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  • Chemical Engineering  (17,092)
  • Engineering  (7,691)
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  • Strömungsmechanik
  • Wiley-Blackwell  (24,790)
  • Sage Publications  (6)
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  • 1
    Electronic Resource
    Electronic Resource
    New York, NY [u.a.] : Wiley-Blackwell
    Process Safety Progress 17 (1998), S. S3 
    ISSN: 1066-8527
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Type of Medium: Electronic Resource
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  • 2
    Electronic Resource
    Electronic Resource
    New York, NY [u.a.] : Wiley-Blackwell
    Process Safety Progress 17 (1998), S. 1-8 
    ISSN: 1066-8527
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: Recent guidelines released by the U.S. EPA define a worst-case scenario as a release under stable atmospheric conditions defined as Pasquil-Gifford stability class F. Unfortunately, very few tests at F stability have been available heretofore to provide a basis for models. Recent test data with propane releases by the German research organization TUV provide a set of 60 experiments conducted specifically to define the effects of atmospheric stability class on dispersion. Of these, 25 tests were at F stability. A comparable number were at each other stability class A through E. In addition 23 tests were at wind speeds under 1.5 m/s in stable atmospheres. This paper reports on adjustments made to our models based on these new data by reducing the originally-postulated sensitivity to stability class. In spite of considerable scatter in the TUV data, particularly between two different types of propane analyzers, the model allows us to extract information by averaging over the tests.
    Additional Material: 15 Ill.
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  • 3
    Electronic Resource
    Electronic Resource
    New York, NY [u.a.] : Wiley-Blackwell
    Process Safety Progress 17 (1998), S. 9-15 
    ISSN: 1066-8527
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: The design and deflagration pressure relief vents is based on correlations developed for various types of combustible materials and for enclosures of different strengths. The primary guideline for deflagration vent design in the US is NFPA 68 Guide for Venting of Deflagrations [5]. That document gives guidance for the design of vents for enclosures containing flammable gases, specifically hydrogen, coke oven gas, propane, and methane. Application of the guide to other gases is achieved using the KG value. Values of KG are published for a relatively small number of gases, as seen in Table D-1 of NFPA 68. This work present KG data on several additional gases obtained in a laboratory scale test vessel along with analysis of the results with respect to published values of fundamental burning velocity.
    Additional Material: 9 Ill.
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  • 4
    Electronic Resource
    Electronic Resource
    New York, NY [u.a.] : Wiley-Blackwell
    Process Safety Progress 17 (1998), S. 20-22 
    ISSN: 1066-8527
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: Most audits try to look at a representative selection of the plant procedures and equipment. An alternative is a survey, a look in depth at selected procedures (such as those for testing alarms and trips, issuing permits-to-work, controlling modifications, taking samples or testing relief devices) or selected equipment (such as level glasses or equipment for handling LPG). If the procedure or equipment is well-chosen, surveys may make a bigger contribution to safety, per person-hour, than a conventional audit.
    Additional Material: 1 Tab.
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  • 5
    Electronic Resource
    Electronic Resource
    New York, NY [u.a.] : Wiley-Blackwell
    Process Safety Progress 17 (1998), S. 16-19 
    ISSN: 1066-8527
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: A multi-disciplinary team developed a guideline for determining access restriction zones around vented solids handling equipment. The guideline provides a method for ensuring the discharge from a vented explosion will not cause injury to personnel. The steps in this method include: calculating the extent of external hazards from vented explosions; identifying potential areas where personnel could be exposed to a hazard; identifying ways to eliminate or reduce the hazard area; and establishing and documenting any access restrictions needed. Hazard zone calculations use the latest knowledge from research into fireball size, flame length and external pressure equations in VDI 3673. The guideline provides guidance for using this information. Options for mitigating or reducing external hazards from vented explosions are also described. As part of the project, the team audited several solids handling systems to look for potential oversights in existing restricted access areas. Some of the team's learnings from these audits are reviewed.
    Additional Material: 2 Ill.
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  • 6
    Electronic Resource
    Electronic Resource
    New York, NY [u.a.] : Wiley-Blackwell
    Process Safety Progress 17 (1998), S. 23-31 
    ISSN: 1066-8527
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: In May 1996, the Flammable and Combustible Liquids Code Committee of the National Fire Protection Association (NFPA) proposed for adoption by the Association a new edition of NFPA 30, Flammable and Combustible Liquids Code. This new edition was the culmination of two and one-half years' work by the Committee and included one of the most significant changes to that document in some twenty years: the incorporation of mandatory fire protection criteria for warehouses and other inside areas that store flammable and combustible liquids in containers and portable tanks.
    Additional Material: 2 Ill.
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  • 7
    Electronic Resource
    Electronic Resource
    New York, NY [u.a.] : Wiley-Blackwell
    Process Safety Progress 17 (1998), S. 43-48 
    ISSN: 1066-8527
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: This paper defines situation awareness (SA) and discusses its importance to operator-machine system safety and functioning in the context of process control activities. Specifically, identified are relationships of human detection of critical process cues converying the status of automated control systems and operator interpretation of the meaning and relevance of such information to the potential for negative incidents in chemical processing. Beyond individual operator SA in interacting with control systems, intra- and inter- work team SA are discussed for supporting individual attainment of process control responsibilities. Factors critical to team SA are discussed. “Road blocks” to team SA are also analytically examined. Lastly, methods for assessing individual and team SA are reviewed and vehicles for relating outcomes of these methods to changes in process control operator and team behavior to improve human-machine system safety and performance are relayed.
    Additional Material: 1 Ill.
