Mantle conductivity imaging is one of the scientific goals of the forthcoming Macao Science Satellite-1(MSS-1).To achieve this goal,we develop a data analysis and inversion scheme for satellite magnetic data to probe ...Mantle conductivity imaging is one of the scientific goals of the forthcoming Macao Science Satellite-1(MSS-1).To achieve this goal,we develop a data analysis and inversion scheme for satellite magnetic data to probe global one-dimensional(1D)mantle conductivity structures.Using this scheme,we present a new global mantle conductivity model by analyzing over 8 years of Swarm satellite magnetic data.First,after sophisticated data selection procedures and the removal of core and crustal fields,the inducing and induced spherical harmonic coefficients of magnetic potential due to the magnetospheric ring current are derived.Second,satellite Cresponses are estimated from the time series of these coefficients.Finally,the observed responses are inverted for both smooth and threejump conductivity models using a quasi-Newton algorithm.The obtained conductivity models are in general agreement with previous global mantle conductivity models.A comparison of our conductivity model with the laboratory conductivity model suggests the mean state of the upper mantle and transition zone is relatively dry.This scheme can be used to process the forthcoming Macao Science Satellite-1 magnetic data.展开更多
Micropores are decisive to mechanical properties and thermal deformation capabilities of powder met-allurgy(P/M)Ti alloys sintered compacts.As a result,achieving express densification is of prime im-portance and has a...Micropores are decisive to mechanical properties and thermal deformation capabilities of powder met-allurgy(P/M)Ti alloys sintered compacts.As a result,achieving express densification is of prime im-portance and has attracted increasing attention recently.Induction heating owns the merits of high effi-ciency,short process,and low cost,and thus has huge potential to be used as a sintering approach for the fabrication of P/M Ti alloys.Nevertheless,the facilitated densification behavior associated with induction heating sintering remains unclear so far.To address it,powder metallurgy Ti6Al4V is manufactured via induction heating sintering with which the underlying sintering mechanism is investigated in-depth.It is found that induction heating could generate a fully densified compact in a remarkably shortened time,demonstrating its superior sintering efficiency as compared with conventional resistance furnace heat-ing.COMSOL finite element analysis reveals that the maximum current density during induction heating can reach 10^(6)A m^(–2)though the magnetic field strength is solely 0.02 T,leading to a slight tempera-ture difference of approximately 30℃between the interior and exterior of the billet.Furthermore,the rapid heating essentially starts at sharp corners of particles due to the potent current concentration ef-fect,which facilitates the cracking of the particle surface oxide film and thus enhances the direct contact between them.Moreover,the electromigration effect caused by induction current promotes the diffusion capability of elements,giving rise to expedited densification,alloying,and chemical homogenization.This work provides not only critical insight into the sintering mechanism of induction heating sintering but also significant guidance for low-cost powder metallurgy materials preparation.展开更多
Some new sixth-order compact finite difference schemes for Poisson/Helmholtz equations on rectangular domains in both two-and three-dimensions are developed and analyzed.Different from a few sixth-order compact finite...Some new sixth-order compact finite difference schemes for Poisson/Helmholtz equations on rectangular domains in both two-and three-dimensions are developed and analyzed.Different from a few sixth-order compact finite difference schemes in the literature,the finite difference and weight coefficients of the new methods have analytic simple expressions.One of the new ideas is to use a weighted combination of the source term at staggered grid points which is important for grid points near the boundary and avoids partial derivatives of the source term.Furthermore,the new compact schemes are exact for 2D and 3D Poisson equations if the solution is a polynomial less than or equal to 6.The coefficient matrices of the new schemes are M-matrices for Helmholtz equations with wave number K≤0,which guarantee the discrete maximum principle and lead to the convergence of the new sixth-order compact schemes.Numerical examples in both 2D and 3D are presented to verify the effectiveness of the proposed schemes.展开更多
