedy algorithm.The results show that simulated annealing outperforms the greedy algorithm in generating better solution quality.

High-precision nonisothermal transient wellbore drift flow model suitable for the full flow pattern domain and full dip range

A reliable multiphase flow simulator is an important tool to improve wellbore integrity and production decision-making.To develop a multiphase flow model with high adaptability and high accuracy,we first build a multiphase flow database with 3561 groups of data and developed a drift closure relationship with stable continuity and high adaptability.Second,a high-order numerical scheme with strong fault capture ability is constructed by effectively combining MUSCL technology,van Albada slope limiter and AUSMV numerical scheme.Finally,the energy equation is coupled into the AUSMV numerical scheme of the drift flow model in the form of finite difference.A transient non-isothermal wellbore multiphase flow model with wide applicability is formed by integrating the three technologies,and the effects of various factors on the calculation accuracy are studied.The accuracy of the simulator is verified by comparing the measurement results with the blowout experiment of a full-scale experimental well.

Solving Poisson equation with slowing-down equilibrium distribution for global gyrokinetic simulation

Fusion-born alpha particles in burning plasmas are usually regarded as have a slowing-down distribution,which differs significantly from the Maxwellian distribution of thermal particles in velocity space.A generalized multi-point average method has been developed for gyrokinetic Poisson equation with slowing-down equilibrium distribution using optimization in Fourier space.Its accuracy is verified in both long and short wavelength limits.The influence of changing equilibrium distribution from Maxwellian to slowing-down on gyrokinetic Poisson equation is analyzed to illustrate the significance of the new method.The effect of critical speed in the slowingdown distribution on the field solver is also presented.This method forms an important basis for global gyrokinetic simulation of low-frequency drift Alfvénic turbulence in burning plasmas.

Solving Geometry Problems via Feature Learning and Contrastive Learning of Multimodal Data

This paper presents an end-to-end deep learning method to solve geometry problems via feature learning and contrastive learning of multimodal data.A key challenge in solving geometry problems using deep learning is to automatically adapt to the task of understanding single-modal and multimodal problems.Existing methods either focus on single-modal ormultimodal problems,and they cannot fit each other.A general geometry problem solver shouldobviouslybe able toprocess variousmodalproblems at the same time.Inthispaper,a shared feature-learning model of multimodal data is adopted to learn the unified feature representation of text and image,which can solve the heterogeneity issue between multimodal geometry problems.A contrastive learning model of multimodal data enhances the semantic relevance betweenmultimodal features and maps them into a unified semantic space,which can effectively adapt to both single-modal and multimodal downstream tasks.Based on the feature extraction and fusion of multimodal data,a proposed geometry problem solver uses relation extraction,theorem reasoning,and problem solving to present solutions in a readable way.Experimental results show the effectiveness of the method.

Gas kinetic flux solver based finite volume weighted essentially non-oscillatory scheme for inviscid compressible flows

A high-order gas kinetic flux solver(GKFS)is presented for simulating inviscid compressible flows.The weighted essentially non-oscillatory(WENO)scheme on a uniform mesh in the finite volume formulation is combined with the circular function-based GKFS(C-GKFS)to capture more details of the flow fields with fewer grids.Different from most of the current GKFSs,which are constructed based on the Maxwellian distribution function or its equivalent form,the C-GKFS simplifies the Maxwellian distribution function into the circular function,which ensures that the Euler or Navier-Stokes equations can be recovered correctly.This improves the efficiency of the GKFS and reduces its complexity to facilitate the practical application of engineering.Several benchmark cases are simulated,and good agreement can be obtained in comparison with the references,which demonstrates that the high-order C-GKFS can achieve the desired accuracy.

On the Numerical Solution of Diffraction Problem by Random Spheres Using Electric Field Integral Equation

The aim of this paper is to solve the two-dimensional acoustic scattering problems by random sphere using Electric field integral equation. Some approximations for the two-dimensional case are derived. These various approximations are next numerically validated in the case of high-frequency.

