In this work, AlN films were grown using gallium (Ga) as surfactant on 4° off-axis 4H-SiC substrates via microwave plasma chemical vapor deposition (MPCVD). We have found that AlN growth rate can be greatly impro...In this work, AlN films were grown using gallium (Ga) as surfactant on 4° off-axis 4H-SiC substrates via microwave plasma chemical vapor deposition (MPCVD). We have found that AlN growth rate can be greatly improved due to the catalytic effect of trimethyl-gallium (TMGa), but AlN crystal structure and composition are not affected. When the proportion of TMGa in gas phase was low, crystal quality of AlN can be improved and three-dimensional growth mode of AlN was enhanced with the increase of Ga source. When the proportion of TMGa in gas phase was high, two-dimensional growth mode of AlN was presented, with the increase of Ga source results in the deterioration of AlN crystal quality. Finally, employing a two-step growth approach, involving the initial growth of Ga-free AlN nucleation layer followed by Ga-assisted AlN growth, high quality of AlN film with flat surface was obtained and the full width at half maximum (FWHM) values of 415 nm AlN (002) and (102) planes were 465 and 597 arcsec.展开更多
Growth and electronic properties of ultrathin Ga films on Cd(0001) are investigated by low-temperature scanning tunneling microscopy(STM) and density functional theory(DFT) calculations. It is found that Ga films exhi...Growth and electronic properties of ultrathin Ga films on Cd(0001) are investigated by low-temperature scanning tunneling microscopy(STM) and density functional theory(DFT) calculations. It is found that Ga films exhibit the epitaxial growth with the pseudomorphic 1×1 lattice. The Ga islands deposited at 100 K show a ramified shape due to the suppressed edge diffusion and corner crossing. Furthermore, the majority of Ga islands reveal flat tops and a preferred height of three atomic layers, indicating the electronic growth at low temperature. Annealing to room temperature leads to not only the growth mode transition from electronic growth to conventional Stranski–Krastanov growth, but also the shape transition from ramified islands to smooth compact islands. Scanning tunneling spectroscopy(STS) measurements reveal that the Ga monolayer exhibits metallic behavior. DFT calculations indicate that all the interfacial Ga atoms occupy the energetically favorable hcp-hollow sites of the substrate. The charge density difference analysis demonstrates that the charge transfer from the Cd substrate to the Ga atoms is negligible, and there is weak interaction between Ga atoms and the Cd substrate. These results shall shed important light on fabrication of ultrathin Ga films on metal substrates with novel physical properties.展开更多
The soil chemistry of gallium, indium, and thallium is not well defined, particularly with emerging evidence that these elements have toxic properties and may influence food safety. The purpose of this investigation w...The soil chemistry of gallium, indium, and thallium is not well defined, particularly with emerging evidence that these elements have toxic properties and may influence food safety. The purpose of this investigation was to estimate the soil concentrations of gallium, indium, and thallium and determine if these elements have a soil chemistry like aluminum and therefore demonstrate significant concentration correlations with aluminum. Twenty-seven soil series were selected, and the elemental concentrations were determined using aqua regia digestion with analytical determination performed using inductively coupled plasma emission-mass spectroscopy. The concentrations of gallium, indium, and thallium generally compared with the known literature. Aluminum-gallium and aluminum-thallium exhibited significant concentration correlations across the soil horizons of the sampled soils. Aluminum, gallium, and thallium did demonstrate concentration increases in soil horizons having illuviation of phyllosilicates, implying these phyllosilicates have adsorption and isomorphic substitution behaviors involving these elements.展开更多
