Based on the special positive semidefinite splittings of the saddle point matrix, we propose a new Mternating positive semidefinite splitting （APSS） iteration method for the saddle point problem arising from the fin...Based on the special positive semidefinite splittings of the saddle point matrix, we propose a new Mternating positive semidefinite splitting （APSS） iteration method for the saddle point problem arising from the finite element discretization of the hybrid formulation of the time-harmonic eddy current problem. We prove that the new APSS iteration method is unconditionally convergent for both cases of the simple topology and the general topology. The new APSS matrix can be used as a preconditioner to accelerate the convergence rate of Krylov subspace methods. Numerical results show that the new APSS preconditioner is superior to the existing preconditioners.展开更多
This paper introduces a novel hybrid FEM-BEM method for calculating 3D eddy cur-rent field. In the eddy current region, the eddy current density J is solved by the finite element method (FEM) which is discretized by b...This paper introduces a novel hybrid FEM-BEM method for calculating 3D eddy cur-rent field. In the eddy current region, the eddy current density J is solved by the finite element method (FEM) which is discretized by brick finite element mesh, while in the eddy current free re-gion, the magnetic field intensity H is solved by the boundary element method (BEM) which is dis-cretized by rectangular boundary element mesh. Under the boundary conditions, an algebraic equation group is obtained that only includes J by eliminating H. This method has many advan-tages over traditional ones, such as fewer variables, more convenient coupling between the FEM and the BEM and wider application to multiply-connected regions. The calculated values of two models are in good agreement with experimental results. This shows the validity of our method.展开更多
This paper is devoted to the study of a nonlinear evolution eddy current model of the type δtB（H） ＋ △↓× （ △↓ × H） =0 subject to homogeneous Dirichlet boundary conditions H × v = 0 and a given ...This paper is devoted to the study of a nonlinear evolution eddy current model of the type δtB（H） ＋ △↓× （ △↓ × H） =0 subject to homogeneous Dirichlet boundary conditions H × v = 0 and a given initial datum. Here, the magnetic properties of a soft ferromagnet are linked by a nonlinear material law described by B（H）. We apply the backward Euler method for the time discretization and we derive the error estimates in suitable function spaces. The results depend on the nonlinearity of B（H）.展开更多
In this paper,hp-adaptive finite element methods are studied for timeharmonic Maxwell’s equations.We propose the parallel hp-adaptive algorithms on conforming unstructured tetrahedral meshes based on residual-based a...In this paper,hp-adaptive finite element methods are studied for timeharmonic Maxwell’s equations.We propose the parallel hp-adaptive algorithms on conforming unstructured tetrahedral meshes based on residual-based a posteriori error estimates.Extensive numerical experiments are reported to investigate the efficiency of the hp-adaptive methods for point singularities,edge singularities,and an engineering benchmark problem of Maxwell’s equations.The hp-adaptive methods show much better performance than the h-adaptive method.展开更多
基金This work was supported by the National Natural Science Foundation of China （Grant Nos. 11301521, 11771467, 11071041）, the Natural Science Foundation of Fujian Province （Nos. 2016J01005, 2015J01578）, and the National Post- doctoral Program for Innovative Talents （No. BX201700234）.
文摘Based on the special positive semidefinite splittings of the saddle point matrix, we propose a new Mternating positive semidefinite splitting （APSS） iteration method for the saddle point problem arising from the finite element discretization of the hybrid formulation of the time-harmonic eddy current problem. We prove that the new APSS iteration method is unconditionally convergent for both cases of the simple topology and the general topology. The new APSS matrix can be used as a preconditioner to accelerate the convergence rate of Krylov subspace methods. Numerical results show that the new APSS preconditioner is superior to the existing preconditioners.
文摘This paper introduces a novel hybrid FEM-BEM method for calculating 3D eddy cur-rent field. In the eddy current region, the eddy current density J is solved by the finite element method (FEM) which is discretized by brick finite element mesh, while in the eddy current free re-gion, the magnetic field intensity H is solved by the boundary element method (BEM) which is dis-cretized by rectangular boundary element mesh. Under the boundary conditions, an algebraic equation group is obtained that only includes J by eliminating H. This method has many advan-tages over traditional ones, such as fewer variables, more convenient coupling between the FEM and the BEM and wider application to multiply-connected regions. The calculated values of two models are in good agreement with experimental results. This shows the validity of our method.
基金the BOF/GOA-project No.01G00607 of Ghent Universitythe grant number 3G008206 of the Fund for Scientific Research-Flanders
文摘This paper is devoted to the study of a nonlinear evolution eddy current model of the type δtB（H） ＋ △↓× （ △↓ × H） =0 subject to homogeneous Dirichlet boundary conditions H × v = 0 and a given initial datum. Here, the magnetic properties of a soft ferromagnet are linked by a nonlinear material law described by B（H）. We apply the backward Euler method for the time discretization and we derive the error estimates in suitable function spaces. The results depend on the nonlinearity of B（H）.
基金supported in part by the National Basic Research Project under the grant 2011CB309703,by the Funds for Creative Research Groups of China(Grant No.11021101)by China NSF under the grant 60873177+2 种基金supported in part by China NSF under the grants 11031006 and 11171334by the Funds for Creative Research Groups of China(Grant No.11021101)by the National Magnetic Confinement Fusion Science Program(Grant No.2011GB105003).
文摘In this paper,hp-adaptive finite element methods are studied for timeharmonic Maxwell’s equations.We propose the parallel hp-adaptive algorithms on conforming unstructured tetrahedral meshes based on residual-based a posteriori error estimates.Extensive numerical experiments are reported to investigate the efficiency of the hp-adaptive methods for point singularities,edge singularities,and an engineering benchmark problem of Maxwell’s equations.The hp-adaptive methods show much better performance than the h-adaptive method.
