Computers & Mathematics with Applications最新文献

英文中文

On nonlinear magnetic field solvers using local Quasi-Newton updates

IF 2.9 2区数学 Q1 MATHEMATICS, APPLIED

Computers & Mathematics with Applications

Pub Date : 2025-01-30 DOI: 10.1016/j.camwa.2025.01.033

H. Egger , F. Engertsberger , L. Domenig , K. Roppert , M. Kaltenbacher

Fixed-point or Newton-methods are typically employed for the numerical solution of nonlinear systems arising from discretization of nonlinear magnetic field problems. We here discuss an alternative strategy which uses Quasi-Newton updates locally, at every material point, to construct appropriate linearizations of the material behavior during the nonlinear iteration. The resulting scheme shows similar fast convergence as the Newton-method but, like the fixed-point methods, does not require derivative information of the underlying material law. As a consequence, the method can be used for the efficient solution of models with hysteresis which involve nonsmooth material behavior. The implementation of the proposed scheme can be realized in standard finite-element codes in parallel to the fixed-point and the Newton method. A full convergence analysis of all three methods is established proving global mesh-independent convergence. The theoretical results and the performance of the nonlinear iterative schemes are evaluated by computational tests for a typical benchmark problem.

{"title":"On nonlinear magnetic field solvers using local Quasi-Newton updates","authors":"H. Egger , F. Engertsberger , L. Domenig , K. Roppert , M. Kaltenbacher","doi":"10.1016/j.camwa.2025.01.033","DOIUrl":"10.1016/j.camwa.2025.01.033","url":null,"abstract":"<div><div>Fixed-point or Newton-methods are typically employed for the numerical solution of nonlinear systems arising from discretization of nonlinear magnetic field problems. We here discuss an alternative strategy which uses Quasi-Newton updates locally, at every material point, to construct appropriate linearizations of the material behavior during the nonlinear iteration. The resulting scheme shows similar fast convergence as the Newton-method but, like the fixed-point methods, does not require derivative information of the underlying material law. As a consequence, the method can be used for the efficient solution of models with hysteresis which involve nonsmooth material behavior. The implementation of the proposed scheme can be realized in standard finite-element codes in parallel to the fixed-point and the Newton method. A full convergence analysis of all three methods is established proving global mesh-independent convergence. The theoretical results and the performance of the nonlinear iterative schemes are evaluated by computational tests for a typical benchmark problem.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"183 ","pages":"Pages 20-31"},"PeriodicalIF":2.9,"publicationDate":"2025-01-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143102666","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Accelerating simulations of turbulent flows over waves leveraging GPU parallelization

IF 2.9 2区数学 Q1 MATHEMATICS, APPLIED

Computers & Mathematics with Applications

Pub Date : 2025-01-30 DOI: 10.1016/j.camwa.2025.01.031

Anqing Xuan, Ziyan Ren, Lian Shen

We present a highly efficient solver, accelerated by graphics processing units (GPUs), for simulations of turbulent flows over wave surfaces. The solver employs a boundary-fitted curvilinear grid, which is horizontally discretized by a Fourier-based pseudospectral scheme, enabling accurate and efficient resolution of turbulence motions and wave geometry effects across scales. Our GPU implementation incorporates optimizations including kernel fusion for computing derivatives using the fast Fourier transform and a mixed-precision iterative solver for the pressure Poisson equation. A parallel tridiagonal solver is developed to solve the batched systems arising from the iterative Poisson solver on multiple GPUs. Our GPU solver is validated against a canonical problem of turbulence over waves, demonstrating the solver's accuracy. Performance tests indicate substantial speed improvement of up to 80% enabled by the proposed optimizations. Good parallel scalability suggests the solver's capability for large-scale simulations of turbulent flows over waves.

引用次数: 0

Efficient spectral method for the fourth order elliptic equation with a variable coefficient on the unit disc

IF 2.9 2区数学 Q1 MATHEMATICS, APPLIED

Computers & Mathematics with Applications

Pub Date : 2025-01-30 DOI: 10.1016/j.camwa.2025.01.023

Suna Ma

In this paper, an efficient spectral-Galerkin method is proposed to solve the fourth order elliptic equation with a variable coefficient on the unit disc. The efficiency of the method is rest with the use of properly designed orthogonal polynomials as basis functions, which preserve the block-diagonal matrix structure of the discretized system with a constant coefficient and also work well with the general variable coefficient. Further, the three-term recurrence relation for orthogonal polynomials on the unit disc is explored to reduce the computational complexity of assembling the mass matrix. Then optimal error estimates are established. Finally, numerical experiments are carried out to illustrate the effectiveness of the proposed spectral method.

