For the sake of a more accurate shell boundary and calculation of radiation heat transfer in the Directional Solidification(DS) process, a radiation heat transfer model based on the Finite Element Method(FEM)is develo...For the sake of a more accurate shell boundary and calculation of radiation heat transfer in the Directional Solidification(DS) process, a radiation heat transfer model based on the Finite Element Method(FEM)is developed in this study. Key technologies, such as distinguishing boundaries automatically, local matrix and lumped heat capacity matrix, are also stated. In order to analyze the effect of withdrawing rate on DS process,the solidification processes of a complex superalloy turbine blade in the High Rate Solidification(HRS) process with different withdrawing rates are simulated; and by comparing the simulation results, it is found that the most suitable withdrawing rate is determined to be 5.0 mm·min^(-1). Finally, the accuracy and reliability of the radiation heat transfer model are verified, because of the accordance of simulation results with practical process.展开更多
In designing a horizontal directional drilling (HDD) pipeline project, designers face the challenge of determining the regions of maximum and minimum stresses on pipelines, ensuring the stability of the bore-hole from...In designing a horizontal directional drilling (HDD) pipeline project, designers face the challenge of determining the regions of maximum and minimum stresses on pipelines, ensuring the stability of the bore-hole from collapse and minimizing the stresses induced on the pipeline due to the bore-profile. This study analyses the stress induced on an HDD pipeline system using the ANSYS Version 18, mechanical APDL finite element (FE) software. The pipeline used as the case study was a gas transmission pipeline installed in south-west Nigeria. A macro-file for ANSYS Version 18, mechanical APDL used to model the pipeline was developed. The results showed that the maximum and minimum stresses induced on the HDD pipeline were at the top and bottom of the pipe, respectively;while the stresses on the sides were uniform (≈888 kg/cm2) all through the pipeline, irrespective of element number. The maximum stress occurred at the curvature point with the highest entry angle (10°), resulting in a maximum deflection at this point. The model stress validation performed by comparing results with theoretical solutions, both with respect to radius of curvature and internal pressure, showed percentage difference (errors) less than 10%. The cross sectional area validation showed a percentage difference of 0.059%.展开更多
An analysis of a 3 dB lumped-element directional coupler （LEDC） based on arbitrary terminal impedance is described numerically. To solve the conflicted requirement for broad bandwidth and small size in LEDC, a new s...An analysis of a 3 dB lumped-element directional coupler （LEDC） based on arbitrary terminal impedance is described numerically. To solve the conflicted requirement for broad bandwidth and small size in LEDC, a new structure of coupler is introduced, which can significantly improve bandwidth and whose size is only 3 cm×4 cm on the conditions of the frequency domain of 410 MHz to 490 MHz. The measure results are in good agreement with simulations despite the unexpected resistor loss.展开更多
In this article, a direct stress approach based on finite element analysis to determine the stress intensity factor is improved. Firstly, by comparing the rigorous solution against the asymptotic solution for a proble...In this article, a direct stress approach based on finite element analysis to determine the stress intensity factor is improved. Firstly, by comparing the rigorous solution against the asymptotic solution for a problem of an infinite plate embedded a central crack, we found that the stresses in a restrictive interval near the crack tip given by the rigorous solution can be used to determine the stress intensity factor, which is nearly equal to the stress intensity factor given by the asymptotic solution. Secondly, the crack problem is solved numerically by the finite element method. Depending on the modeling capability of the software, we designed an adaptive mesh model to simulate the stress singularity. Thus, the stress result in an appropriate interval near the crack tip is fairly approximated to the rigorous solution of the corresponding crack problem. Therefore, the stress intensity factor may be calculated from the stress distribution in the appropriate interval, with a high accuracy.展开更多