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  • 8
    ISSN: 1066-8527
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: The knowledge of the ingition behavior of dust-air mixtures due to electrical sparks (MIE, Minimum Ignition Energy) and hot surfaces (MIT, Minimum Ignition Temperature) is important for risk assessments in chemical production plants. The ignition behavior determines the extent and hence the cost of preventive protection measures.This paper describes the use of the minimum ignition energy and minimum ignition temperature as very important safety indexes in practice.Based on the latest results from large scale experiments on pneumatic filling of silos with polymeric materials and new results of full scale filling tests using Flexible Intermediate Bulk Containers (FIBC) manufactured from a variety of materials, guidance can be given to ensure safe operation in different situations such as filling, emptying operations, type of powder handled.The aim of this paper is to assist people dealing with product. It reflects the present state of the art and current knowledge of the assessment and measures associated with powder handling.
    Additional Material: 12 Ill.
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  • 9
    Electronic Resource
    Electronic Resource
    New York, NY [u.a.] : Wiley-Blackwell
    Process Safety Progress 17 (1998), S. S3 
    ISSN: 1066-8527
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Type of Medium: Electronic Resource
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  • 10
    Electronic Resource
    Electronic Resource
    New York, NY [u.a.] : Wiley-Blackwell
    Process Safety Progress 17 (1998), S. 83-85 
    ISSN: 1066-8527
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: Safety, health and loss prevention are major areas of interst for the American Institute of Chemical Engineers (AIChE). There has been an evolution of these concerns over the years in the Institute just as it has in industry. This article chronicles this evolution.
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  • 11
    Electronic Resource
    Electronic Resource
    New York, NY [u.a.] : Wiley-Blackwell
    Process Safety Progress 17 (1998), S. 171-175 
    ISSN: 1066-8527
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: An explosion occurred in a petroleum product storage tank at a refinery. The liquid petroleum product was a heavy oil used as an asphalt extender. There were no injuries, but the cleanup was costly. The storage tank was one of several which received the product stream from a dehydration unit. The accident occurred shortly after the refinery was brought back on-line following a shutdown for schduled maintenance.This was the first incident of this kind to occur at this facility. Analysis of the process data and eyewitness observations indicated that the dehydration tower, which was supposed to be maintained at a minimum of 100°C during the shutdown, was allowed to drift below 100°C for an unknown period of time. This deviation enabled liquid water to enter the storage tank. Three operational factors contributed to the accident. Corrective actions were recommended to prevent a recurrence of a similar incident.
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  • 12
    Electronic Resource
    Electronic Resource
    New York, NY [u.a.] : Wiley-Blackwell
    Process Safety Progress 17 (1998), S. 157-170 
    ISSN: 1066-8527
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: Risk analysis in chemical process industries is an elaborate exercise involving several steps from preliminary hazard identification to development of credible accident scenarios, to preparation of strategies for prevention or control of damage.All this requires substantial inputs of time and money. In order to get an approximate yet workable assessment of risk at much lesser costs, indices have been developed which link typical findings of elaborate risk analysis to scales of risk. The scales, in turn, provide workable measures of hazards/risks/safety.In the past, indices have been reported for swift risk assessment - the noteworthy among them include Dow fire and explosion index, Mond fire, explosion and toxicity index, IFAL index, and mortality index. A few rapid ranking techniques have also been proposed.This paper presents a new system of methodologies for Hazard Identification and Ranking (HIRA). The system consists of two indices: one for fire and explosion hazards and another for the hazard due to likely release of toxic chemical. The magnitudes of these indices indicate the severity of the likely accident; in terms of the size of the impacted area.HIRA has been applied to a typical chemical process industry - a sulfolane plant - and its performance has been compared with that of the Dow's and the Mond's indices. The study reveals that HIRA is more sensitive and accurate than the other indices.
    Additional Material: 12 Ill.
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  • 13
    Electronic Resource
    Electronic Resource
    New York, NY [u.a.] : Wiley-Blackwell
    Process Safety Progress 17 (1998), S. 184-189 
    ISSN: 1066-8527
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: Dust explosions have been with us for a long time. The first record of a dust explosion occurred in Turin, Italy, on December 14, 1785 [1]. The detailed record of this event is left to us by Count Morozzo. The event took place in Mr. Giacomelli's bakery. We know from his account that the weather was unseasonably dry, that a boy who worked in the bakery was using a shovel to stir and transfer the flour to a chute from a store room to the bakery and he had a lighted lamp to work by. The rest, as the saying goes, is history. No one was killed, and the building was saved by the sagacious fact of having plenty of windows. Since that first record, of course, there have been many explosions with much loss of life and significant economic consequences.
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  • 14
    Electronic Resource
    Electronic Resource
    New York, NY [u.a.] : Wiley-Blackwell
    Process Safety Progress 17 (1998), S. 176-183 
    ISSN: 1066-8527
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: The safest method to prevent fires and explosions of flammable mixtures in the first place. This method requires detailed knowledge of the flammability region as a function of the fuel, oxygen, and nitrogen concentrations. A triangular flammability diagram is the most useful tool to display the flammability region, and to determine if a flammable mixture is present during plant operations.This paper describes how to draw and use a flammability diagram. A procedure to estimate the flammability region using the available and sometimes limited data is discussed. The paper also shows how to use the flammability diagram with plant operations involving inerting and purging, and from bringing vessels into and out of service. A compilation of flammability diagrams for 30 materials, based on previously published data is provided.An automated apparatus for acquiring data for a flammability diagram is described. The apparatus consists of a 20-L sphere with an automated gas mixing system, a fuse-wire ignition system, and a high speed pressure measurement and data acquisition system. Data derived from the apparatus includes flammability limits, maximum pressure during combustion, and the maximum pressure rate. The effect of fuse-wire ignitor dynamics on the results is studied. A flammability diagram for methane drawn from data obtained from the apparatus, is presented.
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  • 15
    Electronic Resource
    Electronic Resource
    New York, NY [u.a.] : Wiley-Blackwell
    Process Safety Progress 17 (1998), S. 190-195 
    ISSN: 1066-8527
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: The RSST DIERS vent sizing methodology is revised to provide realistic design equations for reactive systems consistent with available large-scale experience. Using easy to obtain RSST data such as rate of temperature rise and rate of pressure rise excellent agreement is illustrated for hybrid, vapor and gassy reactive systems.
