A robust adaptive algebraic multigrid linear solver for structural mechanics

The numerical simulation of structural mechanics applications via finite elements usually requires the solution of large-size and ill-conditioned linear systems, especially when accurate results are sought for derived variables interpolated with lower order functions, like stress or deformation fields. Such task represents the most time-consuming kernel in commercial simulators; thus, it is of significant interest the development of robust and efficient linear solvers for such applications. In this context, direct solvers, which are based on LU factorization techniques, are often used due to their robustness and easy setup; however, they can reach only superlinear complexity, in the best case, thus, have limited applicability depending on the problem size. On the other hand, iterative solvers based on algebraic multigrid (AMG) preconditioners can reach up to linear complexity for sufficiently regular problems but do not always converge and require more knowledge from the user for an efficient setup. In this work, we present an adaptive AMG method specifically designed to improve its usability and efficiency in the solution of structural problems. We show numerical results for several practical applications with millions of unknowns and compare our method with two state-of-the-art linear solvers proving its efficiency and robustness.Comment: 50 pages, 16 figures, submitted to CMAM

Algorithms and data structures for adaptive multigrid elliptic solvers

Adaptive refinement and the complicated data structures required to support it are discussed. These data structures must be carefully tuned, especially in three dimensions where the time and storage requirements of algorithms are crucial. Another major issue is grid generation. The options available seem to be curvilinear fitted grids, constructed on iterative graphics systems, and unfitted Cartesian grids, which can be constructed automatically. On several grounds, including storage requirements, the second option seems preferrable for the well behaved scalar elliptic problems considered here. A variety of techniques for treatment of boundary conditions on such grids are reviewed. A new approach, which may overcome some of the difficulties encountered with previous approaches, is also presented

Adaptive restoration of text images containing touching and broken characters

For document processing systems, automated data entry is generally performed by optical character recognition (OCR) systems. To make these systems practical, reliable OCR systems are essential. However, distortions in document images cause character recognition errors, thereby, reducing the accuracy of OCR systems. In document images, most OCR errors are caused by broken and touching characters. This thesis presents an adaptive system to restore text images distorted by touching and broken characters. The adaptive system uses the distorted text image and the output from an OCR system to generate the training character image. Using the training image and the distorted image, the system trains an adaptive restoration filter and then uses the trained filter to restore the distorted text image. To demonstrate the performance of this technique, it was applied to several distorted images containing touching or broken characters. The results show that this technique can improve both pixel and OCR accuracy of distorted text images containing touching or broken characters

Color image quality measures and retrieval

The focus of this dissertation is mainly on color image, especially on the images with lossy compression. Issues related to color quantization, color correction, color image retrieval and color image quality evaluation are addressed. A no-reference color image quality index is proposed. A novel color correction method applied to low bit-rate JPEG image is developed. A novel method for content-based image retrieval based upon combined feature vectors of shape, texture, and color similarities has been suggested. In addition, an image specific color reduction method has been introduced, which allows a 24-bit JPEG image to be shown in the 8-bit color monitor with 256-color display. The reduction in download and decode time mainly comes from the smart encoder incorporating with the proposed color reduction method after color space conversion stage. To summarize, the methods that have been developed can be divided into two categories: one is visual representation, and the other is image quality measure. Three algorithms are designed for visual representation: (1) An image-based visual representation for color correction on low bit-rate JPEG images. Previous studies on color correction are mainly on color image calibration among devices. Little attention was paid to the compressed image whose color distortion is evident in low bit-rate JPEG images. In this dissertation, a lookup table algorithm is designed based on the loss of PSNR in different compression ratio. (2) A feature-based representation for content-based image retrieval. It is a concatenated vector of color, shape, and texture features from region of interest (ROI). (3) An image-specific 256 colors (8 bits) reproduction for color reduction from 16 millions colors (24 bits). By inserting the proposed color reduction method into a JPEG encoder, the image size could be further reduced and the transmission time is also reduced. This smart encoder enables its decoder using less time in decoding. Three algorithms are designed for image quality measure (IQM): (1) A referenced IQM based upon image representation in very low-dimension. Previous studies on IQMs are based on high-dimensional domain including spatial and frequency domains. In this dissertation, a low-dimensional domain IQM based on random projection is designed, with preservation of the IQM accuracy in high-dimensional domain. (2) A no-reference image blurring metric. Based on the edge gradient, the degree of image blur can be measured. (3) A no-reference color IQM based upon colorfulness, contrast and sharpness

Space Mapping With Adaptive Response Correction for Microwave Design Optimization

Output space mapping is a technique introduced to enhance the robustness of the space-mapping optimization process in case the space-mapped coarse model cannot provide sufficient matching with the fine model. The technique often works very well; however, in some cases it fails. Especially in the microwave area where the typical model response (e.g., 21) is a highly nonlinear function of the free parameter (e.g., frequency), the output spacemapping correction term may actually increase the mismatch between the surrogate and fine models for points other than the one at which the term was calculated, as in the surrogate model optimization process. In this paper, an adaptive response correction scheme is presented to work in conjunction with space-mapping optimization algorithms. This technique is designed to alleviate the difficulties of the standard output space mapping by adaptive adjustment of the response correction term according to the changes of the space-mapped coarse model response. Examples indicate the robustness of our approach