Beta flecks are one of the most common defects occur in someα+βandβtitanium alloys.In this study,formation of beta flecks in Ti-17 alloy was investigated by directional solidification experiments.Samples were direc...Beta flecks are one of the most common defects occur in someα+βandβtitanium alloys.In this study,formation of beta flecks in Ti-17 alloy was investigated by directional solidification experiments.Samples were directionally solidified under a constant temperature gradient of 2×10^4 K/m and a wide range of withdrawal rates(R)from 3 mm/h to 150 mm/h.We find that macrostructure of the directionally solidified Ti-17 samples can be characterized by"four zones and two lines"after the heat treatment.Profile of the solid-liquid interface transits from planar to cellular to dendritic shape with solidification rate increasing from 3 mm/h to 150 mm/h.The critical rates for planar to cellular(Rc1)transition and cellular to dendritic(Rc2)transition can be well predicted based on the traditional solidification theory.Dark and light contrast areas in macrostructure are directly related to elemental segregation.Dark contrast areas are rich of Cr,Zr but lean of Mo,while no apparent segregation is found in light contrast areas and the mean level of Cr,Zr is lower and Mo is higher in this area than that in dark contrast areas.We conclude thatβ-flecks in Ti-17 titanium alloy are induced by segregation of alloying elements with k<1 and their shape and size are determined by solidification conditions.Based on the findings of the present article and other literatures,three types ofβ-flecks are proposed and their formation mechanisms are discussed.展开更多
The mechanical properties of outwash deposits which are taken as unconsolidated geo-materials with the characteristics of non-uniformity, heterogeneity and multiphase have attracted much attention in engineering. Acco...The mechanical properties of outwash deposits which are taken as unconsolidated geo-materials with the characteristics of non-uniformity, heterogeneity and multiphase have attracted much attention in engineering. According to the results of laboratory direct shear test on the remolded samples, the soil particle parameters of numerical model based on in-situ particle size cumulative curves and 3D granular discrete element method were determined. Then, numerical experiments on different lithology, stone content and gradation composition were conducted. The results show that it is not a flat surface but a shear band that yields in the sample. The curve of particle velocity vs distance from the designed shear surface of test model that is taken as a datum plane in the vertical section of sample shows in "S" shape. The shear disturbance area is about twice the maximum diameter of stone blocks. The greater the stiffness of stone is, the rougher the shear surface is. The shear strength of outwash deposits is largely controlled by lithology and stone content, and the bite force between stone blocks is the root reason of larger friction angle. It is also shown that strain hardening and low shear dilatancy occur under high confining pressure as well as possibility of shear shrinkage. But it is easy to behave shear dilatation and strain softening under low confining pressure. The relationship between particle frictional coefficient and stone content presents an approximately quadratic parabola increase. The strain energy first increases and then drops with the increase of frictional energy. The cohesion increases with soil stiffness increasing but decreases with stone stiffness increasing. Numerical results are consistent with the laboratory test results of remolded samples, which indicate that this method can be a beneficial supplement to determine the parameters of engineering deposit bodies.展开更多
In coalmines of China, horizontal directional drilling （HDD） is an increasingly popular method for underground in-seam gas drainage. Numerical simulation, especially finite element analysis, is often used as an effe...In coalmines of China, horizontal directional drilling （HDD） is an increasingly popular method for underground in-seam gas drainage. Numerical simulation, especially finite element analysis, is often used as an effective method to improve HDD operation. These improvements focus on rock-breaking efficiency, directional precision, stability of the borehole wall, and reliability of the drill equipment. On the basis of underground drilling characteristics, typical numerical simulation exam- ples in drilling techniques and equipment are summarized and analyzed. In the end, the future development trends of numerical simulation in underground in-seam drilling are proposed.展开更多
To predict hot tearing susceptibility(HTS)during solidification and improve the quality of Al alloy castings,constitutive equations for AA6111 alloys were developed using a direct finite element(FE)method.A hot tearin...To predict hot tearing susceptibility(HTS)during solidification and improve the quality of Al alloy castings,constitutive equations for AA6111 alloys were developed using a direct finite element(FE)method.A hot tearing model was established for direct chill(DC)casting of industrial AA6111 alloys via coupling FE model and hot tearing criterion.By applying this model to real manufacture processes,the effects of casting speed,bottom cooling,secondary cooling,and geometric variations on the HTS were revealed.The results show that the HTS of the billet increases as the speed and billet radius increase,while it reduces as the interfacial heat transfer coefficient at the bottom or secondary water-cooling rate increases.This model shows the capabilities of incorporating maximum pore fraction in simulating hot tearing initiation,which will have a significant impact on optimizing casting conditions and chemistry for minimizing HTS and thus controlling the casting quality.展开更多
