In this paper, combining the idea of difference method and finite element method, we construct a difference scheme for a self-adjoint problem in conservation form. Its solution uniformly converges to that of the origi...In this paper, combining the idea of difference method and finite element method, we construct a difference scheme for a self-adjoint problem in conservation form. Its solution uniformly converges to that of the original differential equation problem with order h3.展开更多
In this paper, a novel stochastic method named as the moment-based stochastic edge-based finite element method(MSES-FEM)is proposed to deal with the uncertain electromagnetic problems. First, electromagnetic and mecha...In this paper, a novel stochastic method named as the moment-based stochastic edge-based finite element method(MSES-FEM)is proposed to deal with the uncertain electromagnetic problems. First, electromagnetic and mechanical field are formulated by smoothed Galerkin Weak Form under edge-based smoothed finite element method(ES-FEM) scheme. The moment analysis is then applied to obtain the first four moments of the responses and to observe the effects of each random variable on electromagnetic field responses. The maximum entropy theory is employed to calculate the probability density functions(PDFs) of the responses. A quasi-static electromagnetic problem and a practical electromagnetic forming problem(EMF) are performed. The proposed method successfully solves stochastic electromagnetic forming analysis under the uncertain parameters. Numerical results obtained by the proposed MSES-FEM are quite satisfactory with the ones by the Monte Carlo simulation(MCS).展开更多
文摘In this paper, combining the idea of difference method and finite element method, we construct a difference scheme for a self-adjoint problem in conservation form. Its solution uniformly converges to that of the original differential equation problem with order h3.
基金supported by the National Key R&D Program of China(Grant No. 2017YFB1002704)the Hunan Provincial Innovation Foundation for Postgraduate of China (Grant No. CX2018B202)+1 种基金the National Natural Science Foundation of China (Grant No. 11872177)the Foundation for Innovative Research Groups of the National Natural Science Foundation of China (Grant No. 51621004)。
文摘In this paper, a novel stochastic method named as the moment-based stochastic edge-based finite element method(MSES-FEM)is proposed to deal with the uncertain electromagnetic problems. First, electromagnetic and mechanical field are formulated by smoothed Galerkin Weak Form under edge-based smoothed finite element method(ES-FEM) scheme. The moment analysis is then applied to obtain the first four moments of the responses and to observe the effects of each random variable on electromagnetic field responses. The maximum entropy theory is employed to calculate the probability density functions(PDFs) of the responses. A quasi-static electromagnetic problem and a practical electromagnetic forming problem(EMF) are performed. The proposed method successfully solves stochastic electromagnetic forming analysis under the uncertain parameters. Numerical results obtained by the proposed MSES-FEM are quite satisfactory with the ones by the Monte Carlo simulation(MCS).