Fixed-point fast sweeping methods are a class of explicit iterative methods developed in the literature to efficiently solve steady-state solutions of hyperbolic partial differential equations(PDEs).As other types of ...Fixed-point fast sweeping methods are a class of explicit iterative methods developed in the literature to efficiently solve steady-state solutions of hyperbolic partial differential equations(PDEs).As other types of fast sweeping schemes,fixed-point fast sweeping methods use the Gauss-Seidel iterations and alternating sweeping strategy to cover characteristics of hyperbolic PDEs in a certain direction simultaneously in each sweeping order.The resulting iterative schemes have a fast convergence rate to steady-state solutions.Moreover,an advantage of fixed-point fast sweeping methods over other types of fast sweeping methods is that they are explicit and do not involve the inverse operation of any nonlinear local system.Hence,they are robust and flexible,and have been combined with high-order accurate weighted essentially non-oscillatory(WENO)schemes to solve various hyperbolic PDEs in the literature.For multidimensional nonlinear problems,high-order fixed-point fast sweeping WENO methods still require quite a large amount of computational costs.In this technical note,we apply sparse-grid techniques,an effective approximation tool for multidimensional problems,to fixed-point fast sweeping WENO methods for reducing their computational costs.Here,we focus on fixed-point fast sweeping WENO schemes with third-order accuracy(Zhang et al.2006[41]),for solving Eikonal equations,an important class of static Hamilton-Jacobi(H-J)equations.Numerical experiments on solving multidimensional Eikonal equations and a more general static H-J equation are performed to show that the sparse-grid computations of the fixed-point fast sweeping WENO schemes achieve large savings of CPU times on refined meshes,and at the same time maintain comparable accuracy and resolution with those on corresponding regular single grids.展开更多
The anisotropic properties and applications ofβ-gallium oxide(β-Ga_(2)O_(3))are comprehensively reviewed.All the anisotropic properties are essentially resulted from the anisotropic crystal structure.The process flo...The anisotropic properties and applications ofβ-gallium oxide(β-Ga_(2)O_(3))are comprehensively reviewed.All the anisotropic properties are essentially resulted from the anisotropic crystal structure.The process flow of how to exfoliate nanoflakes from bulk material is introduced.Anisotropic optical properties,including optical bandgap,Raman and photolumines-cence characters are comprehensively reviewed.Three measurement configurations of angle-resolved polarized Raman spec-tra(ARPRS)are reviewed,with Raman intensity formulas calculated with Raman tensor elements.The method to obtain the Raman tensor elements of phonon modes through experimental fitting is also introduced.In addition,the anisotropy in elec-tron mobility and affinity are discussed.The applications,especially polarization photodetectors,based onβ-Ga_(2)O_(3)were summa-rized comprehensively.Three kinds of polarization detection mechanisms based on material dichroism,1D morphology and metal-grids are discussed in-depth.This review paper provides a framework for anisotropic optical and electric properties ofβ-Ga_(2)O_(3),as well as the applications based on these characters,and is expected to lead to a wider discussion on this topic.展开更多
Asynchronous federated learning(AsynFL)can effectivelymitigate the impact of heterogeneity of edge nodes on joint training while satisfying participant user privacy protection and data security.However,the frequent ex...Asynchronous federated learning(AsynFL)can effectivelymitigate the impact of heterogeneity of edge nodes on joint training while satisfying participant user privacy protection and data security.However,the frequent exchange of massive data can lead to excess communication overhead between edge and central nodes regardless of whether the federated learning(FL)algorithm uses synchronous or asynchronous aggregation.Therefore,there is an urgent need for a method that can simultaneously take into account device heterogeneity and edge node energy consumption reduction.This paper proposes a novel Fixed-point Asynchronous Federated Learning(FixedAsynFL)algorithm,which could mitigate the resource consumption caused by frequent data communication while alleviating the effect of device heterogeneity.FixedAsynFL uses fixed-point quantization to compress the local and global models in AsynFL.In order to balance energy consumption and learning accuracy,this paper proposed a quantization scale selection mechanism.This paper examines the mathematical relationship between the quantization scale and energy consumption of the computation/communication process in the FixedAsynFL.Based on considering the upper bound of quantization noise,this paper optimizes the quantization scale by minimizing communication and computation consumption.This paper performs pertinent experiments on the MNIST dataset with several edge nodes of different computing efficiency.The results show that the FixedAsynFL algorithm with an 8-bit quantization can significantly reduce the communication data size by 81.3%and save the computation energy in the training phase by 74.9%without significant loss of accuracy.According to the experimental results,we can see that the proposed AsynFixedFL algorithm can effectively solve the problem of device heterogeneity and energy consumption limitation of edge nodes.展开更多