The strategies that minimize the overall solution time of multiple linear systems in 3D finite element method (FEM) modeling of direct current (DC) resistivity were discussed. A global stiff matrix is assembled and st...The strategies that minimize the overall solution time of multiple linear systems in 3D finite element method (FEM) modeling of direct current (DC) resistivity were discussed. A global stiff matrix is assembled and stored in two parts separately. One part is associated with the volume integral and the other is associated with the subsurface boundary integral. The equivalent multiple linear systems with closer right-hand sides than the original systems were constructed. A recycling Krylov subspace technique was employed to solve the multiple linear systems. The solution of the seed system was used as an initial guess for the subsequent systems. The results of two numerical experiments show that the improved algorithm reduces the iterations and CPU time by almost 50%, compared with the classical preconditioned conjugate gradient method.展开更多
This paper presents alternating direction finite volume element methods for three-dimensional parabolic partial differential equations and gives four computational schemes, one is analogous to Douglas finite differenc...This paper presents alternating direction finite volume element methods for three-dimensional parabolic partial differential equations and gives four computational schemes, one is analogous to Douglas finite difference scheme with second-order splitting error, the other two schemes have third-order splitting error, and the last one is an extended LOD scheme. The L2 norm and H1 semi-norm error estimates are obtained for the first scheme and second one, respectively. Finally, two numerical examples are provided to illustrate the efficiency and accuracy of the methods.展开更多
A new alternating direction (AD) finite element (FE) scheme for 3-dimensional nonlinear parabolic equation and parabolic integro-differential equation is studied. By using AD,the 3-dimensional problem is reduced to a ...A new alternating direction (AD) finite element (FE) scheme for 3-dimensional nonlinear parabolic equation and parabolic integro-differential equation is studied. By using AD,the 3-dimensional problem is reduced to a family of single space variable problems, calculation work is simplified; by using FE, high accuracy is kept; by using various techniques for priori estimate for differential equations such as inductive hypothesis reasoning, the difficulty arising from the nonlinearity is treated. For both FE and ADFE schemes, the convergence properties are rigorously demonstrated, the optimal H1- and L2-norm space estimates and the O((△t)2) estimate for time variable are obtained.展开更多
This paper shows that the alternating direction method can be used to solve the structured inverse quadratic eigenvalue problem with symmetry, positive semi-definiteness and sparsity requirements. The results of numer...This paper shows that the alternating direction method can be used to solve the structured inverse quadratic eigenvalue problem with symmetry, positive semi-definiteness and sparsity requirements. The results of numerical examples show that the proposed method works well.展开更多
In this paper, we study the mixed element method for Sobolev equations. A time-discretization procedure is presented and analysed and the optimal order error estimates are derived.For convenience in practical computat...In this paper, we study the mixed element method for Sobolev equations. A time-discretization procedure is presented and analysed and the optimal order error estimates are derived.For convenience in practical computation, an alternating-direction iterative scheme of the mixed fi-nite element method is formulated and its stability and converbence are proved for the linear prob-lem. A numerical example is provided at the end of this paper.展开更多
A three-dimensional finite element thermal model in direct metal laser sintering(DMLS) including the effect of powder-to-solid transition were established to predict sintering zone, which benefited the determination o...A three-dimensional finite element thermal model in direct metal laser sintering(DMLS) including the effect of powder-to-solid transition were established to predict sintering zone, which benefited the determination of suitable process parameters in DMLS. The nonlinear transient model of the metals thermal conductivity for powder-to-solid transition was developed. The model uses solid thermal properties of material in liquid-phase zone, transitional ones in sintering or sintered zone and powder ones in unsintered zones of powder bed to predict, respectively. Sintering zone boundary was estimated by maximum temperature history profile. Experiments were carried out using multi-component Cu-based metal powder. Compared experimental and predicted results, the mean error of sintering depth and width are 7.8% and 14.4%, respectively, which confirms the accuracy of the FEM prediction.展开更多
