As an efficient artificial truncating boundary condition, conformal perfectly matched layer (CPML) is a kind of multilayer anisotropic absorbing media. To reduce computing effort of CPML, this article proposes a layer...As an efficient artificial truncating boundary condition, conformal perfectly matched layer (CPML) is a kind of multilayer anisotropic absorbing media. To reduce computing effort of CPML, this article proposes a layer-oriented element integration algorithm. In this algorithm, the relative dielectric constant and permeability are considered as constants for each the very thin monolayer of CPML, and the element integration of multilayer along the normal direction is substituted by the element integration of m...展开更多
This paper presents a finite element procedure for solving transient, multidimensional convection-diffusion equations. The procedure is based on the characteristic Galerkin method with an implicit algorithm using prec...This paper presents a finite element procedure for solving transient, multidimensional convection-diffusion equations. The procedure is based on the characteristic Galerkin method with an implicit algorithm using precise integration method. With the operator splitting procedure, the precise integration method is introduced to determine the material derivative in the convection-diffusion equation, consequently, the physical quantities of material points. An implicit algorithm with a combination of both the precise and the traditional numerical integration procedures in time domain in the Lagrange coordinates for the characteristic Galerkin method is formulated. The stability analysis of the algorithm shows that the unconditional stability of present implicit algorithm is enhanced as compared with that of the traditional implicit numerical integration procedure. The numerical results validate the presented method in solving convection-diffusion equations. As compared with SUPG method and explicit characteristic Galerkin method, the present method gives the results with higher accuracy and better stability.展开更多
A general and efficient parallel approach is proposed for the first time to parallelize the hybrid finiteelement-boundary-integral-multi-level fast multipole algorithm （FE-BI-MLFMA）. Among many algorithms of FE-BI-M...A general and efficient parallel approach is proposed for the first time to parallelize the hybrid finiteelement-boundary-integral-multi-level fast multipole algorithm （FE-BI-MLFMA）. Among many algorithms of FE-BI-MLFMA, the decomposition algorithm （DA） is chosen as a basis for the parallelization of FE-BI-MLFMA because of its distinct numerical characteristics suitable for parallelization. On the basis of the DA, the parallelization of FE-BI-MLFMA is carried out by employing the parallelized multi-frontal method for the matrix from the finiteelement method and the parallelized MLFMA for the matrix from the boundary integral method respectively. The programming and numerical experiments of the proposed parallel approach are carried out in the high perfor- mance computing platform CEMS-Liuhui. Numerical experiments demonstrate that FE-BI-MLFMA is efficiently parallelized and its computational capacity is greatly improved without losing accuracy, efficiency, and generality.展开更多
Numerical challenges,incorporating non-uniqueness,non-convexity,undefined gradients,and high curvature,of the positive level sets of yield function are encountered in stress integration when utilizing the return-mappi...Numerical challenges,incorporating non-uniqueness,non-convexity,undefined gradients,and high curvature,of the positive level sets of yield function are encountered in stress integration when utilizing the return-mapping algorithm family.These phenomena are illustrated by an assessment of four typical yield functions:modified spatially mobilized plane criterion,Lade criterion,Bigoni-Piccolroaz criterion,and micromechanics-based upscaled Drucker-Prager criterion.One remedy to these issues,named the"Hop-to-Hug"(H2H)algorithm,is proposed via a convexification enhancement upon the classical cutting-plane algorithm(CPA).The improved robustness of the H2H algorithm is demonstrated through a series of integration tests in one single material point.Furthermore,a constitutive model is implemented with the H2H algorithm into the Abaqus/Standard finite-element platform.Element-level and structure-level analyses are carried out to validate the effectiveness of the H2H algorithm in convergence.All validation analyses manifest that the proposed H2H algorithm can offer enhanced stability over the classical CPA method while maintaining the ease of implementation,in which evaluations of the second-order derivatives of yield function and plastic potential function are circumvented.展开更多
By modeling direct transient heat conduction problems via finite element method (FEM) and precise integral algorithm, a new approach is presented to solve transient inverse heat conduction problems with multi-variable...By modeling direct transient heat conduction problems via finite element method (FEM) and precise integral algorithm, a new approach is presented to solve transient inverse heat conduction problems with multi-variables. Firstly, the spatial space and temporal domain are discretized by FEM and precise integral algorithm respectively. Then, the high accuracy semi-analytical solution of direct problem can be got. Finally, based on the solution, the computing model of inverse problem and expression of sensitivity analysis are established. Single variable and variables combined identifications including thermal parameters, boundary conditions and source-related terms etc. are given to validate the approach proposed in 1-D and 2-D cases. The effects of noise data and initial guess on the results are investigated. The numerical examples show the effectiveness of this approach.展开更多
基金National Natural Science Foundation of China (10477018) Science and Technology Innovation Foundation of North-western Polytechnical University (W016143)
文摘As an efficient artificial truncating boundary condition, conformal perfectly matched layer (CPML) is a kind of multilayer anisotropic absorbing media. To reduce computing effort of CPML, this article proposes a layer-oriented element integration algorithm. In this algorithm, the relative dielectric constant and permeability are considered as constants for each the very thin monolayer of CPML, and the element integration of multilayer along the normal direction is substituted by the element integration of m...
