杂质对溶胶-凝胶SiO2薄膜激光损伤的影响

 采用溶胶-凝胶法制备了含有吸收性杂质和非吸收性杂质的SiO₂增透膜,采用波长为1 064 nm的激光对其进行了小光斑激光预处理,对比研究了预处理前后的激光损伤差异,研究表明：激光预处理对于洁净的SiO₂薄膜影响不大;含10 μm SiO₂颗粒杂质的样品微透镜效应很明显,容易成为损伤起始的种子,激光预处理后情况有所改善;含有CeO₂颗粒杂质的样品表现出了很强的吸收性质,损伤阈值降低到不足洁净样品的一半。所有样品激光预处理后损伤形貌未发生变化,透光率峰值均有约50 nm的蓝移。     

Quasi‐optimal preconditioners for finite element approximations of diffusion dominated convection–diffusion equations on (nearly) equilateral triangle meshes

The paper is devoted to the spectral analysis of effective preconditioners for linear systems obtained via a finite element approximation to diffusion‐dominated convection–diffusion equations. We consider a model setting in which the structured finite element partition is made by equilateral triangles. Under such assumptions, if the problem is coercive and the diffusive and convective coefficients are regular enough, then the proposed preconditioned matrix sequences exhibit a strong eigenvalue clustering at unity, the preconditioning matrix sequence and the original matrix sequence are spectrally equivalent, and under the constant coefficients assumption, the eigenvector matrices have a mild conditioning. The obtained results allow to prove the conjugate gradient optimality and the generalized minimal residual quasi‐optimality in the case of structured uniform meshes. The interest of such a study relies on the observation that automatic grid generators tend to construct equilateral triangles when the mesh is fine enough. Numerical tests, both on the model setting and in the non‐structured case, show the effectiveness of the proposal and the correctness of the theoretical findings. Copyright © 2014 John Wiley & Sons, Ltd.     

Block preconditioners for linear systems arising from multiscale collocation with compactly supported RBFs

Symmetric collocation methods with RBFs allow approximation of the solution of a partial differential equation, even if the right‐hand side is only known at scattered data points, without needing to generate a grid. However, the benefit of a guaranteed symmetric positive definite block system comes at a high computational cost. This cost can be alleviated somewhat by considering compactly supported RBFs and a multiscale technique. But the condition number and sparsity will still deteriorate with the number of data points. Therefore, we study certain block diagonal and triangular preconditioners. We investigate ideal preconditioners and determine the spectra of the preconditioned matrices before proposing more practical preconditioners based on a restricted additive Schwarz method with coarse grid correction. Numerical results verify the effectiveness of the preconditioners. Copyright © 2015 John Wiley & Sons, Ltd.     

Tuned preconditioners for inexact two‐sided inverse and Rayleigh quotient iteration

Convergence results are provided for inexact two‐sided inverse and Rayleigh quotient iteration, which extend the previously established results to the generalized non‐Hermitian eigenproblem and inexact solves with a decreasing solve tolerance. Moreover, the simultaneous solution of the forward and adjoint problem arising in two‐sided methods is considered, and the successful tuning strategy for preconditioners is extended to two‐sided methods, creating a novel way of preconditioning two‐sided algorithms. Furthermore, it is shown that inexact two‐sided Rayleigh quotient iteration and the inexact two‐sided Jacobi‐Davidson method (without subspace expansion) applied to the generalized preconditioned eigenvalue problem are equivalent when a certain number of steps of a Petrov–Galerkin–Krylov method is used and when this specific tuning strategy is applied. Copyright © 2014 John Wiley & Sons, Ltd.     

低速湍流模拟的预处理技术研究

本文开展低速湍流的预处理技术研究. 该预处理技术采用守恒型变量及主控方程与湍流方程相耦合的隐式求解方法, 并为确保迭代求解稳定性, 发展了合理的参考马赫数定义、双时间步无矩阵方法迭代求解形式以及湍流源项隐式处理方法等, 从而真正实现全速湍流软件平台统一形式. 在喷管、翼型和方柱等低速湍流数值模拟中, 本文方法正确刻画了流场结构特征, 计算与理论、实验等相关结果符合较好, 具有很强的迭代收敛性和结果精度.     

Boundary element preconditioners for a hypersingular integral equation on an interval

We propose an almost optimal preconditioner for the iterative solution of the Galerkin equations arising from a hypersingular integral equation on an interval. This preconditioning technique, which is based on the single layer potential, was already studied for closed curves [11,14]. For a boundary element trial space, we show that the condition number is of order (1 + | log h _min|)², where h _min is the length of the smallest element. The proof requires only a mild assumption on the mesh, easily satisfied by adaptive refinement algorithms.     

Iterative solution of a coupled mixed and standard Galerkin discretization method for elliptic problems

In this paper, we consider approximation of a second‐order elliptic problem defined on a domain in two‐dimensional Euclidean space. Partitioning the domain into two subdomains, we consider a technique proposed by Wieners and Wohlmuth [9] for coupling mixed finite element approximation on one subdomain with a standard finite element approximation on the other. In this paper, we study the iterative solution of the resulting linear system of equations. This system is symmetric and indefinite (of saddle‐point type). The stability estimates for the discretization imply that the algebraic system can be preconditioned by a block diagonal operator involving a preconditioner for H (div) (on the mixed side) and one for the discrete Laplacian (on the finite element side). Alternatively, we provide iterative techniques based on domain decomposition. Utilizing subdomain solvers, the composite problem is reduced to a problem defined only on the interface between the two subdomains. We prove that the interface problem is symmetric, positive definite and well conditioned and hence can be effectively solved by a conjugate gradient iteration. Copyright © 2001 John Wiley & Sons, Ltd.     

Strengthened Cauchy–Bunyakowski–Schwarz inequality for a three‐dimensional elasticity system

The constant γ of the strengthened Cauchy–Bunyakowski–Schwarz (CBS) inequality plays a fundamental role in the convergence rate of multilevel iterative methods. The main purpose of this work is to give an estimate of the constant γ for a three‐dimensional elasticity system. The theoretical results obtained are practically important for the successful implementation of the finite element method to large‐scale modelling of complicated structures as they allow us to construct optimal order algebraic multilevel iterative solvers for a wide class of real‐life elasticity problems. Copyright © 2001 John Wiley & Sons, Ltd.     

The structure of the boundary element matrix for the three-dimensional Dirichlet problem in elasticity

The algebraic properties of the matrix arising for the three-dimensional Dirichlet problem for Lamé equations in a rotational domain by the boundary element method are considered. The use of the special basis leads to a matrix having a block structure with sparse blocks. The possible strategies for the efficient solution of the above problem are discussed. © 1998 John Wiley & Sons, Ltd.     

Iterative solution of panel method discretizations for potential flow problems. The modal multipolar preconditioning

The iterative solution of linear systems arising from panel method discretization of three‐dimensional (3D) exterior potential problems coming mainly from aero‐hydrodynamic engineering problems, is discussed. An original preconditioning based on an approximate eigenspace decomposition is proposed, which corrects bad conditioning arising from a pair of surfaces that are very close to each other, which is a very common situation in slender wings and other aerodynamic profiles. This preconditioning has been tested with the standard Bi‐conjugate gradient (Bi‐CG) and conjugate gradient squared (CGS) iterative methods. Copyright © 2000 John Wiley & Sons, Ltd.