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  • 16
    Electronic Resource
    Electronic Resource
    New York, NY [u.a.] : Wiley-Blackwell
    Process Safety Progress 17 (1998), S. 200-208 
    ISSN: 1066-8527
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Additional Material: 14 Ill.
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  • 17
    Electronic Resource
    Electronic Resource
    New York, NY [u.a.] : Wiley-Blackwell
    Process Safety Progress 17 (1998), S. 209-212 
    ISSN: 1066-8527
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: HFC-227ea (CF3CHFCF3;1, 1, 1, 2, 3, 3, 3-heptafluoropropane) is an effective replacement for Halon 1301 in fire suppression systems, providing rapid extinguishment of flames through a combination of physical and chemical mechanisms. The vast majority of applications for HFC-227ea involve the protection of Class A hazards, which are characterized by low fuel loadings and low energy output, with fire sizes often in the range of 5-10 kW. Mid- and large-scale testing has demonstrated that HFC-227ea, at its minimum design concentration of 7.0% v/v, is effective at extinguishing fires typical of those expected to occur in electronic data processing (EDP) facilities, telecommunication facilities and anechoic chambers. The levels of HF produced following extinguishment of typical Class a fires with HFC-227ea were well below the estimated mammalian LC50 and the human Dangerous Toxic Load (DTL), and do not appear to present a threat to electronic equipment.
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  • 18
    ISSN: 1066-8527
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: A new method is described to enhance the management of process safety risks such that the number and type of safety systems protecting against any hazard are consistently predicated upon risk. Further, that such an assignment of safety systems can be made consistent throughout an organization. This consistency is gained through standardization of qualitative risk ranking and by setting company guidelines.
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  • 19
    Electronic Resource
    Electronic Resource
    New York, NY [u.a.] : Wiley-Blackwell
    Process Safety Progress 17 (1998), S. 288-296 
    ISSN: 1066-8527
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: An ammonia storage tank was built at the BASF Antwerp site in 1969 on land reclaimed from the sea. After several years of operation uneven foundation settlement, of up 2, occurred. In order to assure stability of this area for the next operation period (at least 10 years) measures were taken to ensure continued safe operation. One key measure was strain gauge monitoring at the location of maximum stress.
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  • 20
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    ISSN: 1069-8299
    Keywords: Convection-diffusion equation ; difference method ; AGE (alternating group explicit) method ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Some modified AGE methods for the convection-diffusion equation are developed in this paper. Firstly, there is a treatment on the convection term in the equation which is different from that in the AGE method by Evans and Abdullah (1985). Secondly, upwind-type schemes are used for the convection dominated diffusion problems. All the modified AGE methods in the paper are unconditionally stable. The numerical example is given to show the effectiveness of the methods. The methods have the obvious property of parallelism. © 1998 John Wiley & Sons, Ltd.
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  • 21
    ISSN: 1069-8299
    Keywords: Delaunay triangulation ; mesh colouring ; mesh coarsening ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A new algorithm is described for automatic coarsening of Delaunay triangulations. The method automatically identifies the nodes of the mesh which are candidates for deletion in each region to be coarsened. The mesh coarsening procedure is to regenerate a Delaunay triangulation for all the remaining nodes in the solution domain. The adapted mesh retains a high quality for two reasons: (i) because a set of nodes have been used to obtain the coarse mesh, which are equidistant apart in some sense defined by the original mesh; (ii) because the triangulation is Delaunay. A two-dimensional example demonstrates the quality of the mesh after coarsening. © 1998 John Wiley & Sons, Ltd.
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  • 22
    ISSN: 1069-8299
    Keywords: arc-length method ; user control ; accumulated arc-length control ; non-linear analysis ; predefined deformation states ; convergence ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The arc-length method has been widely used in non-linear analysis of structures. While it can handle complex load-deflection paths effectively, the analyst has no control over the load incrementation scheme to achieve convergence to specific locations along the load-deflection path. There are a number of situations in which such control is necessary, for example when convergence to predefined load levels, displacement levels or stress levels is required. This paper describes an improved arc-length method in which this deficiency is overcome. © 1998 John Wiley & Sons, Ltd.
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  • 23
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    ISSN: 1069-8299
    Keywords: boundary integral ; spectral strip ; curvature geometries ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The non-element boundary spectral strip method is developed for solution of problems in curvature domains. The method, which uses a spectral Fourier approximation for expansion of the variables along the boundaries, shows an exponential convergence behaviour. A remarkable reduction in problem size and improved accuracy of results is achieved by the method as compared to the boundary element method. The method is illustrated by some physical problems from elastostatics. © 1998 John Wiley & Sons, Ltd.
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  • 24
    ISSN: 1069-8299
    Keywords: filling of thin section ; finite element method ; surface tension ; interface element ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: An interface element to model the pressure discontinuity due to surface tension when applied to the filling of a thin section cavity is presented. The equations used to form the element matrix for the interface element are the line integral form of the continuity and momentum equations. During the development of the finite element model, the pressure difference across the free surface due to surface tension is treated as an additional traction and is applied to all element sides which form the free surface. Simple numerical examples are then presented to illustrate the technique on the filling of a rectangular thin section cavity. © 1998 John Wiley & Sons, Ltd.
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  • 25
    ISSN: 1069-8299
    Keywords: finite elements ; pollutant ; saturated porous medium ; semi-implicit method ; velocity correction ; mass transfer ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A practical problem of pollutant migration has been studied for different concentration differences and mass diffusivities using the finite element method. The results indicate that the pollutant takes years to travel 10 m into the water-saturated soil when the mass diffusivity and concentration differences are less. © 1998 John Wiley & Sons, Ltd.
