An Iterative Two-Grid Method of A Finite Element PML Approximation for the Two Dimensional Maxwell Problem

2012 ◽  
Vol 4 (2) ◽  
pp. 175-189
Author(s):  
Chunmei Liu ◽  
Shi Shu ◽  
Yunqing Huang ◽  
Liuqiang Zhong ◽  
Junxian Wang
Keyword(s):  
Finite Element ◽  
Saddle Point ◽  
Grid Method ◽  
Variational Problems ◽  
Auxiliary System ◽  
Point System ◽  
Saddle Point System ◽  
System 2 ◽  
System 1 ◽  
Coarse Space

AbstractIn this paper, we propose an iterative two-grid method for the edge finite element discretizations (a saddle-point system) of Perfectly Matched Layer(PML) equations to the Maxwell scattering problem in two dimensions. Firstly, we use a fine space to solve a discrete saddle-point system of H(grad) variational problems, denoted by auxiliary system 1. Secondly, we use a coarse space to solve the original saddle-point system. Then, we use a fine space again to solve a discrete H(curl)-elliptic variational problems, denoted by auxiliary system 2. Furthermore, we develop a regularization diagonal block preconditioner for auxiliary system 1 and use H-X preconditioner for auxiliary system 2. Hence we essentially transform the original problem in a fine space to a corresponding (but much smaller) problem on a coarse space, due to the fact that the above two preconditioners are efficient and stable. Compared with some existing iterative methods for solving saddle-point systems, such as PMinres, numerical experiments show the competitive performance of our iterative two-grid method.

Quantum Hall effect in a saddle-point system

1998 ◽  
Vol 2 (1-4) ◽  
pp. 523-526
Author(s):  
M.V Budantsev ◽  
Z.D Kvon ◽  
A.G Pogosov ◽  
E.B Olshanetskii ◽  
D.K Maude ◽  
...  
Keyword(s):  
Saddle Point ◽  
Hall Effect ◽  
Quantum Hall Effect ◽  
Quantum Hall ◽  
Point System ◽  
Saddle Point System

scholarly journals Improving the Solution of Least Squares Support Vector Machines with Application to a Blast Furnace System

2012 ◽  
Vol 2012 ◽  
pp. 1-12 ◽  
Author(s):  
Ling Jian ◽  
Shuqian Shen ◽  
Yunquan Song
Keyword(s):  
Blast Furnace ◽  
Support Vector Machines ◽  
Saddle Point ◽  
Least Squares ◽  
Null Space ◽  
Support Vector ◽  
Point System ◽  
Trend Prediction ◽  
Vector Machines ◽  
Saddle Point System

The solution of least squares support vector machines (LS-SVMs) is characterized by a specific linear system, that is, a saddle point system. Approaches for its numerical solutions such as conjugate methods Sykens and Vandewalle (1999) and null space methods Chu et al. (2005) have been proposed. To speed up the solution of LS-SVM, this paper employs the minimal residual (MINRES) method to solve the above saddle point system directly. Theoretical analysis indicates that the MINRES method is more efficient than the conjugate gradient method and the null space method for solving the saddle point system. Experiments on benchmark data sets show that compared with mainstream algorithms for LS-SVM, the proposed approach significantly reduces the training time and keeps comparable accuracy. To heel, the LS-SVM based on MINRES method is used to track a practical problem originated from blast furnace iron-making process: changing trend prediction of silicon content in hot metal. The MINRES method-based LS-SVM can effectively perform feature reduction and model selection simultaneously, so it is a practical tool for the silicon trend prediction task.

A New Two-Grid Method for Expanded Mixed Finite Element Solution of Nonlinear Reaction Diffusion Equations

2017 ◽  
Vol 9 (3) ◽  
pp. 757-774 ◽  
Author(s):  
Shang Liu ◽  
Yanping Chen
Keyword(s):  
Finite Element ◽  
Mixed Finite Element ◽  
Grid Method ◽  
Reaction Diffusion ◽  
Reaction Diffusion Equations ◽  
Diffusion Equations ◽  
Reaction Diffusion Equation ◽  
Nonlinear Reaction ◽  
Expanded Mixed Finite Element ◽  
Coarse Space

AbstractIn the paper, we present an efficient two-grid method for the approximation of two-dimensional nonlinear reaction-diffusion equations using a expanded mixed finite-element method. We transfer the nonlinear reaction diffusion equation into first order nonlinear equations. The solution of the nonlinear system on the fine space is reduced to the solutions of two small (one linear and one non-linear) systems on the coarse space and a linear system on the fine space. Moreover, we obtain the error estimation for the two-grid algorithm. It is showed that coarse space can be extremely coarse and achieve asymptotically optimal approximation as long as the mesh sizes satisfy. An numerical example is also given to illustrate the effectiveness of the algorithm.