In the era of accelerated development in artificial intelligence as well as explosive growth of information and data throughput,underlying hardware devices that can integrate perception and memory while simultaneously...In the era of accelerated development in artificial intelligence as well as explosive growth of information and data throughput,underlying hardware devices that can integrate perception and memory while simultaneously offering the bene-fits of low power consumption and high transmission rates are particularly valuable.Neuromorphic devices inspired by the human brain are considered to be one of the most promising successors to the efficient in-sensory process.In this paper,a homojunction-based multi-functional optoelectronic synapse(MFOS)is proposed and testified.It enables a series of basic electri-cal synaptic plasticity,including paired-pulse facilitation/depression(PPF/PPD)and long-term promotion/depression(LTP/LTD).In addition,the synaptic behaviors induced by electrical signals could be instead achieved through optical signals,where its sen-sitivity to optical frequency allows the MFOS to simulate high-pass filtering applications in situ and the perception capability integrated into memory endows it with the information acquisition and processing functions as a visual system.Meanwhile,the MFOS exhibits its performances of associative learning and logic gates following the illumination with two different wave-lengths.As a result,the proposed MFOS offers a solution for the realization of intelligent visual system and bionic electronic eye,and will provide more diverse application scenarios for future neuromorphic computing.展开更多
Discrete Tomography(DT)is a technology that uses image projection to reconstruct images.Its reconstruction problem,especially the binary image(0–1matrix)has attracted strong attention.In this study,a fixed point iter...Discrete Tomography(DT)is a technology that uses image projection to reconstruct images.Its reconstruction problem,especially the binary image(0–1matrix)has attracted strong attention.In this study,a fixed point iterative method of integer programming based on intelligent optimization is proposed to optimize the reconstructedmodel.The solution process can be divided into two procedures.First,the DT problem is reformulated into a polyhedron judgment problembased on lattice basis reduction.Second,the fixed-point iterativemethod of Dang and Ye is used to judge whether an integer point exists in the polyhedron of the previous program.All the programs involved in this study are written in MATLAB.The final experimental data show that this method is obviously better than the branch and bound method in terms of computational efficiency,especially in the case of high dimension.The branch and bound method requires more branch operations and takes a long time.It also needs to store a large number of leaf node boundaries and the corresponding consumptionmatrix,which occupies a largememory space.展开更多
Liquid metal gallium has been widely used in numerous fields, from nuclear engineering, catalysts, and energy storage to electronics owing to its remarkable thermal and electrical properties along with low viscosity a...Liquid metal gallium has been widely used in numerous fields, from nuclear engineering, catalysts, and energy storage to electronics owing to its remarkable thermal and electrical properties along with low viscosity and nontoxicity. Compared with high-temperature liquid metals, room-temperature liquid metals, such as gallium(Ga), are emerging as promising alternatives for fabricating advanced energy storage devices, such as phase change materials, by harvesting the advantageous properties of their liquid state maintained without external energy input. However, the thermal and electrical properties of liquid metals at the phase transition are rather poorly studied, limiting their practical applications. In this study, we reported on the physical properties of the solid–liquid phase transition of Ga using a custom-designed, solid–liquid electrical and thermal measurement system. We observed that the electrical conductivity of Ga progressively decreases with an increase in temperature. However, the Seebeck coefficient of Ga increases from 0.2 to 2.1 μV/K, and thermal conductivity from 7.6 to 33 W/(K·m). These electrical and thermal properties of Ga at solid–liquid phase transition would be useful for practical applications.展开更多