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  • 26
    ISSN: 1069-8299
    Keywords: transient dynamics ; interaction of the crack sides ; crack propagation ; time domain formulation ; boundary element method ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: For two-dimensional solids the multiregion concept and the time-domain approach in the boundary element method are employed to model cracks in transient dynamics. The propagation of cracks and the closing and opening of crack sides are simulated by disconnecting and connecting degrees of freedom of a stationary mesh, as was also demonstrated recently in statics by Beer. An iterative technique is developed to determine the changes of the extent of the area where there is connection, contact or no contact at the interface between dynamically loaded regions. © 1998 John Wiley & Sons, Ltd.
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  • 27
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    ISSN: 1069-8299
    Keywords: 3D mesh generation ; adaptive refinement ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: An adaptive finite element (FE) method for the solution of three-dimensional elasto-static problems is described. The computational domain is represented by an assembly of tetrahedral elements and the mesh adaptation is achieved by a 3D bisection method using an error estimator procedure coupled with an automatic 3D mesh generator. The performance of the method is demonstrated using a number of examples. © 1998 John Wiley & Sons, Ltd.
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  • 28
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    ISSN: 1069-8299
    Keywords: assumed natural strain ; plate bending ; triangular ; finite element ; six-node ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In this paper, a six-node triangular C0 plate bending element is developed by the assumed natural strain method. In the element, all the sampled natural transverse shear strains are chosen such that the latter has a favourable constraint index and the strains are optimized with respect to a linear pure moment field. The element passes the patch tests, yields satisfactory accuracy and shows no sign of shear locking in all the problems considered. Copyright © 1998 John Wiley & Sons, Ltd.
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  • 29
    ISSN: 1069-8299
    Keywords: finite elements ; explicit dynamics ; near incompressible deformation ; large strains ; tetrahedron ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper presents a simple linear tetrahedron element that can be used in explicit dynamics applications involving nearly incompressible materials or incompressible materials modelled using a penalty formulation. The element prevents volumetric locking by defining nodal volumes and evaluating average nodal pressures in terms of these volumes. Two well-known examples relating to the impact of elasto-plastic bars are used to demonstrate the ability of the element to model large isochoric strains without locking. © 1998 John Wiley & Sons, Ltd.
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  • 30
    ISSN: 1069-8299
    Keywords: hypersingular integral equation ; plane elasticity crack problem ; stress intensity factors ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The hypersingular integral equation approach is suggested to solve the plane elasticity crack problem with circular boundary. The complex variable function method is used in the formulation. In the equation the crack opening displacement function is used as the unknown function, and the traction on the crack face as the right-hand term. A numerical integration rule is used to evaluate the hypersingular integral. Numerical examples are given to demonstrate the use of the approach. © 1998 John Wiley & Sons, Ltd.
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  • 31
    ISSN: 1069-8299
    Keywords: multibody systems ; non-linear analysis ; static equilibrium ; constrained optimization ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper presents four different approaches to the solution of the non-linear static-equilibrium problem in complex linkages, including rigid and elastic elements. The error function is based on the potential of the system, and includes rigid elements by means of non-linear constraints. To this end use is made of Lagrange multipliers, along with the primal-dual method, penalty functions and weighted stiffness, comparisons being made between them. A Newton-Raphson method is used in seeking function minima for equilibrium positions. This procedure is also directly applicable to the other linkage and multibody position problems. © 1998 John Wiley & Sons, Ltd.
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  • 32
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    ISSN: 1069-8299
    Keywords: temporal acceleration ; viscoelastic ; recovery ; Taylor-Galerkin ; finite elements ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper presents a finite element study based on a technique associated with time extrapolation to accelerate the convergence rate to the steady state for viscoelastic flows. The approach adopted is a local extrapolation method attributed to Neville. Temporal extrapolation is embedded within a time-marching Taylor-Galerkin/pressure-correction scheme as applied to the solution of model channel flow, 4:1 plane contraction flow and flow past a circular cylinder. In particular, consideration is given to obtaining steady-state solutions for an Oldroyd-B model. When extrapolation is performed for stress and velocity or pressure, then stress and velocity overshoot, which consequently leads to divergence. In contrast, a stable numerical scheme emerges when only the stress is extrapolated. © 1998 John Wiley & Sons, Ltd.
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  • 33
    ISSN: 1069-8299
    Keywords: identification ; viscoelasticity ; correspondence principle ; boundary elements ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A parameter identification procedure for viscoelastic materials is presented, which is formulated based on the elastic-viscoelastic correspondence principle. The proposed method is developed by using Newton's iteration scheme, the method of least squares and the one-dimensional minimization method. The boundary element discretization and the numerical inversion of the Laplace transform are used for linear viscoelastic analysis. Two numerical examples are included to demonstrate the validity of the method. © 1998 John Wiley & Sons, Ltd.
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  • 34
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    Chichester : Wiley-Blackwell
    ISSN: 1069-8299
    Keywords: hypersingular integral equation ; continuous elements ; stress analysis ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In this paper, a method for the evaluation of boundary stresses directly from the BEM solution of elastostatic problems using the static boundary integral equation is presented. The technique is valid for corners and edges as well as smooth points on the boundary, and involves defining a new interpolation function for continuous elements which incorporate certain continuity conditions arising from the hypersingular nature of the integrals involved. An integration technique based on the singularity subtraction method using series expansions is adopted for the hypersingular intergrals. Results are shown to be more accurate than those obtained with conventional techniques. © 1998 John Wiley & Sons, Ltd.
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  • 35
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    Chichester : Wiley-Blackwell
    ISSN: 1069-8299
    Keywords: finite element ; plate bending ; triangular element ; displacement method ; polynomial function ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper investigates the importance and accuracy of a family of high-order triangular elements. After a brief review of characteristics of high-order triangular elements, six new incompatible 13-node triangular elements are presented. The accuracy of the proposed elements is illustrated by comparing their numerical results with the other investigators' solutions, and the best element is introduced. © 1998 John Wiley & Sons, Ltd.