引用次数: 0

A mass and charge conservative fully discrete scheme for a 3D diffuse interface model of the two-phase inductionless MHD flows

IF 2.9 2区数学 Q1 MATHEMATICS, APPLIED

Computers & Mathematics with Applications

Pub Date : 2025-01-28 DOI: 10.1016/j.camwa.2025.01.020

Xiaorong Wang , Xuerui Mao , Shipeng Mao , Xiaoming He

In this paper, we study the phase field model on a three-dimensional bounded domain for a two-phase, incompressible, inductionless magnetohydrodynamic (MHD) system, which is important for many engineering applications. To efficiently and accurately solve this multi-physics nonlinear system, we present a fully discrete scheme that ensures both mass and charge conservation. Making use of the discrete energy law, we demonstrate that the fully discrete scheme satisfies unconditional energy stability. Subsequently, by utilizing the Leray-Schauder principle, we establish the existence of solutions to the discrete scheme. As both mesh size and time step size tend to zero, we prove that the discrete solutions converge to the weak solution of the continuous problem. Finally, several three-dimensional numerical experiments, including the accuracy test, the bubble coalescence, the drop deformation and the Kelvin-Helmholtz (KH) instability, are performed to validate the reliability and efficiency of the proposed numerical scheme.

引用次数: 0

A hybrid reduced-order model for segregated fluid-structure interaction solvers in an ALE approach at high Reynolds number

IF 2.9 2区数学 Q1 MATHEMATICS, APPLIED

Computers & Mathematics with Applications

Pub Date : 2025-01-23 DOI: 10.1016/j.camwa.2025.01.004

Valentin Nkana Ngan , Giovanni Stabile , Andrea Mola , Gianluigi Rozza

This study introduces a first step for constructing a hybrid reduced-order models (ROMs) for segregated fluid-structure interaction in an Arbitrary Lagrangian-Eulerian (ALE) approach at a high Reynolds number using the Finite Volume Method (FVM). The ROM is driven by proper orthogonal decomposition (POD) with hybrid techniques that combines the classical Galerkin projection and two data-driven methods (radial basis networks, and neural networks/ long short term memory). Results demonstrate the ROM's ability to accurately capture the physics of fluid-structure interaction phenomena. This approach is validated through a case study focusing on flow-induced vibration (FIV) of a pitch-plunge airfoil at a high Reynolds number (

R e = 10^{7}

引用次数: 0

Block ω-circulant preconditioners for parabolic equations 屏蔽抛物方程的ω-循环预调节器

IF 2.9 2区数学 Q1 MATHEMATICS, APPLIED

Computers & Mathematics with Applications

Pub Date : 2025-01-22 DOI: 10.1016/j.camwa.2025.01.019

Po Yin Fung, Sean Y. Hon

In this study, a novel class of block ω-circulant preconditioners is developed for the all-at-once linear system that emerges from solving parabolic equations using first and second order discretization schemes for time. We establish a unifying preconditioning framework for ω-circulant preconditioners, extending and modifying the preconditioning approach recently proposed in (Zhang and Xu, 2024 [27]) and integrating some existing results in the literature. The proposed preconditioners leverage fast Fourier transforms for efficient diagonalization, facilitating parallel-in-time execution. Theoretically, these preconditioners ensure that eigenvalue clustering around ±1 is achieved, fostering fast convergence under the minimal residual method. Furthermore, when using the generalized minimal residual method, the effectiveness of these preconditioners is supported by the singular value clustering at unity. Numerical experiments validate the performance of the developed preconditioning strategies.