The luminescent phosphor powder in the fluorescent lamp constitutes 2%of the lamp’s weight.It can be mentioned that fluorescent wastes are a crucial raw material to produce rare earth oxides.In the present study,micr...The luminescent phosphor powder in the fluorescent lamp constitutes 2%of the lamp’s weight.It can be mentioned that fluorescent wastes are a crucial raw material to produce rare earth oxides.In the present study,microwave leaching process was conducted to dissolve rare earth elements yttrium(Y),europium(Eu),and remaining rare earth elements(REEs)present in the phosphor powder of the fluorescent lamp.and the yields were compared.In the microwave leaching process,the effects of the temperature(80-160℃),acid type(hydrochloric acid(HCl),nitric acid(HNO_(3)),sulphuric acid(H_(2)SO_(4))),acid concentration(0.5-6 mol/L),solid to liquid ratio(0.1:10-0.5:10)and reaction time(5-90 min)parameters on leaching efficiencies of varying rare earth elements and calcium were investigated.The highest yield was obtained in the direct microwave leaching of fluorescent waste with the experimental conditions of 6 mol/L HCl,160℃,0.1:10 solid-to-liquid ratio(S:L),and 90 min.Activation energy calculations were made,and kinetic models of the reactions were obtained,and it is observed that Y and Eu dissolution is diffusion-controlled,on the other hand,lanthanum(La),cerium(Ce),and terbium(Tb)were examined to be chemical reaction controlled.Moreover,calcium(Ca)and gadolinium(Gd)seem coherent with the mixed model.Concurrently,mathematical models of all experimental studies are created with the response surface Box-Behnken method and the correlation coefficients of all the models are over 90%.展开更多
Helmert’s second method of condensation is an effective method for terrain reduction in the geoid and quasi-geoid determinations. Condensing the masses outside the geoid to a surface layer on the geoid produces sever...Helmert’s second method of condensation is an effective method for terrain reduction in the geoid and quasi-geoid determinations. Condensing the masses outside the geoid to a surface layer on the geoid produces several forms of topographic effects: direct effect on gravity, secondary indirect effect on gravity and indirect effects on the (quasi-) geoid, respectively. To strike a balance between computation accuracy and numerical efficiency, the global integration region of topographic effects is usually divided into near zone and far zone. We focus on the computation of near-zone topographic effects, which are functions of actual topographic masses and condensed masses. Since there have already been mature formulas for gravitational attraction and potential of actual topographic masses using rectangular prism model, we put forward surface element model for condensed masses. Afterwards, the formulas for near-zone direct and indirect effects are obtained easily by combining the rectangular prism model and surface element model. To overcome the planar approximation errors involved with the new formulas for near-zone topographic effects, the Earth’s curvature can be taken into account. It is recommended to apply the formulas based on the rectangular prism and surface element considering the Earth’s curvature to calculate near-zone topographic effects for high-accuracy demand to determine geoid and quasi-geoid.展开更多
Petroleum science has made remarkable progress in organic geochcmistry and in the research into the theories of petroleum origin, its transport and accumulation. In estimating the oil-gas resources of a basin, the kno...Petroleum science has made remarkable progress in organic geochcmistry and in the research into the theories of petroleum origin, its transport and accumulation. In estimating the oil-gas resources of a basin, the knowledge of its evolutionary history and especially the numerical computation of fluid flow and the history of its changes under heat is vital. The mathematical model can be described as a coupled system of nonlinear partial differentical equations with initial-boundary value problems. This thesis, from actual conditions such as the effect of fluid compressibility and the three-dimensional characteristic of large-scale science-engineering computation, we put forward a kind of characteristic finite element alternating-direction schemes and obtain optimal order estimates in L^2 norm for the error in the approximate assumption.展开更多
Based on the concept of the constitutive relation error along with the residuals of both the origin and the dual problems, a goal-oriented error estimation method with extended degrees of freedom is developed. It lead...Based on the concept of the constitutive relation error along with the residuals of both the origin and the dual problems, a goal-oriented error estimation method with extended degrees of freedom is developed. It leads to the high quality locM error bounds in the problem of the direct-solution steady-state dynamic analysis with a frequency-domain finite element, which involves the enrichments with plural variable basis functions. The solution of the steady-state dynamic procedure calculates the harmonic response directly in terms of the physical degrees of freedom in the model, which uses the mass, damping, and stiffness matrices of the system. A three-dimensional finite element example is carried out to illustrate the computational procedures.展开更多