New homogenization method for diffusion equations

2018 ◽  
Vol 33 (2) ◽  
pp. 85-93 ◽  
Author(s):  
Yuri A. Kuznetsov
Keyword(s):  
Saddle Point ◽  
Diffusion Coefficients ◽  
Diffusion Problem ◽  
Homogenization Method ◽  
Diffusion Equations ◽  
Point System ◽  
Algebraic Problem ◽  
Saddle Point System ◽  
Saddle Point Matrix ◽  
Diffusion Problems

Abstract In this paper, we propose and investigate a new homogenization method for diffusion problems in domains with multiple inclusions with large values of diffusion coefficients. The diffusion problem is approximated by the P1-finite element method on a triangular mesh. The underlying algebraic problem is replaced by a special system with a saddle point matrix. For the solution of the saddle point system we use the typical asymptotic expansion. We prove the error estimates and convergence of the expanded solutions. Numerical results confirm the theoretical conclusions.

scholarly journals Milk Production, Body Weight, Body Condition Score, Activity, and Rumination of Organic Dairy Cattle Grazing Two Different Pasture Systems Incorporating Cool- and Warm-Season Forages

Animals ◽  
2021 ◽  
Vol 11 (2) ◽  
pp. 264
Author(s):  
Kathryn E. Ritz ◽  
Bradley J. Heins ◽  
Roger D. Moon ◽  
Craig C. Sheaffer ◽  
Sharon L. Weyers
Keyword(s):  
Body Weight ◽  
Milk Production ◽  
Body Condition Score ◽  
Warm Season ◽  
Cool Season ◽  
Organic Dairy ◽  
Condition Score ◽  
Annual Grasses ◽  
System 2 ◽  
System 1

Organic dairy cows were used to evaluate the effect of two organic pasture production systems (temperate grass species and warm-season annual grasses and cool-season annuals compared with temperate grasses only) across two grazing seasons (May to October of 2014 and 2015) on milk production, milk components (fat, protein, milk urea nitrogen (MUN), somatic cell score (SCS)), body weight, body condition score (BCS), and activity and rumination (min/day). Cows were assigned to two pasture systems across the grazing season at an organic research dairy in Morris, Minnesota. Pasture System 1 was cool-season perennials (CSP) and Pasture System 2 was a combination of System 1 and warm-season grasses and cool-season annuals. System 1 and System 2 cows had similar milk production (14.7 and 14.8 kg d−1), fat percentage (3.92% vs. 3.80%), protein percentage (3.21% vs. 3.17%), MUN (12.5 and 11.5 mg dL−1), and SCS (4.05 and 4.07), respectively. Cows in System 1 had greater daily rumination (530 min/day) compared to cows in System 2 (470 min/day). In summary, warm-season annual grasses may be incorporated into grazing systems for pastured dairy cattle.

scholarly journals Comparison of Three Fungicide Spray Advisories for Lettuce Downy Mildew

Plant Disease ◽  
2001 ◽  
Vol 85 (8) ◽  
pp. 895-900 ◽  
Author(s):  
B. M. Wu ◽  
K. V. Subbarao ◽  
A. H. C. van Bruggen ◽  
S. T. Koike
Keyword(s):  
Downy Mildew ◽  
Drip Irrigation ◽  
Leaf Wetness ◽  
Lettuce Downy Mildew ◽  
Advisory System ◽  
System 2 ◽  
Forecasting System ◽  
Low Incidence ◽  
System 1 ◽  
First Time

