Search results for: preconditioning

Authors: Nadaniela Egidi, Pierluigi Maponi

Abstract:

The approximate solution of a time-harmonic electromagnetic scattering problem for inhomogeneous media is required in several application contexts and its two-dimensional formulation is a Fredholm integral equation of second kind. This integral equation provides a formulation for the direct scattering problem but has to be solved several times in the numerical solution of the corresponding inverse scattering problem. The discretization of this Fredholm equation produces large and dense linear systems that are usually solved by iterative methods. To improve the efficiency of these iterative methods, we use the Symmetric SOR preconditioning and propose an algorithm to evaluate the associated relaxation parameter. We show the efficiency of the proposed algorithm by several numerical experiments, where we use two Krylov subspace methods, i.e. Bi-CGSTAB and GMRES.

Keywords: Fredholm integral equation, iterative method, preconditioning, scattering problem.

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Authors: Azita Tajaddini, Ramleh Shamsi

Abstract:

In this paper, we present the block generalized minimal residual (BGMRES) method in order to solve the generalized Sylvester matrix equation. However, this method may not be converged in some problems. We construct a polynomial preconditioner based on BGMRES which shows why polynomial preconditioner is superior to some block solvers. Finally, numerical experiments report the effectiveness of this method.

Keywords: Linear matrix equation, Block GMRES, matrix Krylov subspace, polynomial preconditioner.

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Authors: Lina Yan, Shiheng Wang, Ke Wang

Abstract:

A preconditioned Jacobi (PJ) method is provided for solving fuzzy linear systems whose coefficient matrices are crisp Mmatrices and the right-hand side columns are arbitrary fuzzy number vectors. The iterative algorithm is given for the preconditioned Jacobi method. The convergence is analyzed with convergence theorems. Numerical examples are given to illustrate the procedure and show the effectiveness and efficiency of the method.

Keywords: preconditioning, M-matrix, Jacobi method, fuzzy linear system (FLS).

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Authors: Z. Zainuddin, W. D. Wan Rosli, R. Lanouette, S. Sathasivam

Abstract:

This paper reports work done to improve the modeling of complex processes when only small experimental data sets are available. Neural networks are used to capture the nonlinear underlying phenomena contained in the data set and to partly eliminate the burden of having to specify completely the structure of the model. Two different types of neural networks were used for the application of pulping problem. A three layer feed forward neural networks, using the Preconditioned Conjugate Gradient (PCG) methods were used in this investigation. Preconditioning is a method to improve convergence by lowering the condition number and increasing the eigenvalues clustering. The idea is to solve the modified odified problem M-1 Ax= M-1b where M is a positive-definite preconditioner that is closely related to A. We mainly focused on Preconditioned Conjugate Gradient- based training methods which originated from optimization theory, namely Preconditioned Conjugate Gradient with Fletcher-Reeves Update (PCGF), Preconditioned Conjugate Gradient with Polak-Ribiere Update (PCGP) and Preconditioned Conjugate Gradient with Powell-Beale Restarts (PCGB). The behavior of the PCG methods in the simulations proved to be robust against phenomenon such as oscillations due to large step size.

Keywords: Convergence, pulping modeling, neural networks, preconditioned conjugate gradient.

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Authors: W. D. Wan Rosli, Z. Zainuddin, R. Lanouette, S. Sathasivam

Abstract:

This paper reports work done to improve the modeling of complex processes when only small experimental data sets are available. Neural networks are used to capture the nonlinear underlying phenomena contained in the data set and to partly eliminate the burden of having to specify completely the structure of the model. Two different types of neural networks were used for the application of Pulping of Sugar Maple problem. A three layer feed forward neural networks, using the Preconditioned Conjugate Gradient (PCG) methods were used in this investigation. Preconditioning is a method to improve convergence by lowering the condition number and increasing the eigenvalues clustering. The idea is to solve the modified problem where M is a positive-definite preconditioner that is closely related to A. We mainly focused on Preconditioned Conjugate Gradient- based training methods which originated from optimization theory, namely Preconditioned Conjugate Gradient with Fletcher-Reeves Update (PCGF), Preconditioned Conjugate Gradient with Polak-Ribiere Update (PCGP) and Preconditioned Conjugate Gradient with Powell-Beale Restarts (PCGB). The behavior of the PCG methods in the simulations proved to be robust against phenomenon such as oscillations due to large step size.

Keywords: Convergence, Modeling, Neural Networks, Preconditioned Conjugate Gradient.

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Authors: Khairul Bariah Sulaiman, Tajul Aris Yang

Abstract:

Fermentation is well known as an essential process to develop chocolate flavor in dried cocoa beans. Besides developing the precursor of cocoa flavor, it also induces the color changes in the beans. The fermentation process is influenced by various factors such as planting material, preconditioning of cocoa pod and fermentation technique. Therefore, this study was conducted to evaluate color of Malaysian cocoa beans and how the duration of pods storage and fermentation technique using shallow box will effect on its color characteristics. There are two factors being studied i.e. duration of cocoa pod storage (0, 2, 4 and 6 days) and duration of cocoa fermentation (0, 1, 2, 3, 4 and 5 days). The experiment is arranged in 4 x 6 factorial designs with 24 treatments and arrangement is in a Completely Randomised Design (CRD). The produced beans are inspected for color changes under artificial light during cut test and divided into four groups of color namely fully brown, purple brown, fully purple and slaty. Cut tests indicated that cocoa beans which are directly dried without undergone fermentation has the highest slaty percentage. However, application of pods storage before fermentation process is found to decrease the slaty percentage. In contrast, the percentages of fully brown beans start to dominate after two days of fermentation, especially from four and six days of pods storage batch. Whereas, almost all batches of cocoa beans have a percentage of fully purple less than 20%. Interestingly, the percentage of purple brown beans are scattered in the entire beans batch regardless any specific trend. Meanwhile, statistical analysis using General Linear Model showed that the pods storage has a significant effect on the color characteristic of the Malaysian dried beans compared to fermentation duration.