This paper is concerned with some nonlinear reaction - diffusion models. To solve this kind of models, the modified Laplace finite element scheme and the alternating direction finite element scheme are established for...This paper is concerned with some nonlinear reaction - diffusion models. To solve this kind of models, the modified Laplace finite element scheme and the alternating direction finite element scheme are established for the system of patrical differential equations. Besides, the finite difference method is utilized for the ordinary differential equation in the models. Moreover, by the theory and technique of prior estimates for the differential equations, the convergence analyses and the optimal L2- norm error estimates are demonstrated.展开更多
基金financially supported by the Program for New Century Excellent Talents in University(No.NCET-13-0229,NCET-09-0396)the National Science & Technology Key Projects of Numerical Control(No.2012ZX04010-031,2012ZX0412-011)the National High Technology Research and Development Program("863"Program)of China(No.2013031003)
文摘For the sake of a more accurate shell boundary and calculation of radiation heat transfer in the Directional Solidification(DS) process, a radiation heat transfer model based on the Finite Element Method(FEM)is developed in this study. Key technologies, such as distinguishing boundaries automatically, local matrix and lumped heat capacity matrix, are also stated. In order to analyze the effect of withdrawing rate on DS process,the solidification processes of a complex superalloy turbine blade in the High Rate Solidification(HRS) process with different withdrawing rates are simulated; and by comparing the simulation results, it is found that the most suitable withdrawing rate is determined to be 5.0 mm·min^(-1). Finally, the accuracy and reliability of the radiation heat transfer model are verified, because of the accordance of simulation results with practical process.
文摘In designing a horizontal directional drilling (HDD) pipeline project, designers face the challenge of determining the regions of maximum and minimum stresses on pipelines, ensuring the stability of the bore-hole from collapse and minimizing the stresses induced on the pipeline due to the bore-profile. This study analyses the stress induced on an HDD pipeline system using the ANSYS Version 18, mechanical APDL finite element (FE) software. The pipeline used as the case study was a gas transmission pipeline installed in south-west Nigeria. A macro-file for ANSYS Version 18, mechanical APDL used to model the pipeline was developed. The results showed that the maximum and minimum stresses induced on the HDD pipeline were at the top and bottom of the pipe, respectively;while the stresses on the sides were uniform (≈888 kg/cm2) all through the pipeline, irrespective of element number. The maximum stress occurred at the curvature point with the highest entry angle (10°), resulting in a maximum deflection at this point. The model stress validation performed by comparing results with theoretical solutions, both with respect to radius of curvature and internal pressure, showed percentage difference (errors) less than 10%. The cross sectional area validation showed a percentage difference of 0.059%.
文摘An analysis of a 3 dB lumped-element directional coupler （LEDC） based on arbitrary terminal impedance is described numerically. To solve the conflicted requirement for broad bandwidth and small size in LEDC, a new structure of coupler is introduced, which can significantly improve bandwidth and whose size is only 3 cm×4 cm on the conditions of the frequency domain of 410 MHz to 490 MHz. The measure results are in good agreement with simulations despite the unexpected resistor loss.
基金financial support of the National Natural Science Foundation of China (Grant 11572226)
文摘In this article, a direct stress approach based on finite element analysis to determine the stress intensity factor is improved. Firstly, by comparing the rigorous solution against the asymptotic solution for a problem of an infinite plate embedded a central crack, we found that the stresses in a restrictive interval near the crack tip given by the rigorous solution can be used to determine the stress intensity factor, which is nearly equal to the stress intensity factor given by the asymptotic solution. Secondly, the crack problem is solved numerically by the finite element method. Depending on the modeling capability of the software, we designed an adaptive mesh model to simulate the stress singularity. Thus, the stress result in an appropriate interval near the crack tip is fairly approximated to the rigorous solution of the corresponding crack problem. Therefore, the stress intensity factor may be calculated from the stress distribution in the appropriate interval, with a high accuracy.