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  • 36
    ISSN: 1069-8299
    Keywords: shell element ; large strain ; sheet metal stamping ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The paper presents a general method of large strain determination over the deformed surface of a sheet metal stamping. It is demonstrated that the conventional degenerated shell element with two normal rotation degrees of freedom is not suitable for large deformation, especially when large element rotation is present. This inaccuracy is primarily caused by the fact that the displacement field description used in the degenerated shell element is only a first-order approximation with respect to the two rotation degrees of freedom, and is therefore suitable only for small rotation angles. The new method presented in this paper replaces the two rotation DOFs with three new degrees of freedom to describe the rotation of the surface normal so that the element deformation can be accurately described with no limitation on the amount of deformation and rotation involved. The advantages of this new method are: (i) a linear and accurate expression of the displacement field in terms of nodal DOFs is obtained; (ii) the formulation is easily incorporated into any existing degenerated shell elements; (iii) the strain calculation is accurate for any amount of element rigid body rotation; (iv) if the method is used in surface grid analysis, the algorithm will not only provide correct surface strains, but also their variation through the thickness direction, i.e. the bending deformation. © 1998 John Wiley & Sons, Ltd.
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  • 37
    ISSN: 1069-8299
    Keywords: finite elements ; adaptive analysis ; error estimate ; rh-method ; r-method ; h-method ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: An rh-method, which combines r- and h-methods, is proposed for cost-effective adaptive FE analysis in two-dimensional linear elastic problems. Through various numerical test examples, the rh-method is compared with the h-method. From these examples it is concluded that the rh-method has the advantages of both the r- and h-methods, so that the rh-method can minimize the computational time required for the adaptive analysis. The algorithm of the rh-method can be implemented easily in existing h-adaptive FE codes, since the r-method is independently combined with the h-method. © 1998 John Wiley & Sons, Ltd.
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  • 38
    ISSN: 1069-8299
    Keywords: boundary-only element analysis ; thermal cracking ; crack trajectory ; singular elements ; traction formula ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A boundary element procedure is developed concerning the prediction of the quasistatic crack growth in uniformly heated bimaterials. This procedure assumes the existence of an initial small crack in one of the two phases, and further cracking progress from this point due to thermal loading. The resulting mixed boundary value problem is solved by applying an incremental boundary-only method in conjunction with the multidomain technique. Fracture characterizing parameters are evaluated utilizing special crack tip singular elements and appropriate formulas. The crack path is predicted using the strain energy release rate criterion, and the mesh is updated at the end of each increment. The presented results are in good agreement with previously reported experimental results and those obtained by the finite element method. Various numerical studies were conducted and interpreted concerning crack-path dependence on individual material property mismatch. © 1998 John Wiley & Sons, Ltd.
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  • 39
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    Chichester : Wiley-Blackwell
    ISSN: 1069-8299
    Keywords: structural optimization ; approximation concepts ; envelope function ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In the present paper, a quasi-analytic method for solving structural optimization problems has been developed by co-ordinated use of mathematical transformations, high-quality approximation and a two-level approximation strategy. The method which has the advantages of both generality in applications and high efficiency in computations is especially of benefit to large practical design problems. Several typical examples of different sorts have been optimized to test its power. © 1998 John Wiley & Sons, Ltd.
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  • 40
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    Chichester : Wiley-Blackwell
    ISSN: 1069-8299
    Keywords: shell problem ; Naghdi model ; finite elements ; mixed elements ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The subject of this work is the construction of some special finite elements for the numerical solution of Naghdi cylindrical shell problems. The standard numerical approximation of the shell problem is subjected to the shear and membrane locking phenomenon, i.e. the numerical solution degenerates for low thickness. The most common way to avoid locking is the use of modified bilinear forms to describe the shear and membrane energy of the shell. In this paper we build a family of special finite elements that still follow the above strategy by introducing a linear operator that reduces the influence both of the shear and membrane energy terms. The main idea comes from the non-standard mixed interpolated tensorial components (MITC) formulation for Reissner-Mindlin plates. The performance of the new elements is then tested for solving benchmark problems involving very thin shells. The results show both the properties of convergence and robustness. Copyright © 1998 John Wiley & Sons, Ltd.
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  • 41
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    Chichester : Wiley-Blackwell
    ISSN: 1069-8299
    Keywords: inverse problems ; dual systems ; vibrating rod ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The discretization of the differential equation governing the axial vibration of a rod with varying cross-section leads to a specially structured matrix pencil. This paper deals with the reconstruction of this pencil from its spectrum. An iterative algorithm for this problem and an analytic characterization of complementary solutions are given. The method is demonstrated on some examples. © 1998 John Wiley & Sons, Ltd.
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  • 42
    ISSN: 1069-8299
    Keywords: finite elements ; electromagnetics ; numerical simulation ; electric furnaces ; electrodes ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In this paper we give a numerical method based on finite element discretizations to simulate the thermoelectrical behaviour of electrodes for electric reduction furnaces. After introducing the mathematical model we take advantage of the cylindrical symmetry of the problem to compute boundary conditions for the Maxwell equations. Thermal and electrical problems are coupled and non-linear because of the Joule effect and the fact that thermal conductivity and electrical resistivity depend on temperature. A classical piecewise linear finite element method on a triangular mesh is used to discretize weak formulations in cylindrical co-ordinates for the two problems. Then an iterative algorithm is proposed to solve the coupled discrete system. Numerical results are shown both for an analytical test and for a real industrial electrode. © 1998 John Wiley & Sons, Ltd.
