This paper proposes a two-parameter block triangular splitting(TPTS)preconditioner for the general block two-by-two linear systems.The eigenvalues of the corresponding preconditioned matrix are proved to cluster aroun...This paper proposes a two-parameter block triangular splitting(TPTS)preconditioner for the general block two-by-two linear systems.The eigenvalues of the corresponding preconditioned matrix are proved to cluster around 0 or 1 under mild conditions.The limited numerical results show that the TPTS preconditioner is more efficient than the classic block-diagonal and block-triangular preconditioners when applied to the flexible generalized minimal residual(FGMRES)method.展开更多
This paper presents an investigation into the effect of surface asperities on the over-rolling of bearing surfaces in transient elastohydrodynamic lubrication(EHL) line contact. The governing equations are discretized...This paper presents an investigation into the effect of surface asperities on the over-rolling of bearing surfaces in transient elastohydrodynamic lubrication(EHL) line contact. The governing equations are discretized by the finite difference method. The resulting nonlinear system of algebraic equations is solved by the Jacobian-free Newtongeneralized minimal residual(GMRES) from the Krylov subspace method(KSM). The acceleration of the GMRES iteration is accomplished by a wavelet-based preconditioner.The profiles of the lubricant pressure and film thickness are obtained at each time step when the indented surface moves through the contact region. The prediction of pressure as a function of time provides an insight into the understanding of fatigue life of bearings.The analysis confirms the need for the time-dependent approach of EHL problems with surface asperities. This method requires less storage and yields an accurate solution with much coarser grids. It is stable, efficient, allows a larger time step, and covers a wide range of parameters of interest.展开更多
Abstract Recently a, monotone generalized directional derixrative has been introduced for Lipschitz functions. This concept has been applied to represent and optimize nonsmooth functions. The second a.pplication resul...Abstract Recently a, monotone generalized directional derixrative has been introduced for Lipschitz functions. This concept has been applied to represent and optimize nonsmooth functions. The second a.pplication result,ed relevant for parallel computing, by allowing to define minimization algorithms with high degree of inherent parallelism. The paper presents first the theoretical background, namely the notions of monotone generalized directional derivative and monotone generalized subdifferential. Then it defines the tools for the procedures, that is a necessary optimality condition and a steel>est descent direction. Therefore the minimization algorithms are outlined. Successively the used architectures and the performed numerical expertence are described, by listing and commenting the t.ested functions and the obtained results.展开更多
We report results on electronic, transport, and bulk properties of rock-salt magnesium selenide (MgSe), from density functional theory (DFT) calculations. We utilized a local density approximation (LDA) potential and ...We report results on electronic, transport, and bulk properties of rock-salt magnesium selenide (MgSe), from density functional theory (DFT) calculations. We utilized a local density approximation (LDA) potential and the linear combination of atomic orbitals formalism (LCAO). We followed the Bagayoko, Zhao, and Williams (BZW) method, as enhanced by Ekuma and Franklin (BZW-EF), to perform a generalized minimization of the energy, down to the actual ground state of the material. We describe the successive, self-consistent calculations, with augmented basis sets, that are needed for this generalized minimization. Due to the generalized minimization, our results have the full, physical content of DFT, as per the second DFT theorem [AIP Advances, 4, 127104 (2014)]. Our calculated, indirect bandgap of 2.49 eV, for a room temperature lattice constant of 5.460 <span style="white-space:nowrap;">Å</span>, agrees with experimental findings. We present the ground-state band structure, the related total and partial densities of states, DOS and PDOS, respectively, and electron and hole effective masses for the material. Our calculated bulk modulus of 63.1 GPa is in excellent agreement with the experimental value of 62.8 ± 1.6 GPa. Our predicted equilibrium lattice constant, at zero temperature, is 5.424 <span style="white-space:nowrap;">Å</span>, with a corresponding indirect bandgap of 2.51 eV. We discuss the reasons for the agreements between our findings and available, corresponding, experimental ones, particularly for the band gap, unlike the previous DFT results obtained with ab-initio LDA or GGA potentials.展开更多
This paper presents a new mathematical model for the highly nonlinear problem of frictional con- tact. A programming model, multipole boundary element method (BEM), was developed for 3-D elastic con- tact with frict...This paper presents a new mathematical model for the highly nonlinear problem of frictional con- tact. A programming model, multipole boundary element method (BEM), was developed for 3-D elastic con- tact with friction to replace the Monte Carlo method. A numerical example shows that the optimization pro- gramming model for the point-to-surface contact with friction and the fast optimization generalized minimal residual algorithm (GMRES(m)) significantly improve the analysis of such problems relative to the conven- tional BEM.展开更多