在本研究中，开发了一类新的块循环预调节器，用于使用一阶和二阶时间离散格式求解抛物方程产生的一次性线性系统。我们建立了ω-循环预调节器的统一预处理框架，扩展和修改了（Zhang and Xu, 2024[27]）中最近提出的预处理方法，并整合了一些文献中的现有结果。所提出的预调节器利用快速傅里叶变换进行有效的对角化，促进并行执行。理论上，这些预条件保证了特征值在±1附近聚类，促进了最小残差法下的快速收敛。此外，当使用广义最小残差法时，这些预条件的有效性得到了单位奇异值聚类的支持。数值实验验证了所提出的预处理策略的有效性。

引用次数: 0

A staggered discontinuous Galerkin method for solving SN transport equation on arbitrary polygonal grids 任意多边形网格上求解SN输运方程的交错不连续伽辽金法

IF 2.9 2区数学 Q1 MATHEMATICS, APPLIED

Computers & Mathematics with Applications

Pub Date : 2025-01-22 DOI: 10.1016/j.camwa.2025.01.018

Deng Wang , Zupeng Jia

This paper proposes a staggered discontinuous Galerkin (SDG) method for solving the 2D

S_{N}

transport equation on arbitrary polygonal mesh. The new method allows rough grids such as highly distorted quadrilateral grids and general polygonal grids. More importantly, it is numerical flux free, different from the standard discontinuous Galerkin (DG) method using upwind flux, and thus gains the advantage of not demanding a sweeping algorithm to determine the computational ordering of all elements. The sweeping process not only requires a significant amount of computation, but also encounters deadlocks due to the presence of cycles in the corresponding directed graph on deformed three-dimensional polyhedral meshes. Additionally, there are challenges with sweeping stability on curved meshes. Our method naturally avoids these problems such that it can be generalized to high-order schemes on curved meshes. Convergence of the new method is analyzed in the linear case, and we have shown that it is optimally convergent for sufficiently smooth transport solution and appropriate total cross section. Numerical results are consistent with the theoretical analysis. The tests also show that our method employing linear elements can maintain second-order accuracy on rough grids mentioned earlier, demonstrating good robustness, and be able to model material interfaces with sharp changes of the angular flux. Moreover, the asymptotic-preserving property can be observed by scaling the cross section parameter in the thick diffusive limit problem. A test employing quadratic elements is also provided, which preliminarily demonstrates the feasibility and effectiveness of our method in higher-order scenarios.

提出了一种求解任意多边形网格上二维SN输运方程的交错不连续伽辽金（SDG）方法。新方法允许粗糙网格，如高度变形的四边形网格和一般多边形网格。更重要的是，它与使用逆风通量的标准不连续伽辽金（DG）方法不同，它是数值通量自由的，因此不需要扫描算法来确定所有元素的计算顺序。扫描过程不仅需要大量的计算量，而且由于在变形的三维多面体网格上相应的有向图中存在循环而导致死锁。此外，在弯曲网格上的扫描稳定性也存在挑战。我们的方法自然地避免了这些问题，因此它可以推广到曲面网格上的高阶格式。分析了新方法在线性情况下的收敛性，并证明了该方法在充分光滑的输运解和适当的总横截面下是最优收敛的。数值结果与理论分析一致。实验还表明，采用线性单元的方法可以在粗糙网格上保持二阶精度，具有良好的鲁棒性，并且可以模拟角通量急剧变化的材料界面。此外，通过缩放厚扩散极限问题的截面参数，可以观察到该问题的渐近保持性质。通过二次元的实验，初步验证了该方法在高阶场景下的可行性和有效性。

{"title":"A staggered discontinuous Galerkin method for solving SN transport equation on arbitrary polygonal grids","authors":"Deng Wang , Zupeng Jia","doi":"10.1016/j.camwa.2025.01.018","DOIUrl":"10.1016/j.camwa.2025.01.018","url":null,"abstract":"<div><div>This paper proposes a staggered discontinuous Galerkin (SDG) method for solving the 2D <span><math><msub><mrow><mi>S</mi></mrow><mrow><mi>N</mi></mrow></msub></math></span> transport equation on arbitrary polygonal mesh. The new method allows rough grids such as highly distorted quadrilateral grids and general polygonal grids. More importantly, it is numerical flux free, different from the standard discontinuous Galerkin (DG) method using upwind flux, and thus gains the advantage of not demanding a sweeping algorithm to determine the computational ordering of all elements. The sweeping process not only requires a significant amount of computation, but also encounters deadlocks due to the presence of cycles in the corresponding directed graph on deformed three-dimensional polyhedral meshes. Additionally, there are challenges with sweeping stability on curved meshes. Our method naturally avoids these problems such that it can be generalized to high-order schemes on curved meshes. Convergence of the new method is analyzed in the linear case, and we have shown that it is optimally convergent for sufficiently smooth transport solution and appropriate total cross section. Numerical results are consistent with the theoretical analysis. The tests also show that our method employing linear elements can maintain second-order accuracy on rough grids mentioned earlier, demonstrating good robustness, and be able to model material interfaces with sharp changes of the angular flux. Moreover, the asymptotic-preserving property can be observed by scaling the cross section parameter in the thick diffusive limit problem. A test employing quadratic elements is also provided, which preliminarily demonstrates the feasibility and effectiveness of our method in higher-order scenarios.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"182 ","pages":"Pages 102-121"},"PeriodicalIF":2.9,"publicationDate":"2025-01-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143020191","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

