In this paper, we consider the nonconforming rotated Q1 element for the second order elliptic problem on the non-tensor product anisotropic meshes, i.e. the anisotropic affine quadrilateral meshes. Though the interpolation error is divergent on the anisotropic meshes,we overcome this difficulty by constructing another proper operator. Then we give the optimal approximation error and the consistency error estimates under the anisotropic affine quadrilateral meshes. The results of this paper provide some hints to derive the anisotropic error of some finite elements whose interpolations do not satisfy the anisotropic interpolation properties. Lastly, a numerical test is carried out, which coincides with our theoretical analysis.
In this paper we prove the uniform convergence of the standard multigrid V-cycle algorithm with the Gauss-Seidel relaxation performed only on the new nodes and their "immediate" neighbors for discrete elliptic problems on the adaptively refined finite element meshes using the newest vertex bisection algorithm. The proof depends on sharp estimates on the relationship of local mesh sizes and a new stability estimate for the space decomposition based on the Scott-Zhang interpolation operator. Extensive numerical results are reported, which confirm the theoretical analysis.
为了简化亚100nm SOI MOSFET BSIMSOI4的模型参数提取过程,实现全局优化,使用了遗传算法技术,并提出了保留多个最优的自适应遗传算法.该算法通过保留最优个体的多个拷贝,对适应度高和适应度低的个体分别进行诱导变异和动态变异,在进化起始阶段和终止阶段分别执行随机交叉和诱导交叉,既具有全局优化特性,又加速了局部搜索过程,提高了最终解的质量.不同种群数和进化代数条件下的参数提取实例表明,该算法提取精度高、速度快,全局优化稳定性好;适当增加种群数,有利于加速算法的全局收敛过程.
In this paper,an energy-compatibility condition is used for stress optimization in the derivation of new accurate 8-node hexahedral elements for threedimensional elasticity.Equivalence of the proposed hybrid method to an enhanced strains method is established,which makes it easy to extend the method to general nonlinear problems.Numerical tests show that the resultant elements possess high accuracy at coarse meshes,are insensitive to mesh distortions and free from volume locking in the analysis of beams,plates and shells.
In this paper, we propose three gradient recovery schemes of higher order for the linear interpolation. The first one is a weighted averaging method based on the gradients of the linear interpolation on the uniform mesh, the second is a geometric averaging method constructed from the gradients of two cubic interpolation on macro element, and the last one is a local least square method on the nodal patch with cubic polynomials. We prove that these schemes can approximate the gradient of the exact solution on the symmetry points with fourth order. In particular, for the uniform mesh, we show that these three schemes are the same on the considered points. The last scheme is more robust in general meshes. Consequently, we obtain the superconvergence results of the recovered gradient by using the aforementioned results and the supercloseness between the finite element solution and the linear interpolation of the exact solution. Finally, we provide several numerical experiments to illustrate the theoretical results.
