Boundary knot method for 2D and 3D Helmholtz and convection–diffusion problems under complicated geometry

The boundary knot method (BKM) of very recent origin is an inherently meshless, integration‐free, boundary‐type, radial basis function collocation technique for the numerical discretization of general partial differential equation systems. Unlike the method of fundamental solutions, the use of non‐singular general solution in the BKM avoids the unnecessary requirement of constructing a controversial artificial boundary outside the physical domain. The purpose of this paper is to extend the BKM to solve 2D Helmholtz and convection–diffusion problems under rather complicated irregular geometry. The method is also first applied to 3D problems. Numerical experiments validate that the BKM can produce highly accurate solutions using a relatively small number of knots. For inhomogeneous cases, some inner knots are found necessary to guarantee accuracy and stability. The stability and convergence of the BKM are numerically illustrated and the completeness issue is also discussed. Copyright © 2003 John Wiley & Sons, Ltd.     

关于透视投影逆变换基本方程及有关问题的讨论

对《任意曲线透视投影的逆变换》中作出的以下３项研究结果进行了探讨并提出了不同见解：（１）透视投影的逆变换基本方程；（２）根据长方体上一个矩形的投影确定其长宽高之比；（３）由实体的透视图象准确重建其三维信息。     

Fundamental solutions for half plane with an oblique edge crack

An elastic half plane with an oblique edge crack is considered in this paper. A pair of concentrated forces or point dislocations is assumed to act at an arbitrary point in the half plane. The half plane with an edge crack is first mapped into a unit circle by a rational mapping function so that the following analysis can be carried out on the mapped plane analytically. Then the complex stress functions are derived by separating the whole problem into two parts; one is the principal part corresponding to the infinite plane acted on by concentrated forces or dislocations, the other is the holomorphic part, which can be determined by making use of the property of regularity of complex stress functions. The stress intensity factors of the crack can be calculated with different inclined angles of the crack, and the displacement and stress components at an arbitrary position in the half plane can be expressed explicitly.     

Transient Green’s Tensor for a Layered Solid Half-Space With Different Interface Conditions

Pulsed ultrasonic techniques can be and have been used to examine the interface conditions of a bonded structure. To provide a theoretical basis for such testing techniques we model the structure as a layer on top of a half-space, both of different elastic properties, with various interface bonding conditions. The exact dynamic Green’s tensor for such a structure is explicitly derived from the three-dimensional equations of motion. The final solution is a series. Each term of the series corresponds to a successive arrival of a “generalized ray” and each is a definite line integral along a fixed path which can be easily computed numerically. Willis’ method is used in the derivation. A new scheme of automatic generation of the arrivals and ray paths using combinatorial analysis, along with the summation of the corresponding products of reflection coefficients is presented. A FORTRAN code is developed for computation of the Green’s tensor when both the source and the detector are located on the top surface. The Green’s tensor is then used to simulate displacements due to pulsed ultrasonic point sources of known time waveform. Results show that the interface bonding conditions have a great influence on the transient displacements. For example, when the interface bonding conditions vary, some of the first few head waves and regular reflected rays change polarities and amplitudes. This phenomenon can be used to infer the quality of the interface bond of materials in ultrasonic nondestructive evaluation. In addition the results are useful in the study of acoustic microscopy probes, coatings, and geo-exploration.     

浅谈2000版IS09000族质量管理体系标准的结构与特点

结合对2000年版ISO9000族质量管理体系标准的理解和分析,对标准的结构和特点进行了探讨。     

煤气化联合循环发电示范状况和煤气化工艺对比

煤炭气化已被确认为制取管道煤气或合成气的技术。经多方研究已被工业化规模生产和煤气化联合循环发电所证实。本文评述了煤的基本性质对气化效率的影响，煤气化联合循环发电示范厂现状和各种选定用于煤气化联合循环发电的第二代煤气化方法的对比。本文最后阐述了煤气化联合循环发电用于改造高能耗的以煤、油和天然气为燃料的中小规模电厂的现实性。     

大学计算机基础课程基于分级的专题教学方案探索

大学计算机基础课在高校越来越受到重视,结合目前计算机基础教学的现实情况和分级教学的不足,提出了基于分级的专题教学方案。此教学方案在分级的基础上,增设了"应用技能提高"的专题教学和实践教学,以达到提高学生计算机应用能力的目的。此方案有利于保留分级教学的优势,改进其不足;有利于因材施教、提高学生的学习兴趣、发挥教师特长。但是在实施过程中还存在若干问题需要我们进一步研究。     

计算机公共课教学现状及对策研究

通过问卷调查和计算机统计软件,科学分析了现状差异。根据各专业学生对计算机课程的兴趣、计算机基础和各专业对计算机公共课程的要求的差异,针对性采取了教学改革对策:针对不同学科制定不同的教学计划与内容;开发课程教学网站,使课堂教学与网络教学紧密结合;对不同层次的学生分层管理;由"以教师为主"向"学生自主学习"教学模式的转变,收到较好的教学效果。     

一类带谱参数的奇异Sturm-Liouville算子特征的渐近分析工

研究了一类具有转换条件且在一个边界条件中带谱参数的奇异Sturm—Liouville问题．将上述问题的基本解的渐近分析,转化为考虑定义在适当的Hilbert空间H中的一个线性算子A的基本解的渐近分析,同时推导出该奇异的Sturm-Liouville算子A的基本解的渐近式．     

双层芯色散补偿光子晶体光纤

为了抑制通信系统中脉冲的展宽,根据色散补偿理论,提出了一种由单一石英材料制成的双层芯光子晶体光纤(DCCPCF). 该光纤的色散值在155μm处可达到-6000ps/(nm〖DK〗•km). 理论分析表明,在传输过程中内芯基模和外芯缺陷模以相位匹配波长为临界状态,在内芯与外芯之间相互交替传输,并在匹配波长处因模式发生强烈耦合而引起折射率产生大幅度波动. 通过对结构参数d1、d2变化的情况下色散曲线的扰动情况进行分析,可为实际制备工作提供一定的理论指导.