The fast solutions of Crank-Nicolson scheme on quasi-uniform mesh for parabolic prob- lems are discussed. First, to decrease regularity requirements of solutions, some new error estimates are proved. Second, we analyz...The fast solutions of Crank-Nicolson scheme on quasi-uniform mesh for parabolic prob- lems are discussed. First, to decrease regularity requirements of solutions, some new error estimates are proved. Second, we analyze the two characteristics of parabolic discrete scheme, and find that the efficiency of Multigrid Method （MG） is greatly reduced. Nu- merical experiments compare the efficiency of Direct Conjugate Gradient Method （DCG） and Extrapolation Cascadic Multigrid Method （EXCMG）. Last, we propose a Time- Extrapolation Algorithm （TEA）, which takes a linear combination of previous several level solutions as good initial values to accelerate the rate of convergence. Some typical extrapolation formulas are compared numerically. And we find that under certain accuracy requirement, the CG iteration count for the 3-order and 7-level extrapolation formula is about 1/3 of that of DCG＇s. Since the TEA algorithm is independent of the space dimension, it is still valid for quasi-uniform meshes. As only the finest grid is needed, the proposed method is regarded very effective for nonlinear parabolic problems.展开更多
Extrapolation cascadic multigrid(EXCMG)method with conjugate gradient smoother is very efficient for solving the elliptic boundary value problems with linearfinite element discretization.However,it is not trivial to g...Extrapolation cascadic multigrid(EXCMG)method with conjugate gradient smoother is very efficient for solving the elliptic boundary value problems with linearfinite element discretization.However,it is not trivial to generalize the vertex-centred EXCMG method to cell-centeredfinite volume(FV)methods for diffusion equations with strongly discontinuous and anisotropic coefficients,since a non-nested hierarchy of grid nodes are used in the cell-centered discretization.For cell-centered FV schemes,the vertex values(auxiliary unknowns)need to be approximated by cell-centered ones(primary unknowns).One of the novelties is to propose a new gradient transfer(GT)method of interpolating vertex unknowns with cell-centered ones,which is easy to implement and applicable to general diffusion tensors.The main novelty of this paper is to design a multigrid prolongation operator based on the GT method and splitting extrapolation method,and then propose a cell-centered EXCMG method with BiCGStab smoother for solving the large linear system resulting from linear FV discretization of diffusion equations with strongly discontinuous and anisotropic coefficients.Numerical experiments are presented to demonstrate the high efficiency of the proposed method.展开更多
This paper proposes an extrapolation cascadic multigrid(EXCMG)method to solve elliptic problems in domains with reentrant corners.On a class ofλ-graded meshes,we derive some new extrapolation formulas to construct a ...This paper proposes an extrapolation cascadic multigrid(EXCMG)method to solve elliptic problems in domains with reentrant corners.On a class ofλ-graded meshes,we derive some new extrapolation formulas to construct a high-order approximation to the finite element solution on the next finer mesh using the numerical solutions on two-level of grids(current and previous grids).Then,this high-order approximation is used as the initial guess to reduce computational cost of the conjugate gradient method.Recursive application of this idea results in the EXCMG method proposed in this paper.Finally,numerical results for a crack problem and an L-shaped problem are presented to verify the efficiency and effectiveness of the proposed EXCMG method.展开更多
基金financially supported by the National Natural Science Foundation of China(41922027,41830107,42142034,41874086)Innovation-Driven Project of Central South University(2020CX012)+4 种基金Macao FoundationMacao Science and Technology Development Fund(0001/2019/A1)the Pre-research Project on Civil Aerospace Technologies funded by China National Space Administration(D020303)the Hunan Provincial Innovation Foundation for Postgraduate(CX20210277)the Fundamental Research Funds for the Central Universities of Central South University(2021zzts0259)。
文摘Mantle conductivity imaging is one of the scientific goals of the forthcoming Macao Science Satellite-1(MSS-1).To achieve this goal,we develop a data analysis and inversion scheme for satellite magnetic data to probe global one-dimensional(1D)mantle conductivity structures.Using this scheme,we present a new global mantle conductivity model by analyzing over 8 years of Swarm satellite magnetic data.First,after sophisticated data selection procedures and the removal of core and crustal fields,the inducing and induced spherical harmonic coefficients of magnetic potential due to the magnetospheric ring current are derived.Second,satellite Cresponses are estimated from the time series of these coefficients.Finally,the observed responses are inverted for both smooth and threejump conductivity models using a quasi-Newton algorithm.The obtained conductivity models are in general agreement with previous global mantle conductivity models.A comparison of our conductivity model with the laboratory conductivity model suggests the mean state of the upper mantle and transition zone is relatively dry.This scheme can be used to process the forthcoming Macao Science Satellite-1 magnetic data.
