RBFs with Spatially Variable Shape Parameters and Optimized Knot Locations
Radial Basis Function (RBF) with spatially variable shape parameters has been studied in attempt to improve the stability of the interpolation. The RBF interpolation, as we know, is quite efficient and has a wide range of application. However, the RBF interpolation suffers from a contradiction between accuracy and stability, which can be expressed in a form similar to the Uncertainty Principle in quantum mechanics . For global RBFs, the shape of the function is usually controlled by a parameter c. A proper value of c is crucial importance for the stability and accuracy of RBF interpolation, as the condition number of the interpolant matrix may varies exponentially as the shape parameter changes. On the other hand, the exponentially better accuracy can be obtained by choosing a proper c . In the literatures, most RBF researchers emphasize more on accuracy than on stability. For engineering application, however, the stability of the RBF interpolation should be more important, as the relative error can not be evaluated without an exact solution, which is often unavailable for practical problems. In this paper we study the sensitiveness of the condition number of the interpolant matrix to the parameter c. One way suggested in many literatures to circumvent the ill-condition problem is to use spatially variable shape parameter . Although using spatially variable shape parameter may lead to singular interpolation matrix , the non-singularity of an interpolation matrix can be guaranteed by some special parameter variation strategies.The Runge phenomenon, which is best known in high-order polynomial interpolation, also may appear in the RBF interpolation . Large interpolation error often occurs at locations near the boundary. For engineering application, however, accurate interpolation near the boundary is important. Further more, as we know, oscillatory behavior is usually seen in high order Lagrange interpolations when the original function has a jump discontinuity. This is called the Gibbs Phenomenon. The RBF interpolation, especially the global ones, also suffers from the Gibbs Phenomenon. In fact, the function with jump discontinuity can be considered as a special case of the ones that have a large value of the derivative. By varying the shape parameters of the RBF interpolation, both of the Runge phenomenon and the Gibbs Phenomenon can be suppressed.To circumvent the ill-condition problem, many methods have been proposed . These methods can be sorted into seven classes:1.simple preconditioners 2. variable shape parameter 3. transform the global basis function into a truncated basis function 4. the multi-zone method 5. optimization of knot location 6. multilevel approximation schemes 7. block substructuring and partitioning The concept of variable shape parameters in the RBF interpolation has been proposed by many researchers, such as E. J. Kansa , M. D. Buhmann, et al. The main idea is to use different values of shape parameters for the RBFs that with different knot locations. The shape parameters are determined according to the density of RBF knots in a local area. In the optimization of knot location method, the interpolation points are adjusted to follow the peak of the shock wave. The optimization may yield coefficient matrix with lower condition number and better accuracy with even a small number of interpolation points.The methods of variable shape parameter and the optimization of knot location were combined in this paper. The error bounds and the stability of the combined approach were studied in detail. Mathematical proofs for the convergence and stability were presented. In order to find a stable and efficient interpolation scheme, several kinds of 3D RBFs and parameter variation strategies were compared in the numerical examples. Results show that the combined approach is stable and possesses high accuracy. Moreover, in contrast with conventional RBF interpolation, additional interpolation points can be added to improve the accuracy without much loss of stability in our method.The Boundary Face Method  has been combined with the Dual Reciprocal Method to solve 3-D inhomogeneous potential problems. We call the combined method as the Dual Reciprocal Boundary Face Method (DRBFM). In the DRBFM, the combined interpolation approach has been implemented. Numerical examples which demonstrate the stability and accuracy are also presented.......
【作者单位】: State Key Laboratory of Advanced Design and Manufacturing for Vehicle Body,Hunan University,Changsha,410082 China
, State Key Laboratory of Advanced Design and Manufacturing for Vehicle Body,Hunan University,Changsha,410082 China
【关 键 词】: RBFs with Spatially Variable Shape Parameters and Optimized Knot Locations
【会议名称】: 3rd Asia-Pacific international conference on computational methods in engineering
【会议组织】: State Key Laboratory of Advanced Design and Manufacturing for Vehicle Body,Hunan University,Changsha,410082 China;State Key Laboratory of Advanced Design and Manufacturing for Vehicle Body,Hunan University,Changsha,410082 China;
【上篇论文】: 外文会议 - Process Algebra for Event-Driven Runtime Verification: A Case Study of Wireless Network Management
【下篇论文】: 外文会议 - Game based technology to enhance the learning of history and cultural heritage
目的:肿瘤化疗是治疗肿瘤的重要手段之一,它大大提高了一些肿瘤治愈的可能性.然而,肿瘤细胞耐药(Drug resistance)往往导致化疗的失败.肿瘤细胞对一种药物耐药后,往往也会对不同化学结构和不同作用机制的药物同时耐药,这就是多药耐药(Multidrug resistance).目前,研究MDR的机理成为肿瘤研究的主攻方向,其中由多药耐药基因(mdrl)编码的分子量为170kD的P糖蛋白(P- [肿瘤化疗,盐酸千金藤碱,K562细胞,ADR细胞,多药耐药性,P糖蛋白表达]......