A handy tool for assessing tetrahedron-based finite-cell methods and for numerical simulations in spheroidal domains 一个方便的工具，用于评估基于四面体的有限单元方法和球面域的数值模拟

IF 2.9 2区数学 Q1 MATHEMATICS, APPLIED

Computers & Mathematics with Applications

Pub Date : 2025-01-22 DOI: 10.1016/j.camwa.2025.01.017

Andrés León Baldelli , Vitoriano Ruas , Marco Antonio Silva Ramos

A straightforward procedure is presented for the generation of finite-cell meshes consisting of tetrahedrons for curved domains, whose boundary can be expressed in spherical coordinates with origin at a suitable location in its interior. Besides the equation of the boundary, the generation of the mesh depends only on an integer parameter, whose value is associated with its degree of refinement. Several examples indicate that the meshes of a given domain form a quasi-uniform family of partitions, as the value of the integer parameter increases. Mesh quality is optimal in the case of a ball but it remains quite correct as the shape of the domain moves away from perfect sphericity, with a gradual but in all natural downgrade. The procedure is a handy tool for an a priori order-checking of a new finite-cell method, as applied to a given type of boundary value problem posed in curved domains. A MATLAB code was developed to implement this tetrahedrization procedure for domains with three symmetry planes.

给出了一种简单的生成由四面体组成的曲面域有限单元网格的方法，曲面域边界可以用球坐标表示，原点在其内部的合适位置。除边界方程外，网格的生成仅依赖于一个整数参数，其值与其细化程度有关。实例表明，随着整型参数值的增大，给定域的网格会形成准一致的分区族。在球的情况下，网格质量是最佳的，但是当区域的形状远离完美的球形时，它仍然是相当正确的，伴随着逐渐但自然的降级。该程序是一个方便的工具，一个新的有限单元方法的先验顺序检查，适用于给定类型的边值问题提出的曲面域。开发了MATLAB代码来实现具有三个对称平面的域的四面体化过程。

引用次数: 0

Simulation of cartesian cut-cell technique for modeling turbulent flow in asymmetric diffusers using various turbulence models 用不同湍流模型模拟非对称扩散器湍流的直角切割槽技术

IF 2.9 2区数学 Q1 MATHEMATICS, APPLIED

Computers & Mathematics with Applications

Pub Date : 2025-01-21 DOI: 10.1016/j.camwa.2025.01.015

A.S. Dawood , A.S. Amer , R.M. Abumandour , W.A. El-Askary

The process of accurately predicting the behavior of the separated turbulent flow requires extraordinary efforts, whether it is choosing the appropriate computational mesh or using the appropriate turbulence model for that. The present study introduces a comparative numerical investigation for predicting the behavior of turbulent-separated flow in asymmetric diffusers. Numerical simulation using a finite volume approach of incompressible Reynolds Averaged Navier Stokes equations (RANS) with three turbulence models (Standard

k - ε

, Chen-kim, and modified Chen-kim) is here performed in a self-developed FORTRAN code. The treatment of asymmetric diffusers poses challenges due to the complex flow behavior and geometry. To address this, a developed cartesian cut-cell technique is employed, which provides compatibility with solid boundaries and efficiently handles complex geometries This developed cut-cell technique is checked to treat its ability to predict complex turbulent flow with the presence of strong pressure gradient for correctness and convergence, as well as testing the proposed turbulence-models performance. So, verifications are performed by comparing the present computational results of asymmetric-diffuser flow characteristics with available experimental and LES data. The proposed models reveal acceptable agreements in most cases, especially the modified Chen-kim model, which shows a great match with the experimental and LES results for all flow characteristics. The standard k-ε model fails to predict the flow-separation well in most comparisons. Extended computational studies are also introduced to investigate the effects of diffuser cant angles (4 to 15°) and area ratio (2.4 to 7) on the diffuser flow behavior using the successfully modified Chen-kim turbulence model. The parametric study reveals that these two factors strongly affect the diffuser performance, where the pressure recovery, skin friction coefficients, and separation bubble size are provided.