基金supported by the National Key Research and Development Program of China(No.2020YFB2008300)the National Natural Science Foundation of China(Nos.51971097 and 52301147)+2 种基金the Young Elite Scientist Sponsorship Program by China Association for Science and Technology(No.YESS20210054)the Hubei Province Natural Science Foundation(No.ZRMS2022000863)the Fundamental Research Funds for the Central Universities of Huazhong University of Science and Technology(No.2172021XXJS010)and the project supported by State Key Laboratory of Powder Metallurgy,Central South University,Changsha,China.
文摘Micropores are decisive to mechanical properties and thermal deformation capabilities of powder met-allurgy(P/M)Ti alloys sintered compacts.As a result,achieving express densification is of prime im-portance and has attracted increasing attention recently.Induction heating owns the merits of high effi-ciency,short process,and low cost,and thus has huge potential to be used as a sintering approach for the fabrication of P/M Ti alloys.Nevertheless,the facilitated densification behavior associated with induction heating sintering remains unclear so far.To address it,powder metallurgy Ti6Al4V is manufactured via induction heating sintering with which the underlying sintering mechanism is investigated in-depth.It is found that induction heating could generate a fully densified compact in a remarkably shortened time,demonstrating its superior sintering efficiency as compared with conventional resistance furnace heat-ing.COMSOL finite element analysis reveals that the maximum current density during induction heating can reach 10^(6)A m^(–2)though the magnetic field strength is solely 0.02 T,leading to a slight tempera-ture difference of approximately 30℃between the interior and exterior of the billet.Furthermore,the rapid heating essentially starts at sharp corners of particles due to the potent current concentration ef-fect,which facilitates the cracking of the particle surface oxide film and thus enhances the direct contact between them.Moreover,the electromigration effect caused by induction current promotes the diffusion capability of elements,giving rise to expedited densification,alloying,and chemical homogenization.This work provides not only critical insight into the sintering mechanism of induction heating sintering but also significant guidance for low-cost powder metallurgy materials preparation.
基金supported by the National Natural Science Foundation of China(Grant No.42274101)and the Excellent Youth Foundation of Hunan Province of China(Grant No.2018JJ1042)Hongling Hu was supported by the National Natural Science Foundation of China(Grant No.12071128)the Natural Science Foundation of Hunan Province(Grant No.2021JJ30434).Zhilin Li was partially supported by a Simons Grant No.633724.
文摘Some new sixth-order compact finite difference schemes for Poisson/Helmholtz equations on rectangular domains in both two-and three-dimensions are developed and analyzed.Different from a few sixth-order compact finite difference schemes in the literature,the finite difference and weight coefficients of the new methods have analytic simple expressions.One of the new ideas is to use a weighted combination of the source term at staggered grid points which is important for grid points near the boundary and avoids partial derivatives of the source term.Furthermore,the new compact schemes are exact for 2D and 3D Poisson equations if the solution is a polynomial less than or equal to 6.The coefficient matrices of the new schemes are M-matrices for Helmholtz equations with wave number K≤0,which guarantee the discrete maximum principle and lead to the convergence of the new sixth-order compact schemes.Numerical examples in both 2D and 3D are presented to verify the effectiveness of the proposed schemes.