A graph is called a proper refinement of a star graph if it is a refinement of a star graph, but it is neither a star graph nor a complete graph. For a refinement of a star graph G with center c, let G* be the subgra...A graph is called a proper refinement of a star graph if it is a refinement of a star graph, but it is neither a star graph nor a complete graph. For a refinement of a star graph G with center c, let G* be the subgraph of G induced on the vertex set V(G) / {c or end vertices adjacent to c}. In this paper, we study the isomorphic classification of some finite commutative local rings R by investigating their zero-divisor graphs G=Г(R), which is a proper refinement of a star graph with exactly one center c. We determine all finite commutative local rings R such that G* has at least two connected components. We prove that the diameter of the induced graph G* is two if Z(R)2 ≠{0}, Z(R)3 = {0} and Gc is connected. We determine the structure of R which has two distinct nonadjacent vertices a, fl C Z(R)*/{c} such that the ideal [N(a)N(β)]{0} is generated by only one element of Z(R)*/{c}. We also completely determine the correspondence between commutative rings and finite complete graphs Kn with some end vertices adjacent to a single vertex of Kn.展开更多
It is well known that in the noncommutative polynomial ring in serveral variables Buchberger's algorithm does not always terminate.Thus,it is important to characterize noncommutative ideals that admit a finite Gro...It is well known that in the noncommutative polynomial ring in serveral variables Buchberger's algorithm does not always terminate.Thus,it is important to characterize noncommutative ideals that admit a finite Grobner basis.In this context,Eisenbud,Peeva and Sturmfels defined a mapγfrom the noncommutative polynomial ring k〈X_(1),...,X_(n)〉to the commutative one k[x_(1),...,x_(n)]and proved that any ideal J of k〈X_(1),...,X_(n)〉,written as J=γ^(-1)(L)for some ideal L of k[x_(1),...,x_(n)],amits a finite Grobner basis with respect to a special monomial ordering on k〈X_(1),...,X_(n)〉.In this work,we approach the opposite problem.We prove that under some conditions,any ideal J of k〈X_(1),...,X_(n)〉admitting a finite Grobner basis can be written as J=γ^(-1)(L)for some ideal L of k[x_(1),...,x_(n)].展开更多
We develop an efficient and accurate spectral deferred correction(SDC)method for fractional differential equations(FDEs)by extending the algorithm in[14]for classical ordinary differential equations(ODEs).Specifically...We develop an efficient and accurate spectral deferred correction(SDC)method for fractional differential equations(FDEs)by extending the algorithm in[14]for classical ordinary differential equations(ODEs).Specifically,we discretize the resulted Picard integral equation by the SDC method and accelerate the convergence of the SDC iteration by using the generalized minimal residual algorithm(GMRES).We first derive the correction matrix of the SDC method for FDEs and analyze the convergence region of the SDC method.We then present several numerical examples for stiff and non-stiff FDEs including fractional linear and nonlinear ODEs as well as fractional phase field models,demonstrating that the accelerated SDC method is much more efficient than the original SDC method,especially for stiff problems.Furthermore,we resolve the issue of low accuracy arising from the singularity of the solutions by using a geometric mesh,leading to highly accurate solutions compared to uniform mesh solutions at almost the same computational cost.Moreover,for long-time integration of FDEs,using the geometric mesh leads to great computational savings as the total number of degrees of freedom required is relatively small.展开更多
Krylov subspace methods are widely used for solving sparse linear algebraic equations,but they rely heavily on preconditioners,and it is difficult to find an effective preconditioner that is efficient and stable for a...Krylov subspace methods are widely used for solving sparse linear algebraic equations,but they rely heavily on preconditioners,and it is difficult to find an effective preconditioner that is efficient and stable for all problems.In this paper,a novel projection strategy including the orthogonal and the oblique projection is proposed to improve the preconditioner,which can enhance the efficiency and stability of iteration.The proposed strategy can be considered as a minimization process,where the orthogonal projection minimizes the energy norm of error and the oblique projection minimizes the 2-norm of the residual,meanwhile they can be regarded as approaches to correct the approximation by solving low-rank inverse of the matrices.The strategy is a wide-ranging approach and provides a way to transform the constant preconditioner into a variable one.The paper discusses in detail the projection strategy for sparse approximate inverse(SPAI)preconditioner applied to flexible GMRES and conducts the numerical test for problems from different applications.The results show that the proposed projection strategy can significantly improve the solving process,especially for some non-converging and slowly convergence systems.展开更多
基金the National Natural Science Foundation of China under Grant Nos.61273311 and 61803247.