文摘This paper presents a finite element procedure for solving transient, multidimensional convection-diffusion equations. The procedure is based on the characteristic Galerkin method with an implicit algorithm using precise integration method. With the operator splitting procedure, the precise integration method is introduced to determine the material derivative in the convection-diffusion equation, consequently, the physical quantities of material points. An implicit algorithm with a combination of both the precise and the traditional numerical integration procedures in time domain in the Lagrange coordinates for the characteristic Galerkin method is formulated. The stability analysis of the algorithm shows that the unconditional stability of present implicit algorithm is enhanced as compared with that of the traditional implicit numerical integration procedure. The numerical results validate the presented method in solving convection-diffusion equations. As compared with SUPG method and explicit characteristic Galerkin method, the present method gives the results with higher accuracy and better stability.
文摘A general and efficient parallel approach is proposed for the first time to parallelize the hybrid finiteelement-boundary-integral-multi-level fast multipole algorithm （FE-BI-MLFMA）. Among many algorithms of FE-BI-MLFMA, the decomposition algorithm （DA） is chosen as a basis for the parallelization of FE-BI-MLFMA because of its distinct numerical characteristics suitable for parallelization. On the basis of the DA, the parallelization of FE-BI-MLFMA is carried out by employing the parallelized multi-frontal method for the matrix from the finiteelement method and the parallelized MLFMA for the matrix from the boundary integral method respectively. The programming and numerical experiments of the proposed parallel approach are carried out in the high perfor- mance computing platform CEMS-Liuhui. Numerical experiments demonstrate that FE-BI-MLFMA is efficiently parallelized and its computational capacity is greatly improved without losing accuracy, efficiency, and generality.
基金supported by the National Natural Science Foundation of China (Grant Nos.12372376 and U22A20596).
文摘Numerical challenges,incorporating non-uniqueness,non-convexity,undefined gradients,and high curvature,of the positive level sets of yield function are encountered in stress integration when utilizing the return-mapping algorithm family.These phenomena are illustrated by an assessment of four typical yield functions:modified spatially mobilized plane criterion,Lade criterion,Bigoni-Piccolroaz criterion,and micromechanics-based upscaled Drucker-Prager criterion.One remedy to these issues,named the"Hop-to-Hug"(H2H)algorithm,is proposed via a convexification enhancement upon the classical cutting-plane algorithm(CPA).The improved robustness of the H2H algorithm is demonstrated through a series of integration tests in one single material point.Furthermore,a constitutive model is implemented with the H2H algorithm into the Abaqus/Standard finite-element platform.Element-level and structure-level analyses are carried out to validate the effectiveness of the H2H algorithm in convergence.All validation analyses manifest that the proposed H2H algorithm can offer enhanced stability over the classical CPA method while maintaining the ease of implementation,in which evaluations of the second-order derivatives of yield function and plastic potential function are circumvented.
文摘By modeling direct transient heat conduction problems via finite element method (FEM) and precise integral algorithm, a new approach is presented to solve transient inverse heat conduction problems with multi-variables. Firstly, the spatial space and temporal domain are discretized by FEM and precise integral algorithm respectively. Then, the high accuracy semi-analytical solution of direct problem can be got. Finally, based on the solution, the computing model of inverse problem and expression of sensitivity analysis are established. Single variable and variables combined identifications including thermal parameters, boundary conditions and source-related terms etc. are given to validate the approach proposed in 1-D and 2-D cases. The effects of noise data and initial guess on the results are investigated. The numerical examples show the effectiveness of this approach.