无论是选择合适的计算网格还是使用合适的湍流模型，准确预测分离湍流的行为都需要付出巨大的努力。本文介绍了一种预测非对称扩散器中湍流分离流动特性的比较数值研究方法。本文在自行开发的FORTRAN代码中使用有限体积方法对具有三种湍流模型（标准k−ε， Chen-kim和修改的Chen-kim）的不可压缩Reynolds平均Navier Stokes方程（RANS）进行了数值模拟。由于不对称扩散器复杂的流动特性和几何形状，对其处理提出了挑战。为了解决这个问题，采用了一种发达的笛卡尔切割单元技术，它提供了与固体边界的兼容性，并有效地处理复杂的几何形状。这种发展的切割单元技术进行了检查，以处理其预测具有强压力梯度的复杂湍流的正确性和收敛性的能力，以及测试所提出的湍流模型的性能。因此，通过将现有的非对称扩散器流动特性计算结果与现有的实验数据和LES数据进行比较，进行验证。所提出的模型在大多数情况下都显示出可接受的一致性，特别是改进的Chen-kim模型，在所有流动特性上都与实验和LES结果非常吻合。在大多数比较中，标准k-ε模型不能很好地预测流动分离。利用改进的Chen-kim湍流模型，进一步研究了扩散角（4 ~ 15°）和面积比（2.4 ~ 7）对扩散器流动特性的影响。参数化研究表明，压力恢复系数、表面摩擦系数和分离气泡尺寸对扩压器性能有较大影响。

{"title":"Simulation of cartesian cut-cell technique for modeling turbulent flow in asymmetric diffusers using various turbulence models","authors":"A.S. Dawood , A.S. Amer , R.M. Abumandour , W.A. El-Askary","doi":"10.1016/j.camwa.2025.01.015","DOIUrl":"10.1016/j.camwa.2025.01.015","url":null,"abstract":"<div><div>The process of accurately predicting the behavior of the separated turbulent flow requires extraordinary efforts, whether it is choosing the appropriate computational mesh or using the appropriate turbulence model for that. The present study introduces a comparative numerical investigation for predicting the behavior of turbulent-separated flow in asymmetric diffusers. Numerical simulation using a finite volume approach of incompressible Reynolds Averaged Navier Stokes equations (RANS) with three turbulence models (Standard <span><math><mrow><mi>k</mi><mo>−</mo><mrow><mi>ε</mi></mrow></mrow></math></span>, Chen-kim, and modified Chen-kim) is here performed in a self-developed FORTRAN code. The treatment of asymmetric diffusers poses challenges due to the complex flow behavior and geometry. To address this, a developed cartesian cut-cell technique is employed, which provides compatibility with solid boundaries and efficiently handles complex geometries This developed cut-cell technique is checked to treat its ability to predict complex turbulent flow with the presence of strong pressure gradient for correctness and convergence, as well as testing the proposed turbulence-models performance. So, verifications are performed by comparing the present computational results of asymmetric-diffuser flow characteristics with available experimental and LES data. The proposed models reveal acceptable agreements in most cases, especially the modified Chen-kim model, which shows a great match with the experimental and LES results for all flow characteristics. The standard k-ε model fails to predict the flow-separation well in most comparisons. Extended computational studies are also introduced to investigate the effects of diffuser cant angles (4 to 15°) and area ratio (2.4 to 7) on the diffuser flow behavior using the successfully modified Chen-kim turbulence model. The parametric study reveals that these two factors strongly affect the diffuser performance, where the pressure recovery, skin friction coefficients, and separation bubble size are provided.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"182 ","pages":"Pages 84-101"},"PeriodicalIF":2.9,"publicationDate":"2025-01-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143020188","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Analysis of the Picard-Newton finite element iteration for the stationary incompressible inductionless MHD equations 静止不可压缩无感应MHD方程的皮卡德-牛顿有限元迭代分析

IF 2.9 2区数学 Q1 MATHEMATICS, APPLIED

Computers & Mathematics with Applications

Pub Date : 2025-01-16 DOI: 10.1016/j.camwa.2025.01.016

Xiaodi Zhang , Meiying Zhang , Xianghai Zhou

In this paper, we propose and analyze the Picard-Newton finite element iteration for the stationary incompressible inductionless magnetohydrodynamics (MHD) equations. In finite element discretization, the hydrodynamic unknowns are approximated by stable finite element pairs, and the electromagnetic system is discretized by using the face-volume pairs. To solve the nonlinear discretized problem efficiently, our method consists of first applying the Picard iteration and then applying the Newton iteration. The Picard-Newton iteration is proved to be globally stable under the uniqueness condition and quadratically convergent under the stronger uniqueness condition. Thanks to the improved stability property, this solver has a larger convergence basin than the usual Newton iteration. Numerical tests confirm our theoretical analysis and show that the Picard-Newton iteration dramatically excels both the Picard and Newton iterations in several benchmark problems.

