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  • 1
    Electronic Resource
    Electronic Resource
    A SPACE-TIME COUPLED p-VERSION LEAST SQUARES FINITE ELEMENT FORMULATION FOR UNSTEADY TWO-DIMENSIONAL NAVIER-STOKES EQUATIONS (1996)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 39 (1996), S. 2593-2618 
    Details
    ISSN: 0029-5981
    Keywords: space-time coupled ; p-version ; least squares ; time-marching ; accuracy and stability ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper presents a p-version least squares finite element formulation for two-dimensional unsteady fluid flow described by Navier-Stokes equations where the effects of space and time are coupled. The dimensionless form of the Navier-Stokes equations are first cast into a set of first-order differential equations by introducing auxiliary variables. This permits the use of C0 element approximation. The element properties are derived by utilizing the p-version approximation functions in both space and time and then minimizing the error functional given by the space-time integral of the sum of squares of the errors resulting from the set of first-order differential equations. This results in a true space-time coupled least squares minimization procedure. The application of least squares minimization to the set of coupled first-order partial differential equations results in finding a solution vector {δ} which makes gradient of error functional with respect to {δ} a null vector. This is accomplished by using Newton's method with a line search.A time marching procedure is developed in which the solution for the current time step provides the initial conditions for the next time step. Equilibrium iterations are carried out for each time step until the error functional and each component of the gradient of the error functional with respect to nodal degrees of freedom are below a certain prespecified tolerance. The space-time coupled p-version approximation functions provide the ability to control truncation error which, in turn, permits very large time steps. What literally requires hundreds of time steps in uncoupled conventional time marching procedures can be accomplished in a single time step using the present space-time coupled approach. The generality, success and superiority of the present formulation procedure is demonstrated by presenting specific numerical examples for transient couette flow and transient lid driven cavity. The results are compared with the analytical solutions and those reported in the literature. The formulation presented here is ideally suited for space-time adaptive procedures. The element error functional values provide a mechanism for adaptive h, p or hp refinements.
    Additional Material: 8 Ill.
    Type of Medium: Electronic Resource
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    Paper (German National Licenses)
  • 2
    Electronic Resource
    Electronic Resource
    Alteration of circulating antibody response of mice exposed to 9-GHz pulsed microwaves (1980)
    New York, NY [u.a.] : Wiley-Blackwell
    Bioelectromagnetics 1 (1980), S. 397-404 
    Details
    ISSN: 0197-8462
    Keywords: antibody response ; microwaves ; immunology ; 9-GHz pulsed radiation ; infectivity ; mouse ; Life and Medical Sciences ; Occupational Health and Environmental Toxicology
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Biology , Physics
    Notes: A significant increase was observed in the circulating antibody titers of mice exposed to 9-GHz pulsed microwaves at an average power density of 10 mW/ cm2, two hours per day for five days compared with sham-irradiated animals. The mice were previously immunized with type III pneumococcal polysaccharide. Following irradiation, a portion of the immunized animals were challenged with virulent Streptococcus pneumoniae, type III. Ten days after challenge, mortality was essentially the same in the two groups, but during the ten day period, there was a noticeable increase in the survival time of the irradiated animals compared with the sham-irradiated animals, suggesting that the increased circulating antibody response afforded some degree of temporary protection to the animals.
    Additional Material: 3 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/bem.2250010406
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