Fixed-point fast sweeping WENO methods are a class of efficient high-order numerical methods to solve steady-state solutions of hyperbolic partial differential equations(PDEs).The Gauss-Seidel iterations and alternati...Fixed-point fast sweeping WENO methods are a class of efficient high-order numerical methods to solve steady-state solutions of hyperbolic partial differential equations(PDEs).The Gauss-Seidel iterations and alternating sweeping strategy are used to cover characteristics of hyperbolic PDEs in each sweeping order to achieve fast convergence rate to steady-state solutions.A nice property of fixed-point fast sweeping WENO methods which distinguishes them from other fast sweeping methods is that they are explicit and do not require inverse operation of nonlinear local systems.Hence,they are easy to be applied to a general hyperbolic system.To deal with the difficulties associated with numerical boundary treatment when high-order finite difference methods on a Cartesian mesh are used to solve hyperbolic PDEs on complex domains,inverse Lax-Wendroff(ILW)procedures were developed as a very effective approach in the literature.In this paper,we combine a fifthorder fixed-point fast sweeping WENO method with an ILW procedure to solve steadystate solution of hyperbolic conservation laws on complex computing regions.Numerical experiments are performed to test the method in solving various problems including the cases with the physical boundary not aligned with the grids.Numerical results show highorder accuracy and good performance of the method.Furthermore,the method is compared with the popular third-order total variation diminishing Runge-Kutta(TVD-RK3)time-marching method for steady-state computations.Numerical examples show that for most of examples,the fixed-point fast sweeping method saves more than half CPU time costs than TVD-RK3 to converge to steady-state solutions.展开更多
基金supported by the Key Research and Development Program of Jilin Provincial Department of Science and Technology (No. 20210201031GX)Innovation capacity building project of Jilin Province (No. 2023C031-2)The Key Research and Development Program of Jiangsu Province (No. BE2022057-1)。
文摘In this work, AlN films were grown using gallium (Ga) as surfactant on 4° off-axis 4H-SiC substrates via microwave plasma chemical vapor deposition (MPCVD). We have found that AlN growth rate can be greatly improved due to the catalytic effect of trimethyl-gallium (TMGa), but AlN crystal structure and composition are not affected. When the proportion of TMGa in gas phase was low, crystal quality of AlN can be improved and three-dimensional growth mode of AlN was enhanced with the increase of Ga source. When the proportion of TMGa in gas phase was high, two-dimensional growth mode of AlN was presented, with the increase of Ga source results in the deterioration of AlN crystal quality. Finally, employing a two-step growth approach, involving the initial growth of Ga-free AlN nucleation layer followed by Ga-assisted AlN growth, high quality of AlN film with flat surface was obtained and the full width at half maximum (FWHM) values of 415 nm AlN (002) and (102) planes were 465 and 597 arcsec.
基金Project supported by the National Natural Science Foundation of China (Grant Nos.11874304 and 11574253)。
文摘Growth and electronic properties of ultrathin Ga films on Cd(0001) are investigated by low-temperature scanning tunneling microscopy(STM) and density functional theory(DFT) calculations. It is found that Ga films exhibit the epitaxial growth with the pseudomorphic 1×1 lattice. The Ga islands deposited at 100 K show a ramified shape due to the suppressed edge diffusion and corner crossing. Furthermore, the majority of Ga islands reveal flat tops and a preferred height of three atomic layers, indicating the electronic growth at low temperature. Annealing to room temperature leads to not only the growth mode transition from electronic growth to conventional Stranski–Krastanov growth, but also the shape transition from ramified islands to smooth compact islands. Scanning tunneling spectroscopy(STS) measurements reveal that the Ga monolayer exhibits metallic behavior. DFT calculations indicate that all the interfacial Ga atoms occupy the energetically favorable hcp-hollow sites of the substrate. The charge density difference analysis demonstrates that the charge transfer from the Cd substrate to the Ga atoms is negligible, and there is weak interaction between Ga atoms and the Cd substrate. These results shall shed important light on fabrication of ultrathin Ga films on metal substrates with novel physical properties.