Keywords: Cocoa beans, color, fermentation, shallow box.

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Authors: Lukas Horny, Rudolf Zitny, Hynek Chlup, Tomas Adamek, Michal Sara

Abstract:

An inflation–extension test with human vena cava inferior was performed with the aim to fit a material model. The vein was modeled as a thick–walled tube loaded by internal pressure and axial force. The material was assumed to be an incompressible hyperelastic fiber reinforced continuum. Fibers are supposed to be arranged in two families of anti–symmetric helices. Considered anisotropy corresponds to local orthotropy. Used strain energy density function was based on a concept of limiting strain extensibility. The pressurization was comprised by four pre–cycles under physiological venous loading (0 – 4kPa) and four cycles under nonphysiological loading (0 – 21kPa). Each overloading cycle was performed with different value of axial weight. Overloading data were used in regression analysis to fit material model. Considered model did not fit experimental data so good. Especially predictions of axial force failed. It was hypothesized that due to nonphysiological values of loading pressure and different values of axial weight the material was not preconditioned enough and some damage occurred inside the wall. A limiting fiber extensibility parameter Jm was assumed to be in relation to supposed damage. Each of overloading cycles was fitted separately with different values of Jm. Other parameters were held the same. This approach turned out to be successful. Variable value of Jm can describe changes in the axial force – axial stretch response and satisfy pressure – radius dependence simultaneously.

Keywords: Constitutive model, damage, fiber reinforcedcomposite, limiting fiber extensibility, preconditioning, vena cavainferior.

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Authors: Syed Dawood Md. Taimur, Md. Hasanur Rahman, Syeda Fahmida Afrin, Farzana Islam

Abstract:

The concept of myocardial injury, although first recognized from animal studies, is now recognized as a clinical phenomenon that may result in microvascular damage, no-reflow phenomenon, myocardial stunning, myocardial hibernation and ischemic preconditioning. The final consequence of this event is left ventricular (LV) systolic dysfunction leading to increased morbidity and mortality. The typical clinical case of reperfusion injury occurs in acute myocardial infarction (MI) with ST segment elevation in which an occlusion of a major epicardial coronary artery is followed by recanalization of the artery. This may occur spontaneously or by means of thrombolysis and/or by primary percutaneous coronary intervention (PCI) with efficient platelet inhibition by aspirin (acetylsalicylic acid), clopidogrel and glycoprotein IIb/IIIa inhibitors. In recent years, percutaneous coronary intervention (PCI) has become a well-established technique for the treatment of coronary artery disease. PCI improves symptoms in patients with coronary artery disease and it has been increasing safety of procedures. However, peri- and post-procedural myocardial injury, including angiographical slow coronary flow, microvascular embolization, and elevated levels of cardiac enzyme, such as creatine kinase and troponin-T and -I, has also been reported even in elective cases. Furthermore, myocardial reperfusion injury at the beginning of myocardial reperfusion, which causes tissue damage and cardiac dysfunction, may occur in cases of acute coronary syndrome. Because patients with myocardial injury is related to larger myocardial infarction and have a worse long-term prognosis than those without myocardial injury, it is important to prevent myocardial injury during and/or after PCI in patients with coronary artery disease. To date, many studies have demonstrated that adjunctive pharmacological treatment suppresses myocardial injury and increases coronary blood flow during PCI procedures. In this review, we highlight the usefulness of pharmacological treatment in combination with PCI in attenuating myocardial injury in patients with coronary artery disease.

Keywords: Coronary artery disease, Percutaneous coronary intervention, Myocardial injury, Pharmacology.

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Authors: R. Meier, M. Pander

Abstract:

In accordance with the industry 4.0 concept, manufacturing process steps as well as the materials themselves are going to be more and more digitalized within the next years. The “digital twin” representing the simulated and measured dataset of the (semi-finished) product can be used to control and optimize the individual processing steps and help to reduce costs and expenditure of time in product development, manufacturing, and recycling. In the present work, two material characterization methods based on Lamb waves were evaluated and compared. For demonstration purpose, both methods were shown at a standard industrial product - copper ribbons, often used in photovoltaic modules as well as in high-current microelectronic devices. By numerical approximation of the Rayleigh-Lamb dispersion model on measured phase velocities second order elastic constants (Young’s modulus, Poisson’s ratio) were determined. Furthermore, the effective third order elastic constants were evaluated by applying elastic, “non-destructive”, mechanical stress on the samples. In this way, small microstructural variations due to mechanical preconditioning could be detected for the first time. Both methods were compared with respect to precision and inline application capabilities. Microstructure of the samples was systematically varied by mechanical loading and annealing. Changes in the elastic ultrasound transport properties were correlated with results from microstructural analysis and mechanical testing. In summary, monitoring the elastic material properties of plate-like structures using Lamb waves is valuable for inline and non-destructive material characterization and manufacturing process control. Second order elastic constants analysis is robust over wide environmental and sample conditions, whereas the effective third order elastic constants highly increase the sensitivity with respect to small microstructural changes. Both Lamb wave based characterization methods are fitting perfectly into the industry 4.0 concept.

Keywords: Lamb waves, industry 4.0, process control, elasticity, acoustoelasticity.

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