文摘Beta flecks are one of the most common defects occur in someα+βandβtitanium alloys.In this study,formation of beta flecks in Ti-17 alloy was investigated by directional solidification experiments.Samples were directionally solidified under a constant temperature gradient of 2×10^4 K/m and a wide range of withdrawal rates(R)from 3 mm/h to 150 mm/h.We find that macrostructure of the directionally solidified Ti-17 samples can be characterized by"four zones and two lines"after the heat treatment.Profile of the solid-liquid interface transits from planar to cellular to dendritic shape with solidification rate increasing from 3 mm/h to 150 mm/h.The critical rates for planar to cellular(Rc1)transition and cellular to dendritic(Rc2)transition can be well predicted based on the traditional solidification theory.Dark and light contrast areas in macrostructure are directly related to elemental segregation.Dark contrast areas are rich of Cr,Zr but lean of Mo,while no apparent segregation is found in light contrast areas and the mean level of Cr,Zr is lower and Mo is higher in this area than that in dark contrast areas.We conclude thatβ-flecks in Ti-17 titanium alloy are induced by segregation of alloying elements with k<1 and their shape and size are determined by solidification conditions.Based on the findings of the present article and other literatures,three types ofβ-flecks are proposed and their formation mechanisms are discussed.
基金Project(2011CB013504) supported by the National Basic Research Program of ChinaProjects(50911130366, 11172090) supported by the National Natural Science Foundation of ChinaProject supported by Central University Basic Research Special Fund, China
文摘The mechanical properties of outwash deposits which are taken as unconsolidated geo-materials with the characteristics of non-uniformity, heterogeneity and multiphase have attracted much attention in engineering. According to the results of laboratory direct shear test on the remolded samples, the soil particle parameters of numerical model based on in-situ particle size cumulative curves and 3D granular discrete element method were determined. Then, numerical experiments on different lithology, stone content and gradation composition were conducted. The results show that it is not a flat surface but a shear band that yields in the sample. The curve of particle velocity vs distance from the designed shear surface of test model that is taken as a datum plane in the vertical section of sample shows in "S" shape. The shear disturbance area is about twice the maximum diameter of stone blocks. The greater the stiffness of stone is, the rougher the shear surface is. The shear strength of outwash deposits is largely controlled by lithology and stone content, and the bite force between stone blocks is the root reason of larger friction angle. It is also shown that strain hardening and low shear dilatancy occur under high confining pressure as well as possibility of shear shrinkage. But it is easy to behave shear dilatation and strain softening under low confining pressure. The relationship between particle frictional coefficient and stone content presents an approximately quadratic parabola increase. The strain energy first increases and then drops with the increase of frictional energy. The cohesion increases with soil stiffness increasing but decreases with stone stiffness increasing. Numerical results are consistent with the laboratory test results of remolded samples, which indicate that this method can be a beneficial supplement to determine the parameters of engineering deposit bodies.
基金Supported by the National Natural Science Foundation of China （50805010） the Natural Science Foundation of Shaanxi Province （2011JM70 17）
文摘In coalmines of China, horizontal directional drilling （HDD） is an increasingly popular method for underground in-seam gas drainage. Numerical simulation, especially finite element analysis, is often used as an effective method to improve HDD operation. These improvements focus on rock-breaking efficiency, directional precision, stability of the borehole wall, and reliability of the drill equipment. On the basis of underground drilling characteristics, typical numerical simulation exam- ples in drilling techniques and equipment are summarized and analyzed. In the end, the future development trends of numerical simulation in underground in-seam drilling are proposed.
文摘To predict hot tearing susceptibility(HTS)during solidification and improve the quality of Al alloy castings,constitutive equations for AA6111 alloys were developed using a direct finite element(FE)method.A hot tearing model was established for direct chill(DC)casting of industrial AA6111 alloys via coupling FE model and hot tearing criterion.By applying this model to real manufacture processes,the effects of casting speed,bottom cooling,secondary cooling,and geometric variations on the HTS were revealed.The results show that the HTS of the billet increases as the speed and billet radius increase,while it reduces as the interfacial heat transfer coefficient at the bottom or secondary water-cooling rate increases.This model shows the capabilities of incorporating maximum pore fraction in simulating hot tearing initiation,which will have a significant impact on optimizing casting conditions and chemistry for minimizing HTS and thus controlling the casting quality.