目的:FFP经过去白、血液辐照仪辐照去除或灭活白细胞后,测定凝血功能检测指标.评价去白及辐照对凝血系统中各种凝血因子的影响.方法:1.取泸州市中心血站采集的30例健康献血者的FFP 30袋,每袋50ml,采用随机区组单盲(检测者不清楚分组情况)设计.每袋血浆分为3个实验组为一个区组,共30个区组,每个区组内有三个检测样本,共90个分析样本.每次实验,将6例FFP于冰箱中取出解冻后,每例FFP经一次 [新鲜冰冻血浆,白细胞过滤,射线辐照,凝血因子]......
本文研究目的:将冠状动脉造影(CAG)结果与心电图(ECG)变化对比分析,探讨心电图ST/T改变在判断急性冠脉综合征(ACS)患者冠脉血管病变中的应用价值. 研究方法:回顾分析2004年5月至2006年12月以"ACS"收入我院心脏科的患者310例,其中男性215例,女性95例,年龄30-80岁(平均年龄57.60±10.46岁).所有患者均进行CAG和ECG检查.冠状动脉狭窄≥50％有意义.心电 [急性冠脉综合征,冠状动脉造影,心电图,血管病变]......
- Effects of different doses of allergen on acute and subacute mouse models of asthma
Objectives:We aimed to establish ovalbumin (OVA)-induced acute and sub-acute mouse models ofasthma and evaluate effects of intranasal inhalation of various doses of OVA on airways inflammation,remodel [哮喘,发病机制,炎性细胞,动物模型]......
目的：根据不同病理类型及相关亚型甲状腺癌的临床生物学特征，结合声像图特点，创建甲状腺癌、甲状腺乳头状癌及甲状腺癌颈部转移淋巴结的超声分型。同时，将超声应用于甲状腺癌的临床分期，实现对甲状腺癌患者术前合理评估、精确分期及个体化治疗。rn 方法：收集有完整病例记录、有完整的甲状腺肿瘤超声图像及明确病理诊断的甲状腺癌病例407例，通过回顾性研究，计算超声诊断甲状腺癌的准确率，并分析比较不同病理类型及相关 [甲状腺癌,超声诊断,临床分期,病理类型,个体化治疗]......
- Treatment of frozen shoulder by hydraulic distention and manipulation under dynamic arthrography of shoulder joint
Objective The investigation was to evaluate the efficiency of the frozen shoulder treated by hydraulic distention and manipulation under dynamic arthrography of shoulder joint, and analyze the influen [Treatment,frozen shoulder,hydraulic distention,manipulation under,shoulder joint,冻结肩]......
- 中药材商品规格等级标准研制进展 (詹志来,黄璐琦,何雅莉,金艳,杨光)
Ⅰ自然定律——不可抗拒力rn 自古以来，宇宙万物皆由大自然定律衍生，人类若然浪费时光及暴殄天物，将会是罪过的，及破坏人类文明的进程。相反，人类若能善用地球资源，将可建立巩固的平台，为未来世代向前发展提供动力。rn 作为创建楼宇及城市，也许该说是环境建设的专业人士，对于依从宇宙自然定律，是不置疑的责任，亦是良知使然，我们必须要时刻提醒自我的天赋的责任。rn 楼宇的设计师(建筑师、工程师、规划师等)所 [楼宇生命力,楼宇设计,可持续建筑,生命周期,太阳能]......
- Reworking Package on Package components
In 2007 Lead Free Package POP (Package on Package) will be a major new device to hit the streets this year and will challenge many to re-evaluate their soldering and rework products/processes.The impl [POP,package on package,Reworking,components]......