A comparison of transformation methods for evaluating two‐dimensional weakly singular integrals

Accurate numerical evaluation of integrals arising in the boundary element method is fundamental to achieving useful results via this solution technique. In this paper, a number of techniques are considered to evaluate the weakly singular integrals which arise in the solution of Laplace's equation in three dimensions and Poisson's equation in two dimensions. Both are two‐dimensional weakly singular integrals and are evaluated using (in a product fashion) methods which have recently been used for evaluating one‐dimensional weakly singular integrals arising in the boundary element method. The methods used are based on various polynomial transformations of conventional Gaussian quadrature points where the transformation polynomial has zero Jacobian at the singular point. Methods which split the region of integration into sub‐regions are considered as well as non‐splitting methods. In particular, the newly introduced and highly accurate generalized composite subtraction of singularity and non‐linear transformation approach (GSSNT) is applied to various two‐dimensional weakly singular integrals. A study of the different methods reveals complex relationships between transformation orders, position of the singular point, integration kernel and basis function. It is concluded that the GSSNT method gives the best overall results for the two‐dimensional weakly singular integrals studied. Copyright © 2002 John Wiley & Sons, Ltd.     

波动方程数值模拟的隐式差分法

在有限差分波动方程数值模拟中,通常采用高阶差分方法来提高空间导数的数值逼近精度,以实现降低数值频散,提高数值模拟精度的目的。首先对差分频散进行了理论分析;然后讨论了估计一阶空间导数的隐式差分格式,并与通常采用的高阶精度显式差分格式进行了对比分析,结果表明,隐式差分格式能够在更宽的波数范围使差分频散控制在可接受的水平,如8阶精度的显式差分格式所适应的波数带宽约为O．55kmax,而隐式差分格式所适应的波数带宽约为0．7kmax;最后通过模型试算,对隐式差分格式的有效性进行了验证。模拟结果表明,用隐式差分格式在一定程度上降低了差分频散,提高了模拟精度。     

A multigrid accelerated hybrid unstructured mesh method for 3D compressible turbulent flow

 A cell vertex finite volume method for the solution of steady compressible turbulent flow problems on unstructured hybrid meshes of tetrahedra, prisms, pyramids and hexahedra is described. These hybrid meshes are constructed by firstly discretising the computational domain using tetrahedral elements and then by merging certain tetrahedra. A one equation turbulence model is employed and the solution of the steady flow equations is obtained by explicit relaxation. The solution process is accelerated by the addition of a multigrid method, in which the coarse meshes are generated by agglomeration, and by parallelisation. The approach is shown to be effective for the simulation of a number of 3D flows of current practical interest. Sponsored by The Research Council of Norway, project number 125676/410 Dedicated to the memory of Prof. Mike Crisfield, a respected colleague     

Mechanical properties of polyethylene mixtures crystallized under high pressure

The mechanical properties of a medium molecular weight polyethylene (MMW‐PE) and an ultrahigh molecular weight PE (UHMW‐PE) binary mixture with different weight fractions crystallized from the melt at 0.1 and 450 MPa were studied. The tensile modulus, yield stress, and strain were obtained as a function of the weight fractions in the PE mixtures at 25 and 85°C. The tensile modulus in the sample crystallized at 0.1 MPa decreased from 1.5 GPa of pure MMW‐PE to about 0.4 GPa of pure UHMW‐PE with the UHMW‐PE content but it did not decrease with the UHMW‐PE in the sample crystallized at 450 MPa in testing at 25°C. A decreasing rate of the storage modulus E′ of UHMW‐PE in a dynamic measurement for the sample crystallized at 0.1 MPa with the temperature is larger than that of the sample crystallized at 450 MPa. These experimental facts are interpreted in relation to the molecular motion and crystallinity of the sample. © 2003 Wiley Periodicals, Inc. J Appl Polym Sci 87: 1962–1968, 2003     

A note on the Gauss-Jacobi quadrature formulae for singular integral equations of the second kind

A fast and efficient numerical method based on the Gauss-Jacobi quadrature is described that is suitable for solving Fredholm singular integral equations of the second kind that are frequently encountered in fracture and contact mechanics. Here we concentrate on the case when the unknown function is singular at both ends of the interval. Quadrature formulae involve fixed nodal points and provide exact results for polynomials of degree 2n − 1, where n is the number of nodes. Finally, an application of the method to a plane problem involving complete contact is presented.     

带参数的一阶脉冲微分方程边值问题

利用上下解和单调迭代法。讨论了带参数的一阶脉冲微分方程。获得了单边Lipschitz条件下这类方程边值问题的解的存在性。     

声光效应拉曼-内斯方程矩阵级数解法及声光调制器优化设计

提出一种求解正常声光相互作用拉曼 内斯 (Raman Nath)方程的矩阵级数解法 ,该解法直观方便且具有普遍性。计算结果表明 ,对Q =4 1π ,Bragg衍射的效率只有 97 5 % ;对非对称入射 ,以往的Raman Nath近似解误差较大 ;指出提高Bragg衍射效率的有效途径在于提高声光频率比并给出计算声光器件最优长度的计算公式。     

连续梁的简便计算

利用三转角方程，对连续梁的内力进行精确的计算，该方法简捷明了，便于应用。     

压缩式致冷设备的电子宽温域多功能控制

设计并研制了一种用于压缩式致冷设备的电子式定温域多功能控制装置。它除具有控温范围宽、精度高、控温参数易调等优点外，还实现了低成本的温度显示、半自动除霜控制、加电延时保护、过欠压保护等功能。全部采用无触点控制方式，有良好的性能／价格比。