基金This work was supported by the National Natural Science Foundation of China （No. 11071067, 41204082, 11301176）, the Research Fund for the Doctoral Program of Higher Education of China （No. 20120162120036）, the Hunan Provincial Natural Science Foundation of China （No. 14JJ3070） and the Construct Program of the Key Discipline in Hunan Province.
文摘The fast solutions of Crank-Nicolson scheme on quasi-uniform mesh for parabolic prob- lems are discussed. First, to decrease regularity requirements of solutions, some new error estimates are proved. Second, we analyze the two characteristics of parabolic discrete scheme, and find that the efficiency of Multigrid Method （MG） is greatly reduced. Nu- merical experiments compare the efficiency of Direct Conjugate Gradient Method （DCG） and Extrapolation Cascadic Multigrid Method （EXCMG）. Last, we propose a Time- Extrapolation Algorithm （TEA）, which takes a linear combination of previous several level solutions as good initial values to accelerate the rate of convergence. Some typical extrapolation formulas are compared numerically. And we find that under certain accuracy requirement, the CG iteration count for the 3-order and 7-level extrapolation formula is about 1/3 of that of DCG＇s. Since the TEA algorithm is independent of the space dimension, it is still valid for quasi-uniform meshes. As only the finest grid is needed, the proposed method is regarded very effective for nonlinear parabolic problems.
基金supported by Science Challenge Project(Grant No.TZ2016002)the National Natural Science Foundation of China(Grant Nos.41874086 and 11971069)+1 种基金173 Program of China(Grant No.2020-JCJQ-ZD-029)the Excellent Youth Foundation of Hunan Province of China(Grant No.2018JJ1042).
文摘Extrapolation cascadic multigrid(EXCMG)method with conjugate gradient smoother is very efficient for solving the elliptic boundary value problems with linearfinite element discretization.However,it is not trivial to generalize the vertex-centred EXCMG method to cell-centeredfinite volume(FV)methods for diffusion equations with strongly discontinuous and anisotropic coefficients,since a non-nested hierarchy of grid nodes are used in the cell-centered discretization.For cell-centered FV schemes,the vertex values(auxiliary unknowns)need to be approximated by cell-centered ones(primary unknowns).One of the novelties is to propose a new gradient transfer(GT)method of interpolating vertex unknowns with cell-centered ones,which is easy to implement and applicable to general diffusion tensors.The main novelty of this paper is to design a multigrid prolongation operator based on the GT method and splitting extrapolation method,and then propose a cell-centered EXCMG method with BiCGStab smoother for solving the large linear system resulting from linear FV discretization of diffusion equations with strongly discontinuous and anisotropic coefficients.Numerical experiments are presented to demonstrate the high efficiency of the proposed method.
基金Kejia Pan was supported by the National Natural Science Foundation of China(Nos.41474103 and 41204082)the National High Technology Research and Development Program of China(No.2014AA06A602)+3 种基金the Natural Science Foundation of Hunan Province of China(No.2015JJ3148)Dongdong He was supported by the Fundamental Research Funds for the Central Universities,the National Natural Science Foundation of China(No.11402174)the Program for Young Excellent Talents at Tongji University(No.2013KJ012)the Scientific Research Foundation for the Returned Overseas Chinese Scholars,State Education Ministry。
文摘This paper proposes an extrapolation cascadic multigrid(EXCMG)method to solve elliptic problems in domains with reentrant corners.On a class ofλ-graded meshes,we derive some new extrapolation formulas to construct a high-order approximation to the finite element solution on the next finer mesh using the numerical solutions on two-level of grids(current and previous grids).Then,this high-order approximation is used as the initial guess to reduce computational cost of the conjugate gradient method.Recursive application of this idea results in the EXCMG method proposed in this paper.Finally,numerical results for a crack problem and an L-shaped problem are presented to verify the efficiency and effectiveness of the proposed EXCMG method.