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  • 43
    ISSN: 1069-8299
    Keywords: quadrilateral finite-element generation ; three-dimensional surfaces ; CAD/CAM interface ; topological information generation ; node sampling on edges ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In this paper, a general approach to automatic generation of quadrilaterals on three-dimensional surfaces is presented. The approach is based on the mapping method for surface meshing and the looping method for generation of quadrilaterals on the mapped plane. Several schemes including a coedge treatment scheme, an allowable tolerance and distance scheme, a multipatch treatment scheme with new mapping functions and a remapping scheme are proposed. Several realistic application examples are given, which show the generality of the presented approach. © 1998 John Wiley & Sons, Ltd.
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  • 44
    ISSN: 1069-8299
    Keywords: incompressible flow ; generalized streamline operator ; upwinding tensor ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In the present work the backward-facing step problem is analysed in the framework of the finite element method. It is a very well-known benchmark problem for the numerical resolution of the incompressible Navier-Stokes equations. In particular, a generalized streamline operator technique (GSO) is used in the numerical approach to these equations. The results show very good agreement with those reported by other authors using different methodologies. © 1998 John Wiley & Sons, Ltd.
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  • 45
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    ISSN: 1069-8299
    Keywords: phase-change problems ; conduction-advection equation ; upwind weight function ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A finite element formulation for solving transient multidimensional phase-change problems considering advective effects is presented. This temperature-based formulation includes the definition of a phase-change function able to deal with classical isothermal and non-isothermal phase-change cases. Moreover, a new upwind weight function is defined in order to avoid numerical oscillations in problems with dominant advective effects. Further, some important aspects related to its numerical implementation are also addressed. The ability of this methodology is illustrated, firstly, in the solution of a one-dimensional test example. Finally, the numerical simulation of a direct-chill continuous casting process is performed. © 1998 John Wiley & Sons, Ltd.
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  • 46
    ISSN: 1069-8299
    Keywords: fluid dynamics ; multiphase-flow ; lattice gases ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Nearly all CFD methods can be considered as discretization methods for partial differential equations, such as finite difference, finite volume, finite element, spectral or boundary integral element methods. Virtually unrecognized by the scientific mainstream in computational fluid dynamics (CFD) during the last decade, a completely different approach to flow simulation has been developed in computational physics.The basic idea of lattice-gas solvers (LGS) goes back to the cellular automation concept of John von Neumann. LGS use objects (‘cells’), being extremely simple compared to finite boxes or finite elements. The state of a cell is usually described by only a few bits therefore often two orders of magnitude more cells are used for a simulation with LGS than ‘elements’ in a finite element computation. LGS are explicit time-stepping procedures; no equation systems have to be solved. Thus every time-step is extremely cheap in terms of CPU power compared to standard procedures, yet again much shorter time-steps have to be used. LGS are inherently parallel and are suitable to coarse-grain as well as to fine-grain parallelization.The paper will discuss some advantages and disadvantages of lattice-gas solvers and present LG simulation results of two-phase flow with moving boundaries on a microscope scale for a two-dimensional test geometry of randomly distributed equally sized disks where the effect of surface tension on the steady-state saturation will be demonstrated. © 1998 John Wiley & Sons, Ltd.
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  • 47
    ISSN: 1070-5325
    Keywords: regular generalized eigenproblem ; condition number ; backward error ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: In this paper, we present a normwise perturbation theory for the regular generalized eigenproblem Ax = λBx, when λ is a semi-simple and finite eigenvalue, which departs from the classical analysis with the chordal norm [9]. A backward error and a condition number are derived for a choice of flexible measure to represent independent perturbations in the matrices A and B. The concept of optimal backward error associated with an eigenvalue only is also discussed. © 1998 John Wiley & Sons, Ltd.
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  • 48
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    New York, NY [u.a.] : Wiley-Blackwell
    ISSN: 1070-5325
    Keywords: eigenvalues ; Arnoldi ; Krylov subspaces ; preconditioning ; Davidson's method ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The problem of finding interior eigenvalues of a large nonsymmetric matrix is examined. A procedure for extracting approximate eigenpairs from a subspace is discussed. It is related to the Rayleigh-Ritz procedure, but is designed for finding interior eigenvalues. Harmonic Ritz values and other approximate eigenvalues are generated. This procedure can be applied to the Arnoldi method, to preconditioning methods, and to other methods for nonsymmetric eigenvalue problems that use the Rayleigh-Ritz procedure. The subject of estimating the boundary of the entire spectrum is briefly discussed, and the importance of preconditioning for interior eigenvalue problems is mentioned. © 1998 John Wiley & Sons, Ltd.
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  • 49
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    New York, NY [u.a.] : Wiley-Blackwell
    ISSN: 1070-5325
    Keywords: least squares ; QR factorization ; iterative solvers ; parallel algorithms ; multisplitting ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The linear least squares problem, minx∥Ax - b∥2, is solved by applying a multisplitting (MS) strategy in which the system matrix is decomposed by columns into p blocks. The b and x vectors are partitioned consistently with the matrix decomposition. The global least squares problem is then replaced by a sequence of local least squares problems which can be solved in parallel by MS. In MS the solutions to the local problems are recombined using weighting matrices to pick out the appropriate components of each subproblem solution. A new two-stage algorithm which optimizes the global update each iteration is also given. For this algorithm the updates are obtained by finding the optimal update with respect to the weights of the recombination. For the least squares problem presented, the global update optimization can also be formulated as a least squares problem of dimension p. Theoretical results are presented which prove the convergence of the iterations. Numerical results which detail the iteration behavior relative to subproblem size, convergence criteria and recombination techniques are given. The two-stage MS strategy is shown to be effective for near-separable problems. © 1998 John Wiley & Sons, Ltd.
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  • 50
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    New York, NY [u.a.] : Wiley-Blackwell
    ISSN: 1070-5325
    Keywords: preconditioning ; sparse approximate inverse ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We investigate different methods for computing a sparse approximate inverse M for a given sparse matrix A by minimizing ∥AM - E∥ in the Frobenius norm. Such methods are very useful for deriving preconditioners in iterative solvers, especially in a parallel environment. We compare different strategies for choosing the sparsity structure of M and different ways for solving the small least squares problem that are related to the computation of each column of M. Especially we show how we can take full advantage of the sparsity of A. © 1998 John Wiley & Sons, Ltd.