文摘The soil chemistry of gallium, indium, and thallium is not well defined, particularly with emerging evidence that these elements have toxic properties and may influence food safety. The purpose of this investigation was to estimate the soil concentrations of gallium, indium, and thallium and determine if these elements have a soil chemistry like aluminum and therefore demonstrate significant concentration correlations with aluminum. Twenty-seven soil series were selected, and the elemental concentrations were determined using aqua regia digestion with analytical determination performed using inductively coupled plasma emission-mass spectroscopy. The concentrations of gallium, indium, and thallium generally compared with the known literature. Aluminum-gallium and aluminum-thallium exhibited significant concentration correlations across the soil horizons of the sampled soils. Aluminum, gallium, and thallium did demonstrate concentration increases in soil horizons having illuviation of phyllosilicates, implying these phyllosilicates have adsorption and isomorphic substitution behaviors involving these elements.
文摘Fixed-point fast sweeping methods are a class of explicit iterative methods developed in the literature to efficiently solve steady-state solutions of hyperbolic partial differential equations(PDEs).As other types of fast sweeping schemes,fixed-point fast sweeping methods use the Gauss-Seidel iterations and alternating sweeping strategy to cover characteristics of hyperbolic PDEs in a certain direction simultaneously in each sweeping order.The resulting iterative schemes have a fast convergence rate to steady-state solutions.Moreover,an advantage of fixed-point fast sweeping methods over other types of fast sweeping methods is that they are explicit and do not involve the inverse operation of any nonlinear local system.Hence,they are robust and flexible,and have been combined with high-order accurate weighted essentially non-oscillatory(WENO)schemes to solve various hyperbolic PDEs in the literature.For multidimensional nonlinear problems,high-order fixed-point fast sweeping WENO methods still require quite a large amount of computational costs.In this technical note,we apply sparse-grid techniques,an effective approximation tool for multidimensional problems,to fixed-point fast sweeping WENO methods for reducing their computational costs.Here,we focus on fixed-point fast sweeping WENO schemes with third-order accuracy(Zhang et al.2006[41]),for solving Eikonal equations,an important class of static Hamilton-Jacobi(H-J)equations.Numerical experiments on solving multidimensional Eikonal equations and a more general static H-J equation are performed to show that the sparse-grid computations of the fixed-point fast sweeping WENO schemes achieve large savings of CPU times on refined meshes,and at the same time maintain comparable accuracy and resolution with those on corresponding regular single grids.
基金supported by the National Natural Science Foundation of China(Grant No.61505109)Youth Innovative Talents Attracting and Cultivating Plan of Colleges and Universities in Shandong Province(No.21)+1 种基金Youth Innovation Team of colleges and universities in Shandong Province(Grant No.2022KJ223)Shandong Provincial Natural Science Foundation(Grant No.ZR2021QF020).
文摘The anisotropic properties and applications ofβ-gallium oxide(β-Ga_(2)O_(3))are comprehensively reviewed.All the anisotropic properties are essentially resulted from the anisotropic crystal structure.The process flow of how to exfoliate nanoflakes from bulk material is introduced.Anisotropic optical properties,including optical bandgap,Raman and photolumines-cence characters are comprehensively reviewed.Three measurement configurations of angle-resolved polarized Raman spec-tra(ARPRS)are reviewed,with Raman intensity formulas calculated with Raman tensor elements.The method to obtain the Raman tensor elements of phonon modes through experimental fitting is also introduced.In addition,the anisotropy in elec-tron mobility and affinity are discussed.The applications,especially polarization photodetectors,based onβ-Ga_(2)O_(3)were summa-rized comprehensively.Three kinds of polarization detection mechanisms based on material dichroism,1D morphology and metal-grids are discussed in-depth.This review paper provides a framework for anisotropic optical and electric properties ofβ-Ga_(2)O_(3),as well as the applications based on these characters,and is expected to lead to a wider discussion on this topic.