基金Projects(40974077,41164004)supported by the National Natural Science Foundation of ChinaProject(2007AA06Z134)supported by the National High Technology Research and Development Program of China+2 种基金Projects(2011GXNSFA018003,0832263)supported by the Natural Science Foundation of Guangxi Province,ChinaProject supported by Program for Excellent Talents in Guangxi Higher Education Institution,ChinaProject supported by the Foundation of Guilin University of Technology,China
文摘The strategies that minimize the overall solution time of multiple linear systems in 3D finite element method (FEM) modeling of direct current (DC) resistivity were discussed. A global stiff matrix is assembled and stored in two parts separately. One part is associated with the volume integral and the other is associated with the subsurface boundary integral. The equivalent multiple linear systems with closer right-hand sides than the original systems were constructed. A recycling Krylov subspace technique was employed to solve the multiple linear systems. The solution of the seed system was used as an initial guess for the subsequent systems. The results of two numerical experiments show that the improved algorithm reduces the iterations and CPU time by almost 50%, compared with the classical preconditioned conjugate gradient method.
文摘This paper presents alternating direction finite volume element methods for three-dimensional parabolic partial differential equations and gives four computational schemes, one is analogous to Douglas finite difference scheme with second-order splitting error, the other two schemes have third-order splitting error, and the last one is an extended LOD scheme. The L2 norm and H1 semi-norm error estimates are obtained for the first scheme and second one, respectively. Finally, two numerical examples are provided to illustrate the efficiency and accuracy of the methods.
基金The project is supported by China National Key Program for Developing Basic Science G1999032801 and the National Natural Science Foundation of China (No. 19932010).
文摘A new alternating direction (AD) finite element (FE) scheme for 3-dimensional nonlinear parabolic equation and parabolic integro-differential equation is studied. By using AD,the 3-dimensional problem is reduced to a family of single space variable problems, calculation work is simplified; by using FE, high accuracy is kept; by using various techniques for priori estimate for differential equations such as inductive hypothesis reasoning, the difficulty arising from the nonlinearity is treated. For both FE and ADFE schemes, the convergence properties are rigorously demonstrated, the optimal H1- and L2-norm space estimates and the O((△t)2) estimate for time variable are obtained.
基金Supported by Youth Teacher Education and Research Funds of Fujian(Grant No.JAT170911).
文摘This paper shows that the alternating direction method can be used to solve the structured inverse quadratic eigenvalue problem with symmetry, positive semi-definiteness and sparsity requirements. The results of numerical examples show that the proposed method works well.
基金the National Natural Science Foundation of China and China State Key Project for Basic Researches
文摘In this paper, we study the mixed element method for Sobolev equations. A time-discretization procedure is presented and analysed and the optimal order error estimates are derived.For convenience in practical computation, an alternating-direction iterative scheme of the mixed fi-nite element method is formulated and its stability and converbence are proved for the linear prob-lem. A numerical example is provided at the end of this paper.
文摘A three-dimensional finite element thermal model in direct metal laser sintering(DMLS) including the effect of powder-to-solid transition were established to predict sintering zone, which benefited the determination of suitable process parameters in DMLS. The nonlinear transient model of the metals thermal conductivity for powder-to-solid transition was developed. The model uses solid thermal properties of material in liquid-phase zone, transitional ones in sintering or sintered zone and powder ones in unsintered zones of powder bed to predict, respectively. Sintering zone boundary was estimated by maximum temperature history profile. Experiments were carried out using multi-component Cu-based metal powder. Compared experimental and predicted results, the mean error of sintering depth and width are 7.8% and 14.4%, respectively, which confirms the accuracy of the FEM prediction.