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  • 51
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    New York, NY [u.a.] : Wiley-Blackwell
    ISSN: 1070-5325
    Keywords: GMRES ; preconditioning ; invariant subspace ; deflation ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: This paper compares the performance on linear systems of equations of three similar adaptive accelerating strategies for restarted GMRES. The underlying idea is to adaptively use spectral information gathered from the Arnoldi process. The first strategy retains approximations to some eigenvectors from the previous restart and adds them to the Krylov subspace. The second strategy also uses approximated eigenvectors to define a preconditioner at each restart. This paper designs a third new strategy which combines elements of both previous approaches. Numerical results show that this new method is both more efficient and more robust. © 1998 John Wiley & Sons, Ltd.
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  • 52
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    New York, NY [u.a.] : Wiley-Blackwell
    ISSN: 1070-5325
    Keywords: bidiagonalization ; least squares ; minimum norm solution ; rank-deficient ; regularization ; Riley-Golub iteration ; singular value decomposition ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: In this paper we consider the solution of linear least squares problems          minx∥Ax - b∥22 where the matrix A ∊ Rm × n is rank deficient. Put p = min{m, n}, let σi, i = 1, 2,…, p, denote the singular values of A, and let ui and vi denote the corresponding left and right singular vectors. Then the minimum norm solution of the least squares problem has the form x* = ∫ri = 1(uTib/σi)vi, where r ≤ p is the rank of A.The Riley-Golub iteration,          xk + 1 = arg minx{∥Ax - b∥22 + λ∥x - xk∥22} converges to the minimum norm solution if x0 is chosen equal to zero. The iteration is implemented so that it takes advantage of a bidiagonal decomposition of A. Thus modified, the iteration requires only O(p) flops (floating point operations). A further gain of using the bidiagonalization of A is that both the singular values σi and the scalar products uTib can be computed at marginal extra cost. Moreover, we determine the regularization parameter, λ, and the number of iterations, k, in a way that minimizes the difference x* - xk with respect to a certain norm. Explicit rules are derived for calculating these parameters.One advantage of our approach is that the numerical rank can be easily determined by using the singular values. Furthermore, by the iterative procedure, x* is approximated without computing the singular vectors of A. This gives a fast and reliable method for approximating minimum norm solutions of well-conditioned rank-deficient least squares problems. Numerical experiments illustrate the viability of our ideas, and demonstrate that the new method gives more accurate approximations than an approach based on a QR decomposition with column pivoting. © 1998 John Wiley & Sons, Ltd.
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  • 53
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    New York, NY [u.a.] : Wiley-Blackwell
    ISSN: 1070-5325
    Keywords: almost incompressible elasticity ; finite elements ; semi-coarsening refinement ; algebraic multilevel ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The constant γ in the strengthened Cauchy-Buniakowski-Schwarc (CBS) inequality plays a key role in the convergence analysis of the multilevel iterative methods. We consider in this paper the approximation of the two-dimensional elasticity problem by bilinear rectangle finite elements. Two semi-coarsening refinement procedures are studied. We prove for both cases new estimates of the constant γ, uniformly on the Poisson ratio.As a result of the presented analysis we obtain an optimal order algebraic multiLevel iteration (AMLI) method for the case of balanced semi-coarsening mesh refinement. The total computational complexity of the algorithm is proportional to the size of the discrete problem with a proportionality constant independent of the Poisson ratio, that is, the algorithm is of optimal order for almost incompressible elasticity problems. Copyright © 1999 John Wiley & Sons, Ltd.
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  • 54
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    New York, NY [u.a.] : Wiley-Blackwell
    ISSN: 1070-5325
    Keywords: iterative methods ; operator trigonometry ; anti-eigenvector ; Dirichlet problem ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The new operator-trigonometric theory for iterative linear solvers is illustrated by working out its details for the classical model problem for numerical partial differential equations: the Dirichlet problem on the unit square. Copyright © 1999 John Wiley & Sons, Ltd.
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  • 55
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    New York, NY [u.a.] : Wiley-Blackwell
    ISSN: 1070-5325
    Keywords: convergence ; multigrid ; sparse grids ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The convergence behaviour of solution algorithms is investigated for the anisotropic Poisson problem on partially ordered, sparse families of regular grids in 3D. In order to study multilevel techniques on sparse families of grids, first we consider the convergence of a two-level algorithm that applies semi-coarsening successively in each of the coordinate directions. This algorithm shows good convergence, but recursive application of the successive semi-coarsening is not sufficiently efficient. Therefore we introduce another algorithm, which uses collective 3D semi-coarsened coarse grid corrections. The convergence behaviour of this collective version is worse, due to the lack of correspondence between the solutions on the different grids. By solving for the trivial solution we demonstrate that a good convergence behaviour of the collective version of the algorithm can be retained when the different solutions are sufficiently coherent. In order to solve also non-trivial problems, we develop a defect correction process. This algorithm makes use of hierarchical smoothing in order to deal with the problems related to the lack of coherence between the solutions on the different grids. Now good convergence rates are obtained also for non-trivial solutions. All convergence results are obtained for two-level processes. The results show convergence rates which are bounded, independent of the discretisation level and of the anisotropy in the problem. Copyright © 1999 John Wiley & Sons, Ltd.
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  • 56
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    Chichester, West Sussex : Wiley-Blackwell
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: Integral equations associated with the basic boundary value problems for the Laplace and Stokes equations are considered. The integral operators for these integral equations are interpreted as the pseudodifferential operators, and their principal symbols are calculated. The symbols are obtained in terms of the principal curvatures and the coefficients of the first quadratic form of the boundary. As a consequence, the initial approximation is suggested for the iterative methods solving the integral equations. © 1998 by B. G. Teubner Stuttgart-John Wiley & Sons Ltd.