基金This work was funded by National Key R&D Program of China(Grant No.2020YFB0906003).
文摘Asynchronous federated learning(AsynFL)can effectivelymitigate the impact of heterogeneity of edge nodes on joint training while satisfying participant user privacy protection and data security.However,the frequent exchange of massive data can lead to excess communication overhead between edge and central nodes regardless of whether the federated learning(FL)algorithm uses synchronous or asynchronous aggregation.Therefore,there is an urgent need for a method that can simultaneously take into account device heterogeneity and edge node energy consumption reduction.This paper proposes a novel Fixed-point Asynchronous Federated Learning(FixedAsynFL)algorithm,which could mitigate the resource consumption caused by frequent data communication while alleviating the effect of device heterogeneity.FixedAsynFL uses fixed-point quantization to compress the local and global models in AsynFL.In order to balance energy consumption and learning accuracy,this paper proposed a quantization scale selection mechanism.This paper examines the mathematical relationship between the quantization scale and energy consumption of the computation/communication process in the FixedAsynFL.Based on considering the upper bound of quantization noise,this paper optimizes the quantization scale by minimizing communication and computation consumption.This paper performs pertinent experiments on the MNIST dataset with several edge nodes of different computing efficiency.The results show that the FixedAsynFL algorithm with an 8-bit quantization can significantly reduce the communication data size by 81.3%and save the computation energy in the training phase by 74.9%without significant loss of accuracy.According to the experimental results,we can see that the proposed AsynFixedFL algorithm can effectively solve the problem of device heterogeneity and energy consumption limitation of edge nodes.
基金supported by the National Natural Science Foundation of China under Grant(62174068,61625404).
文摘In the era of accelerated development in artificial intelligence as well as explosive growth of information and data throughput,underlying hardware devices that can integrate perception and memory while simultaneously offering the bene-fits of low power consumption and high transmission rates are particularly valuable.Neuromorphic devices inspired by the human brain are considered to be one of the most promising successors to the efficient in-sensory process.In this paper,a homojunction-based multi-functional optoelectronic synapse(MFOS)is proposed and testified.It enables a series of basic electri-cal synaptic plasticity,including paired-pulse facilitation/depression(PPF/PPD)and long-term promotion/depression(LTP/LTD).In addition,the synaptic behaviors induced by electrical signals could be instead achieved through optical signals,where its sen-sitivity to optical frequency allows the MFOS to simulate high-pass filtering applications in situ and the perception capability integrated into memory endows it with the information acquisition and processing functions as a visual system.Meanwhile,the MFOS exhibits its performances of associative learning and logic gates following the illumination with two different wave-lengths.As a result,the proposed MFOS offers a solution for the realization of intelligent visual system and bionic electronic eye,and will provide more diverse application scenarios for future neuromorphic computing.
基金funded by the NSFC under Grant Nos.61803279,71471091,62003231 and 51874205in part by the Qing Lan Project of Jiangsu,in part by the China Postdoctoral Science Foundation under Grant Nos.2020M671596 and 2021M692369+2 种基金in part by the Suzhou Science and Technology Development Plan Project(Key Industry Technology Innovation)under Grant No.SYG202114in part by the Natural Science Foundation of Jiangsu Province under Grant No.BK20200989Postdoctoral Research Funding Program of Jiangsu Province.