Lettuce growers in coastal California have relied mainly on protective fungicide sprays to control downy mildew. Thus, timing of sprays before infection is critical for optimal results. A leaf-wetness-driven, infection-based advisory system, previously developed, did not always perform satisfactorily. In this study, the advisory system was modified by incorporating a pathogen survival component (system 1) or both survival and sporulation components (system 2). These systems were then evaluated in commercial lettuce fields in coastal California during 1996-1998. Three or four treatments were carried out in each field: (i) no spray; (ii) sprays as scheduled by the growers; (iii) sprays following modified system 1; and (iv) sprays following the original advisory system (1996) or modified system 2 (1998). Downy mildew incidence was evaluated every 2 to 9 days. In fields with drip irrigation, the number of fungicide applications was reduced by one or two regardless of the advisory system used compared to the grower's calendar-based schedule, although one unnecessary spray was recommended in 1996 at Soledad and 1997 at Salinas. Under all three systems, disease levels were low (incidence <25% and about 1 lesion per plant) for fields with drip irrigation, but not for fields with sprinklers (incidence up to 100% and 5 to 10 lesions per plant). For the first time, we established that survival and sporulation components are not needed for a lettuce downy mildew forecasting system. Instead, a threshold with a shorter period of morning leaf wetness and high temperatures were found to have potential for improving forecasting efficiency.

scholarly journals Performance of deep learning technology for evaluation of positioning quality in periapical radiography of the maxillary canine

2021 ◽  
Author(s):  
Mizuho Mori ◽  
Yoshiko Ariji ◽  
Motoki Fukuda ◽  
Tomoya Kitano ◽  
Takuma Funakoshi ◽  
...  
Keyword(s):  
Deep Learning ◽  
Characteristic Curve ◽  
Classification Performance ◽  
Learning Systems ◽  
Learning Technology ◽  
System 2 ◽  
Potential Benefits ◽  
System 1 ◽  
Periapical Radiography

Abstract Objectives The aim of the present study was to create and test an automatic system for assessing the technical quality of positioning in periapical radiography of the maxillary canines using deep learning classification and segmentation techniques. Methods We created and tested two deep learning systems using 500 periapical radiographs (250 each of good- and bad-quality images). We assigned 350, 70, and 80 images as the training, validation, and test datasets, respectively. The learning model of system 1 was created with only the classification process, whereas system 2 consisted of both the segmentation and classification models. In each model, 500 epochs of training were performed using AlexNet and U-net for classification and segmentation, respectively. The segmentation results were evaluated by the intersection over union method, with values of 0.6 or more considered as success. The classification results were compared between the two systems. Results The segmentation performance of system 2 was recall, precision, and F measure of 0.937, 0.961, and 0.949, respectively. System 2 showed better classification performance values than those obtained by system 1. The area under the receiver operating characteristic curve values differed significantly between system 1 (0.649) and system 2 (0.927). Conclusions The deep learning systems we created appeared to have potential benefits in evaluation of the technical positioning quality of periapical radiographs through the use of segmentation and classification functions.

A New Class of Oxide Superconductor (Nd, Ce, Sr)2CuO4

1989 ◽  
Vol 156 ◽  
Author(s):  
E. Takayama-Muromachi
Keyword(s):  
Crystal Structure ◽  
Crystal Chemistry ◽  
Superconducting Phase ◽  
Type Structure ◽  
Oxide Superconductor ◽  
New Class ◽  
System 2 ◽  
New Type ◽  
System 1 ◽  
Tetragonal Cell

ABSTRACTSince the discovery of the high-Tc superconductor in the La-Ba-Cu-O system [1], a great deal of experimental and theoretical effort have been made to clarify the nature of the Cu-based oxides. In order to elucidate mechanism of the high-Tc superconductivity, discovery of a new type of superconductor is no doubt of great importance. Recently, Akimitsu et al. found a new oxide superconductor in the Nd-Ce-Sr-Cu-O system [2]. Soon after their discovery, the superconducting phase was isolated and identified [3]. It has a tetragonal cell with space group P4/nmm and has a structure closely related to but different from the K2NiF4− or T'-Nd2CuO4− -type structure. Although, Tc of the Nd-Ce-Sr-Cu oxide is not so high (ca. 20 K) compared with the 1–2–3 or Bi(Tl)-based superconductors, it has aroused interest widely due to a very simple crystal structure. In this article, I will discuss superconductivity and crystal chemistry of the Nd-Ce-Sr-Cu oxide. Also, various compounds isostructural to it will be presented.

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