Shared Memory Semi-Implicit Solver for Hydrodynamical Instability Processes

The Advection-Diffusion Reaction (ADR) equation appears in many problems in nature. This constitutes a general model that is useful in various scenarios, from porous media to atmospheric processes. Particularly, it is used at the interface between two fluids where different types of instabilities due to surface mobility may appear. Together with the ADR equation, the Darcy-Brinkman model describes the phenomena known as fingering that appear in different contexts. The study of this type of system gains in complexity when the number of chemical species dissolved in both fluids increases. With more solutes, the increasing complexity of this phenomenon generally requires much computational power. To face the need for more computational resources, we build a solver tool based on an Alternating Direction Implicit (ADI) scheme that can be run in Central Processing Unit (CPU) and Graphic Processing Unit (GPU) architectures on any notebook. The implementation is done using the MATLAB platform to compare both versions. It is shown that using the GPU version strongly saves both resources and calculation times.

Optimization Model: Resource Distribution for Risk Factors of Type 2 Diabetes Prevention

Type 2 Diabetes, a lifestyle disease, can be prevented/delayed by adopting a healthy lifestyle. Awareness of the same amongst the citizens can be one of the best ways to initiate a decline in the positive census of the disease. We use this paper to illustrate an optimization model where the budget can be distributed based on the census data of the risk factors involved. It uses a non-linear programming model and can easily be modified into a linear one. The alternative options and constraints too, are mentioned in the paper. The results show that the mid-western states need more share of the allocation based on risk factors. The model distributes the percentage of the budget allocated to different states based on a fixed risk factor constraint.

Linear System Solutions of the Navier-Stokes Equations with Application to Flow over a Backward-Facing Step

Many applications in fluid mechanics require the numerical solution of sequences of linear systems typically issued from finite element discretization of the Navier-Stokes equations. The resulting matrices then exhibit a saddle point structure. To achieve this task, a Newton-based root-finding algorithm is usually employed which in turn necessitates to solve a saddle point system at every Newton iteration. The involved linear systems being large scale and ill-conditioned, effective linear solvers must be implemented. Here, we develop and test several methods for solving the saddle point systems, considering in particular the LU factorization, as direct approach, and the preconditioned generalized minimal residual (ΡGMRES) solver, an iterative approach. We apply the various solvers within the root-finding algorithm for Flow over backward facing step systems. The particularity of Flow over backward facing step system is an interesting case for studying the performance and solution strategy of a turbulence model. In this case, the flow is subjected to a sudden increase of cross-sectional area, resulting in a separation of flow starting at the point of expansion, making the system of differential equations particularly stiff. We assess the performance of the direct and iterative solvers in terms of computational time, numbers of Newton iterations and time steps.

基于SMSolver的铝合金附着式升降防护平台竖向主框架结构设计校验

附着式升降防护平台是现代建筑施工,特别是高层建筑施工中的重要装备。竖向主框架是附着式升降防护平台中承受和传递平台的竖向和水平荷载的主要结构,结构构件多并且复杂。本文针对一种铝合金附着式升降防护平台的竖向主框架结构进行研究,采用SM Solver软件静力学方法,计算出竖向主框架各构件的内力,再进行构件材料强度校验。

基于约束满足的卫星地面站资源优化分配问题研究

卫星地面站资源优化分配问题是在给定的时间内,对卫星需要执行的任务分配地面站及执行时间,以便卫星能最大限度地完成任务。该文对该问题建立了CSP模型,并采用ILOGSolver对该模型进行求解。文中最后给出了一个应用实例,并比较了几种不同搜索算法和搜索策略的执行效率。

航空公司机组重调度问题建模和算法研究

不正常航班机组重调度问题是航空公司航班重调度决策研究的重要环节,针对机组重调度问题建模和算法进行研究。采用约束规划建模,基于ILOG Solver优化组件提供的框架,将模拟退火算法嵌入到ILOG Solver框架中对模型进行求解,并给出邻域生成搜索策略和移动的选择策略,使邻域搜索效率获得改善。案例计算结果显示,新的求解方法在CPU时间消耗和目标函数优化两个方面比直接采用ILOG Solver优化组件获得较大改善。

一种基于l_p模约束的FOCUSS迭代EEG源定位新方法

如何有效地从头表记录电位中准确定位脑电源的真实活动位置是神经认知脑功能研究中的一个关键问题.本文在FOCUSS算法迭代基础上,从脑神经活动的局部稀疏性出发,提出了一种新的脑功能成像方法.在该算法中,通过把稀疏性的lp模约束加入到修改的FOCUSS算法的迭代过程中,使算法可以有效地收敛于真实的稀疏源活动位置.利用该方法对随机系统、三层球模型及真实头模型确定的稀疏欠定系统进行了求解模拟实验,结果显示了该方法在求解欠定系统及EEG源定位时具有良好的稳健性.