本文提出并分析了静止不可压缩无感磁流体动力学（MHD）方程的皮卡德-牛顿有限元迭代。在有限元离散中，流体动力未知量用稳定有限元对逼近，电磁系统用面-体对离散。为了有效地求解非线性离散化问题，首先采用皮卡德迭代法，然后采用牛顿迭代法。证明了皮卡德-牛顿迭代在唯一性条件下是全局稳定的，在强唯一性条件下是二次收敛的。由于改进了算法的稳定性，该算法比一般的牛顿迭代具有更大的收敛盆。数值测试证实了我们的理论分析，并表明皮卡德-牛顿迭代在一些基准问题上显著优于皮卡德和牛顿迭代。

引用次数: 0

首页上一页

下一页尾页

类型

全部化学•材料生命科学医学物理工程技术环境•农林材料科学地球科学法学管理学化学环境科学与生态学计算机科学教育学经济学农林科学人文科学生物学数学物理与天体物理心理学综合性期刊其他工业工程理学历史学农学文学信息工程

数据库

全部 ACS Publications Elsevier ieeexplore Springer The Royal Society of Chemistry Wiley

期刊

Computers & Mathematics with Applications

全部 Acc. Chem. Res. ACS Applied Bio Materials ACS Appl. Electron. Mater. ACS Appl. Energy Mater. ACS Appl. Mater. Interfaces ACS Appl. Nano Mater. ACS Appl. Polym. Mater. ACS BIOMATER-SCI ENG ACS Catal. ACS Cent. Sci. ACS Chem. Biol. ACS Chemical Health & Safety ACS Chem. Neurosci. ACS Comb. Sci. ACS Earth Space Chem. ACS Energy Lett. ACS Infect. Dis. ACS Macro Lett. ACS Mater. Lett. ACS Med. Chem. Lett. ACS Nano ACS Omega ACS Photonics ACS Sens. ACS Sustainable Chem. Eng. ACS Synth. Biol. Anal. Chem. BIOCHEMISTRY-US Bioconjugate Chem. BIOMACROMOLECULES Chem. Res. Toxicol. Chem. Rev. Chem. Mater. CRYST GROWTH DES ENERG FUEL Environ. Sci. Technol. Environ. Sci. Technol. Lett. Eur. J. Inorg. Chem. IND ENG CHEM RES Inorg. Chem. J. Agric. Food. Chem. J. Chem. Eng. Data J. Chem. Educ. J. Chem. Inf. Model. J. Chem. Theory Comput. J. Med. Chem. J. Nat. Prod. J PROTEOME RES J. Am. Chem. Soc. LANGMUIR MACROMOLECULES Mol. Pharmaceutics Nano Lett. Org. Lett. ORG PROCESS RES DEV ORGANOMETALLICS J. Org. Chem. J. Phys. Chem. J. Phys. Chem. A J. Phys. Chem. B J. Phys. Chem. C J. Phys. Chem. Lett. Analyst Anal. Methods Biomater. Sci. Catal. Sci. Technol. Chem. Commun. Chem. Soc. Rev. CHEM EDUC RES PRACT CRYSTENGCOMM Dalton Trans. Energy Environ. Sci. ENVIRON SCI-NANO ENVIRON SCI-PROC IMP ENVIRON SCI-WAT RES Faraday Discuss. Food Funct. Green Chem. Inorg. Chem. Front. Integr. Biol. J. Anal. At. Spectrom. J. Mater. Chem. A J. Mater. Chem. B J. Mater. Chem. C Lab Chip Mater. Chem. Front. Mater. Horiz. MEDCHEMCOMM Metallomics Mol. Biosyst. Mol. Syst. Des. Eng. Nanoscale Nanoscale Horiz. Nat. Prod. Rep. New J. Chem. Org. Biomol. Chem. Org. Chem. Front. PHOTOCH PHOTOBIO SCI PCCP Polym. Chem.

﹀