基金BAP project FBA-2021-4691 for their financial support。
文摘The luminescent phosphor powder in the fluorescent lamp constitutes 2%of the lamp’s weight.It can be mentioned that fluorescent wastes are a crucial raw material to produce rare earth oxides.In the present study,microwave leaching process was conducted to dissolve rare earth elements yttrium(Y),europium(Eu),and remaining rare earth elements(REEs)present in the phosphor powder of the fluorescent lamp.and the yields were compared.In the microwave leaching process,the effects of the temperature(80-160℃),acid type(hydrochloric acid(HCl),nitric acid(HNO_(3)),sulphuric acid(H_(2)SO_(4))),acid concentration(0.5-6 mol/L),solid to liquid ratio(0.1:10-0.5:10)and reaction time(5-90 min)parameters on leaching efficiencies of varying rare earth elements and calcium were investigated.The highest yield was obtained in the direct microwave leaching of fluorescent waste with the experimental conditions of 6 mol/L HCl,160℃,0.1:10 solid-to-liquid ratio(S:L),and 90 min.Activation energy calculations were made,and kinetic models of the reactions were obtained,and it is observed that Y and Eu dissolution is diffusion-controlled,on the other hand,lanthanum(La),cerium(Ce),and terbium(Tb)were examined to be chemical reaction controlled.Moreover,calcium(Ca)and gadolinium(Gd)seem coherent with the mixed model.Concurrently,mathematical models of all experimental studies are created with the response surface Box-Behnken method and the correlation coefficients of all the models are over 90%.
基金The National Natural Science Foundation of China (41674025,41674082)The Independent Research Foundation of State Key Laboratory of Geo-information Engineering (SKLGIE2018-ZZ-10).
文摘Helmert’s second method of condensation is an effective method for terrain reduction in the geoid and quasi-geoid determinations. Condensing the masses outside the geoid to a surface layer on the geoid produces several forms of topographic effects: direct effect on gravity, secondary indirect effect on gravity and indirect effects on the (quasi-) geoid, respectively. To strike a balance between computation accuracy and numerical efficiency, the global integration region of topographic effects is usually divided into near zone and far zone. We focus on the computation of near-zone topographic effects, which are functions of actual topographic masses and condensed masses. Since there have already been mature formulas for gravitational attraction and potential of actual topographic masses using rectangular prism model, we put forward surface element model for condensed masses. Afterwards, the formulas for near-zone direct and indirect effects are obtained easily by combining the rectangular prism model and surface element model. To overcome the planar approximation errors involved with the new formulas for near-zone topographic effects, the Earth’s curvature can be taken into account. It is recommended to apply the formulas based on the rectangular prism and surface element considering the Earth’s curvature to calculate near-zone topographic effects for high-accuracy demand to determine geoid and quasi-geoid.
基金Project supported by the National Science Foundation,the National Scaling Programthe Doctoral Foundation of the National Education Commission
文摘Petroleum science has made remarkable progress in organic geochcmistry and in the research into the theories of petroleum origin, its transport and accumulation. In estimating the oil-gas resources of a basin, the knowledge of its evolutionary history and especially the numerical computation of fluid flow and the history of its changes under heat is vital. The mathematical model can be described as a coupled system of nonlinear partial differentical equations with initial-boundary value problems. This thesis, from actual conditions such as the effect of fluid compressibility and the three-dimensional characteristic of large-scale science-engineering computation, we put forward a kind of characteristic finite element alternating-direction schemes and obtain optimal order estimates in L^2 norm for the error in the approximate assumption.
基金Project supported by the National Natural Science Foundation of China (No. 10876100)
文摘Based on the concept of the constitutive relation error along with the residuals of both the origin and the dual problems, a goal-oriented error estimation method with extended degrees of freedom is developed. It leads to the high quality locM error bounds in the problem of the direct-solution steady-state dynamic analysis with a frequency-domain finite element, which involves the enrichments with plural variable basis functions. The solution of the steady-state dynamic procedure calculates the harmonic response directly in terms of the physical degrees of freedom in the model, which uses the mass, damping, and stiffness matrices of the system. A three-dimensional finite element example is carried out to illustrate the computational procedures.
文摘This paper is concerned with some nonlinear reaction - diffusion models. To solve this kind of models, the modified Laplace finite element scheme and the alternating direction finite element scheme are established for the system of patrical differential equations. Besides, the finite difference method is utilized for the ordinary differential equation in the models. Moreover, by the theory and technique of prior estimates for the differential equations, the convergence analyses and the optimal L2- norm error estimates are demonstrated.