文摘Discrete Tomography(DT)is a technology that uses image projection to reconstruct images.Its reconstruction problem,especially the binary image(0–1matrix)has attracted strong attention.In this study,a fixed point iterative method of integer programming based on intelligent optimization is proposed to optimize the reconstructedmodel.The solution process can be divided into two procedures.First,the DT problem is reformulated into a polyhedron judgment problembased on lattice basis reduction.Second,the fixed-point iterativemethod of Dang and Ye is used to judge whether an integer point exists in the polyhedron of the previous program.All the programs involved in this study are written in MATLAB.The final experimental data show that this method is obviously better than the branch and bound method in terms of computational efficiency,especially in the case of high dimension.The branch and bound method requires more branch operations and takes a long time.It also needs to store a large number of leaf node boundaries and the corresponding consumptionmatrix,which occupies a largememory space.
基金the support provided by A*STAR and the Industry Alignment Fund through the Pharos “Hybrid thermoelectric materials for ambient applications” Program (No.1527200021)。
文摘Liquid metal gallium has been widely used in numerous fields, from nuclear engineering, catalysts, and energy storage to electronics owing to its remarkable thermal and electrical properties along with low viscosity and nontoxicity. Compared with high-temperature liquid metals, room-temperature liquid metals, such as gallium(Ga), are emerging as promising alternatives for fabricating advanced energy storage devices, such as phase change materials, by harvesting the advantageous properties of their liquid state maintained without external energy input. However, the thermal and electrical properties of liquid metals at the phase transition are rather poorly studied, limiting their practical applications. In this study, we reported on the physical properties of the solid–liquid phase transition of Ga using a custom-designed, solid–liquid electrical and thermal measurement system. We observed that the electrical conductivity of Ga progressively decreases with an increase in temperature. However, the Seebeck coefficient of Ga increases from 0.2 to 2.1 μV/K, and thermal conductivity from 7.6 to 33 W/(K·m). These electrical and thermal properties of Ga at solid–liquid phase transition would be useful for practical applications.
基金Research was supported by the NSFC Grant 11872210Research was supported by the NSFC Grant 11872210 and Grant No.MCMS-I-0120G01+1 种基金Research supported in part by the AFOSR Grant FA9550-20-1-0055NSF Grant DMS-2010107.
文摘Fixed-point fast sweeping WENO methods are a class of efficient high-order numerical methods to solve steady-state solutions of hyperbolic partial differential equations(PDEs).The Gauss-Seidel iterations and alternating sweeping strategy are used to cover characteristics of hyperbolic PDEs in each sweeping order to achieve fast convergence rate to steady-state solutions.A nice property of fixed-point fast sweeping WENO methods which distinguishes them from other fast sweeping methods is that they are explicit and do not require inverse operation of nonlinear local systems.Hence,they are easy to be applied to a general hyperbolic system.To deal with the difficulties associated with numerical boundary treatment when high-order finite difference methods on a Cartesian mesh are used to solve hyperbolic PDEs on complex domains,inverse Lax-Wendroff(ILW)procedures were developed as a very effective approach in the literature.In this paper,we combine a fifthorder fixed-point fast sweeping WENO method with an ILW procedure to solve steadystate solution of hyperbolic conservation laws on complex computing regions.Numerical experiments are performed to test the method in solving various problems including the cases with the physical boundary not aligned with the grids.Numerical results show highorder accuracy and good performance of the method.Furthermore,the method is compared with the popular third-order total variation diminishing Runge-Kutta(TVD-RK3)time-marching method for steady-state computations.Numerical examples show that for most of examples,the fixed-point fast sweeping method saves more than half CPU time costs than TVD-RK3 to converge to steady-state solutions.
基金financially supported by the National Key Research and Development Project of China (Nos. 2021YFC2902802, 2021YFC2902805, 2021YFC2902602, 2021YFC2902604)the Natural Science Foundation of Guangdong Province,China (No. 2023A1515030145)Guangdong Academy of Science Special Funds,China (Nos. 2020GDASYL-0104027, 2022GDASZH-2022010104, 2021GDASYL-20210302004)。