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  • 57
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    Chichester, West Sussex : Wiley-Blackwell
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We present a bending model for a shallow arch, namely the type of curved rod where the curvature is of the order of the diameter of the cross section. The model is deduced in a rigorous mathematical way from classical tridimensional linear elasticity theory via asymptotic techniques, by taking the limit on a suitable re-scaled formulation of that problem as the diameter of the cross section tends to zero. This model is valid for general cases of applied forces and material, and it allows us to calculate displacements, axial stresses, bending moments and shear forces. The equations present a more general form than in the classical Bernoulli-Navier bending theory for straight slender rods, so that flexures and extensions are proved to be coupled in the most general case. © 1998 by B. G. Teubner Stuttgart-John Wiley & Sons Ltd.
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  • 58
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: In this work we analyse a model for radiative heat transfer in materials that are conductive, grey and semitransparent. Such materials are for example glass, silicon, water and several gases. The most important feature of the model is the non-local interaction due to exchange of radiation. This, together with non-linearity arising from the well-known Stefan-Boltzmann law, makes the resulting heat equation non-monotone. By analysing the terms related to heat radiation we prove that the operator defining the problem is pseudomonotone. Hence, we can prove the existence of weak solution in the cases where coercivity can be obtained. In the general case, we prove the solvability of the system using the technique of sub and supersolutions. © 1998 B. G. Teubner Stuttgart-John Wiley & Sons Ltd.
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  • 59
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    Chichester, West Sussex : Wiley-Blackwell
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: In this paper an initial-boundary-value problem in one-space dimension is studied for the Broadwell model extended to a gas mixture undergoing bimolecular reactions. Techniques of semigroup of bounded positive operators in a suitable Banach space are used to prove existence and uniqueness of the solution on bounded time intervals whose length depends on the initial data. © 1998 B. G. Teubner Stuttgart-John Wiley & Sons Ltd.
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  • 60
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    Chichester, West Sussex : Wiley-Blackwell
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: In the paper we study the problem of control by means of a heat source g for a thermoelastic system of equationsutt - ρ∇·p(θ, ∇u) - νΔut + DΔ2 u = f, cv(θ, ∇u)θt - κΔθ - ρθ[pθ (θ, ∇u)·∇ut] - ν∣∇ut∣2 = g, in a two-dimensional domain, where both viscosity ν and rigidity D are positive. Such a system has been considered in our former papers, and existence of solutions as well as uniqueness have been obtained. Here we prove the continuity and differentiability of solutions under somewhat stronger assumptions. An example of a control problem and necessary optimality conditions are presented. The system has an interpretation as a plate reinforced with shape memory alloy (SMA) wire mesh. © 1998 B. G. Teubner Stuttgart-John Wiley & Sons Ltd.
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  • 61
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We investigate the steady compressible Navier-Stokes equations near the equilibrium state v = 0, ρ = ρ0 (v the velocity, ρ the density) corresponding to a large potential force. We introduce a method of decomposition for such equations: the velocity field v is split into a non-homogeneous incompressible part u (div (ρ0u) = (0) and a compressible (irrotational) part ∇φ. In such a way, the original complicated mixed elliptic-hyperbolic system is split into several ‘standard’ equations: a Stokes-type system for u, a Poisson-type equation for φ and a transport equation for the perturbation of the density σ = ρ - ρ0. For ρ0 = const. (zero potential forces), the method coincides with the decomposition of Novotny and Padula [21]. To underline the advantages of the present approach, we give, as an example, a ‘simple’ proof of the existence of isothermal flows in bounded domains with no-slip boundary conditions. The approach is applicable, with some modifications, to more complicated geometries and to more complicated boundary conditions as we will show in forthcoming papers. © 1998 B.G. Teubner Stuttgart-John Wiley & Sons Ltd.
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  • 62
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The exact solutions for the KdV and the Calogero-Degasperis-Fokas mKdV equations can be obtained by the AKNS class. The technique developed relies on the construction of the wave functions which are solutions of the associated AKNS system; that is, a linear eigenvalue problem in the form of a system of first order partial differential equations. The method of characteristics is used and Bäcklund transformations (BTs) are employed to generate two new solutions from the old. © 1998 B.G. Teubner Stuttgart-John Wiley & Sons Ltd.
    Type of Medium: Electronic Resource
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  • 63
    Electronic Resource
    Electronic Resource
    Chichester, West Sussex : Wiley-Blackwell
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We present an initial-boundary value problem of a quasilinear degenerate parabolic equation for the settling and consolidation of a flocculated suspension. The corresponding definition of generalized solutions is formulated. It is based on an entropy integral inequality in the sense of Kružkov. From this definition, jump and entropy conditions that have to be satisfied at discontinuities, and an entropy condition valid on one boundary of the computational domain are derived. The latter implies a set-valued reformulation of the original boundary condition. It is interpreted geometrically and characterized by the solution of an auxiliary hyperbolic Riemann problem. © 1998 B. G. Teubner Stuttgart-John Wiley & Sons, Ltd.
    Additional Material: 3 Ill.
    Type of Medium: Electronic Resource
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  • 64
    Electronic Resource
    Electronic Resource
    Chichester, West Sussex : Wiley-Blackwell
    ISSN: 0170-4214
    Keywords: solitary wave ; stability ; long wave-short wave resonance equations ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: This paper concerns the orbital stability for solitary waves of the Long Wave-Short Wave resonance equations. Since the abstract results of Grillakis et al. [7, 8] cannot be applied directly, we can extend the abstract stability theory and use the detailed spectral analysis to obtain the stability of the solitary waves. © 1998 B. G. Teubner Stuttgart - John Wiley & Sons, Ltd.