文摘This paper proposes a two-parameter block triangular splitting(TPTS)preconditioner for the general block two-by-two linear systems.The eigenvalues of the corresponding preconditioned matrix are proved to cluster around 0 or 1 under mild conditions.The limited numerical results show that the TPTS preconditioner is more efficient than the classic block-diagonal and block-triangular preconditioners when applied to the flexible generalized minimal residual(FGMRES)method.
基金financial support from the Indian National Science Academy,New Delhi,IndiaBiluru Gurubasava Mahaswamiji Institute of Technology for the encouragement and support。
文摘This paper presents an investigation into the effect of surface asperities on the over-rolling of bearing surfaces in transient elastohydrodynamic lubrication(EHL) line contact. The governing equations are discretized by the finite difference method. The resulting nonlinear system of algebraic equations is solved by the Jacobian-free Newtongeneralized minimal residual(GMRES) from the Krylov subspace method(KSM). The acceleration of the GMRES iteration is accomplished by a wavelet-based preconditioner.The profiles of the lubricant pressure and film thickness are obtained at each time step when the indented surface moves through the contact region. The prediction of pressure as a function of time provides an insight into the understanding of fatigue life of bearings.The analysis confirms the need for the time-dependent approach of EHL problems with surface asperities. This method requires less storage and yields an accurate solution with much coarser grids. It is stable, efficient, allows a larger time step, and covers a wide range of parameters of interest.
文摘Abstract Recently a, monotone generalized directional derixrative has been introduced for Lipschitz functions. This concept has been applied to represent and optimize nonsmooth functions. The second a.pplication result,ed relevant for parallel computing, by allowing to define minimization algorithms with high degree of inherent parallelism. The paper presents first the theoretical background, namely the notions of monotone generalized directional derivative and monotone generalized subdifferential. Then it defines the tools for the procedures, that is a necessary optimality condition and a steel>est descent direction. Therefore the minimization algorithms are outlined. Successively the used architectures and the performed numerical expertence are described, by listing and commenting the t.ested functions and the obtained results.
文摘We report results on electronic, transport, and bulk properties of rock-salt magnesium selenide (MgSe), from density functional theory (DFT) calculations. We utilized a local density approximation (LDA) potential and the linear combination of atomic orbitals formalism (LCAO). We followed the Bagayoko, Zhao, and Williams (BZW) method, as enhanced by Ekuma and Franklin (BZW-EF), to perform a generalized minimization of the energy, down to the actual ground state of the material. We describe the successive, self-consistent calculations, with augmented basis sets, that are needed for this generalized minimization. Due to the generalized minimization, our results have the full, physical content of DFT, as per the second DFT theorem [AIP Advances, 4, 127104 (2014)]. Our calculated, indirect bandgap of 2.49 eV, for a room temperature lattice constant of 5.460 <span style="white-space:nowrap;">Å</span>, agrees with experimental findings. We present the ground-state band structure, the related total and partial densities of states, DOS and PDOS, respectively, and electron and hole effective masses for the material. Our calculated bulk modulus of 63.1 GPa is in excellent agreement with the experimental value of 62.8 ± 1.6 GPa. Our predicted equilibrium lattice constant, at zero temperature, is 5.424 <span style="white-space:nowrap;">Å</span>, with a corresponding indirect bandgap of 2.51 eV. We discuss the reasons for the agreements between our findings and available, corresponding, experimental ones, particularly for the band gap, unlike the previous DFT results obtained with ab-initio LDA or GGA potentials.
基金Supported by the National Natural Science Foundation of China(No. 50075075)
文摘This paper presents a new mathematical model for the highly nonlinear problem of frictional con- tact. A programming model, multipole boundary element method (BEM), was developed for 3-D elastic con- tact with friction to replace the Monte Carlo method. A numerical example shows that the optimization pro- gramming model for the point-to-surface contact with friction and the fast optimization generalized minimal residual algorithm (GMRES(m)) significantly improve the analysis of such problems relative to the conven- tional BEM.
