scholarly journals Computational strategies for surface fitting using thin plate spline finite element methods

2013 ◽  
Vol 54 ◽  
pp. 56 ◽  
Author(s):  
Daryl Matthew Kempthorne ◽  
Ian W Turner ◽  
John A Belward
Keyword(s):  
Finite Element ◽  
Thin Plate ◽  
Finite Element Methods ◽  
Surface Fitting ◽  
Thin Plate Spline ◽  
Spline Finite Element

A Fast Acquisition System for Large-Scale Optical Microscopic Integrated Circuit Chip Images Based on Thin Plate Spline

2013 ◽  
Vol 303-306 ◽  
pp. 1629-1634
Author(s):  
Xu Zhang ◽  
Xi Chen ◽  
Li Xin Wei ◽  
Hong Tu Ma ◽  
Hua Han
Keyword(s):  
Thin Plate ◽  
Integrated Circuit ◽  
Large Scale ◽  
Surface Fitting ◽  
Optical Microscope ◽  
Thin Plate Spline ◽  
Acquisition System ◽  
Acquisition Time ◽  
Fast Acquisition ◽  
Auto Focusing

When large-scale images acquisition conducted on an Integrated Circuit (IC) chip by using an optical microscope, multi-layer routing structure and transparent inter-layer dielectric of IC chips can interfere with auto-focusing of an optical microscope, which significantly increases the images’ acquisition time. To solve the forementioned problems, a fast acquisition system is proposed based on surface fitting. First of all, we obtain focus plane height of multiple scattered points through pre-acquisition. Then, the surface fitting method, with Thin Plate Spline (TPS) model is applied, to get the height of the rest points. Thus the system can acquire correct surface-layer images of an IC chip without background interference. The experimental results suggest that the proposed technology is highly superior to manual acquisition system and auto-focusing based acquisition system in acquisition accuracy and speed, and it also decreases the amount of manual workload by 70%-80%.

scholarly journals Error indicators and adaptive refinement of the discrete thin plate spline smoother

2019 ◽  
Vol 60 ◽  
pp. C33-C51
Author(s):  
Lishan Fang
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Thin Plate ◽  
Thin Plate Spline ◽  
Adaptive Refinement ◽  
Fine Grid ◽  
Computational Costs ◽  
Uniform Grids ◽  
Error Indicators ◽  
Element Method

The discrete thin plate spline is a data fitting and smoothing technique for large datasets. Current research only uses uniform grids for this discrete smoother, which may require a fine grid to achieve a certain accuracy. This leads to a large system of equations and high computational costs. Adaptive refinement adapts the precision of the solution to reduce computational costs by refining only in sensitive regions. The error indicator is an essential part of the adaptive refinement as it identifies whether certain regions should be refined. Error indicators are well researched in the finite element method, but they might not work for the discrete smoother as data may be perturbed by noise and not uniformly distributed. Two error indicators are presented: one computes errors by solving an auxiliary problem and the other uses the bounds of the finite element error. Their performances are evaluated and compared with 2D model problems. References H. Chui and A. Rangarajan. A new point matching algorithm for non-rigid registration. Comput. Vis. Image Und., 89 (23): 114141, 2003. doi:10.1016/S1077-3142(03)00009-2. W. F. Mitchell. A comparison of adaptive refinement techniques for elliptic problems. ACM T. Math. Software, 15 (4): 326347, 1989. doi:10.1145/76909.76912. S. Roberts, M. Hegland, and I. Altas. Approximation of a thin plate spline smoother using continuous piecewise polynomial functions. SIAM J. Numer. Anal., 41(1):208234, 2003. doi:10.1137/S0036142901383296. G. Sewell. Analysis of a finite element method. Springer-Verlag, 1985. doi:10.1007/978-1-4684-6331-6. R. Sprengel, K. Rohr, and H. S. Stiehl. Thin-plate spline approximation for image registration. In P. IEEE EMBS, volume 3, pages 11901191. IEEE, 1996. doi:10.1109/IEMBS.1996.652767. L. Stals. Efficient solution techniques for a finite element thin plate spline formulation. J. Sci. Comput., 63(2):374409, 2015. doi:10.1007/s10915-014-9898-x. G. Wahba. Spline models for observational data, volume 59 of CBMS-NSF Regional Conference Series in Applied Mathematics. SIAM, 1990. doi:10.1137/1.9781611970128.

High-Frequency Vibration Analysis of Thin Plate Based on B-Spline Wavelet on Interval Finite Element Method

2016 ◽  
Author(s):  
Jia Geng ◽  
Xingwu Zhang ◽  
Xuefeng Chen ◽  
Xiaofeng Xue
Keyword(s):  
Finite Element ◽  
Dynamic Response ◽  
Dynamic Analysis ◽  
Frequency Domain ◽  
Thin Plate ◽  
Finite Element Methods ◽  
High Frequency ◽  
Numerical Example ◽  
Modal Density ◽  
High Modal Density

For the dynamic analysis of thin plate bending problems, the Finite Element Methods (FEMs) are the most commonly used numerical techniques in engineering. However, due to the deficiency of low computing efficiency and accuracy, the FEMs can’t be directly used to effectively evaluate dynamic analysis of thin plate with high modal density within low-high frequency domain. In order to solve this problem, the Wavelet Finite Element Methods (WFEMs) has been introduced to solve the problem by improving the computing efficiency and accuracy in this paper. Due to the properties of multi-resolution, the WFEMs own excellently high computing efficiency and accuracy for structure analysis. Furthermore, for the destination of predicting dynamic response of thin plate within high frequency domain, this paper introduces the Multi-wavelet element method based on c1 type wavelet thin plate element and a new assembly procedure to significantly promote the calculating efficiency and accuracy which aim at breaking up the limitation of frequency domain when using the existing WFEMs and traditional FEMs. Besides, the numerical studies are applied to certify the validity of the method by predicting state response of thin plate within 0∼1000Hz based on a special numerical example with high modal density. According to the literature, the frequency domain between 0 to 1000Hz contains the low-high frequency domain aiming at the numerical example. The numerical results show excellent agreement with the reference solutions captured by FEM and analytical expressions respectively. Among these, it is noteworthy that the relative errors between the analytical solutions and numerical solution are less than 0.4% when the dynamic response involved with 1000 modes.

Sign in / Sign up

Export Citation Format

Share Document