基金Supported by National Natural Science Foundation of China (Grant No. 10671122) the first author is supported by Youth Foundation of Shanghai (Grant No. sdl10017) and also partly supported by Natural Science Foundation of Shanghai (Grant No. 10ZR1412500) the second author is partly supported by STCSM (Grant No. 09XD1402500)
文摘A graph is called a proper refinement of a star graph if it is a refinement of a star graph, but it is neither a star graph nor a complete graph. For a refinement of a star graph G with center c, let G* be the subgraph of G induced on the vertex set V(G) / {c or end vertices adjacent to c}. In this paper, we study the isomorphic classification of some finite commutative local rings R by investigating their zero-divisor graphs G=Г(R), which is a proper refinement of a star graph with exactly one center c. We determine all finite commutative local rings R such that G* has at least two connected components. We prove that the diameter of the induced graph G* is two if Z(R)2 ≠{0}, Z(R)3 = {0} and Gc is connected. We determine the structure of R which has two distinct nonadjacent vertices a, fl C Z(R)*/{c} such that the ideal [N(a)N(β)]{0} is generated by only one element of Z(R)*/{c}. We also completely determine the correspondence between commutative rings and finite complete graphs Kn with some end vertices adjacent to a single vertex of Kn.
文摘It is well known that in the noncommutative polynomial ring in serveral variables Buchberger's algorithm does not always terminate.Thus,it is important to characterize noncommutative ideals that admit a finite Grobner basis.In this context,Eisenbud,Peeva and Sturmfels defined a mapγfrom the noncommutative polynomial ring k〈X_(1),...,X_(n)〉to the commutative one k[x_(1),...,x_(n)]and proved that any ideal J of k〈X_(1),...,X_(n)〉,written as J=γ^(-1)(L)for some ideal L of k[x_(1),...,x_(n)],amits a finite Grobner basis with respect to a special monomial ordering on k〈X_(1),...,X_(n)〉.In this work,we approach the opposite problem.We prove that under some conditions,any ideal J of k〈X_(1),...,X_(n)〉admitting a finite Grobner basis can be written as J=γ^(-1)(L)for some ideal L of k[x_(1),...,x_(n)].
基金Z.Mao was supported by the Fundamental Research Funds for the Central Universities(Grant 20720210037)G.E.Karniadakis was supported by the MURI/ARO on Fractional PDEs for Conservation Laws and Beyond:Theory,Numerics and Applications(Grant W911NF-15-1-0562)X.Chen was supported by the Fujian Provincial Natural Science Foundation of China(Grants 2022J01338,2020J01703).
文摘We develop an efficient and accurate spectral deferred correction(SDC)method for fractional differential equations(FDEs)by extending the algorithm in[14]for classical ordinary differential equations(ODEs).Specifically,we discretize the resulted Picard integral equation by the SDC method and accelerate the convergence of the SDC iteration by using the generalized minimal residual algorithm(GMRES).We first derive the correction matrix of the SDC method for FDEs and analyze the convergence region of the SDC method.We then present several numerical examples for stiff and non-stiff FDEs including fractional linear and nonlinear ODEs as well as fractional phase field models,demonstrating that the accelerated SDC method is much more efficient than the original SDC method,especially for stiff problems.Furthermore,we resolve the issue of low accuracy arising from the singularity of the solutions by using a geometric mesh,leading to highly accurate solutions compared to uniform mesh solutions at almost the same computational cost.Moreover,for long-time integration of FDEs,using the geometric mesh leads to great computational savings as the total number of degrees of freedom required is relatively small.
基金supported by the National Key R&D Program of China(Grant No.2021YFB2401700)the National Natural Science Foundation of China(Grant No.11672362).
文摘Krylov subspace methods are widely used for solving sparse linear algebraic equations,but they rely heavily on preconditioners,and it is difficult to find an effective preconditioner that is efficient and stable for all problems.In this paper,a novel projection strategy including the orthogonal and the oblique projection is proposed to improve the preconditioner,which can enhance the efficiency and stability of iteration.The proposed strategy can be considered as a minimization process,where the orthogonal projection minimizes the energy norm of error and the oblique projection minimizes the 2-norm of the residual,meanwhile they can be regarded as approaches to correct the approximation by solving low-rank inverse of the matrices.The strategy is a wide-ranging approach and provides a way to transform the constant preconditioner into a variable one.The paper discusses in detail the projection strategy for sparse approximate inverse(SPAI)preconditioner applied to flexible GMRES and conducts the numerical test for problems from different applications.The results show that the proposed projection strategy can significantly improve the solving process,especially for some non-converging and slowly convergence systems.