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  • 1
    Electronic Resource
    Electronic Resource
    On theR-order of coupled sequences arising in single-step type methods (1988)
    Springer
    Numerische Mathematik 53 (1988), S. 653-661 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65H10 ; 15A48 ; CR: G1.5
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary As shown in preceding papers of the authors, the verification of anR-convergence order τ for sequences coupled by a system (1.1) of basic inequalities can be reduced to the positive solvability of system (3.3) of linear inequalities. Further, the bestR-order $$\bar \tau$$ implied by (1.1) is equal to the minimal spectral radius of certain matrices composed from the exponents occuring in (1.1). Now, these results are proven in a unified and essentially simpler way. Moreover, they are somewhat extended in order to facilitate applications to concrete methods.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01397134
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    On the R-order of coupled sequences III (1983)
    Springer
    Computing 30 (1983), S. 157-169 
    Details
    ISSN: 1436-5057
    Keywords: 65H10 ; 15A48 ; Iterative parallel processes ; best individualR-orders ; ordered positive decomposition
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Description / Table of Contents: Zusammenfassung Für konvergente Folgen {x n,1 },...,{x n,s }, welche über ein System (2) von Ungleichungen miteinander verkoppelt sind, werden die besten individuellenR-Ordnungen τ1,...,τ s bestimmt. Dazu wird gezeigt, daß diese gleich den Spektralradien von bestimmten Matrizen sind, welche aus Exponenten in (2) gebildet werden.
    Notes: Abstract For convergent sequences {x n,1 },...{x n,s } coupled by a system (2) of inequalities the optimal individualR-orders τ1,...,τ s are determined as the spectral radii of certain matrices composed of exponents appearing in (2).
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02280786
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  • 3
    Electronic Resource
    Electronic Resource
    Determination of the cone radius for positive concave operators (1984)
    Springer
    Computing 33 (1984), S. 37-49 
    Details
    ISSN: 1436-5057
    Keywords: 65H10 ; 90C30 ; 15A48 ; Iterative processes ; bestR-orders ; cone radius of concave operators ; spectral radii ; partial ordering
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Description / Table of Contents: Zusammenfassung Die Berechnung der bestenR-Ordnung von Folgen aus iterativen Näherungsverfahren führt auf die Ermittlung des hier eingeführten Kegelradius bestimmter konkaver Operatoren. Das Hauptergebnis der Arbeit ist die Darstellung des Kegelradius als Infimum der Spektralradien aller den konkaven Operator majorisierenden linearen Operatoren. Diese Charakterisierung ist von numerischem Intersse.
    Notes: Abstract The computation of bestR-orders of sequences produced by iterative methods leads to the determination of the cone radius of certain concave operators. The main result of the paper is the representation of the cone radius as the infimum of spectral radii of all linear operators majorizing the concave operator. This characterization is of numerical interest.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02243074
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  • 4
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    CME Flux Rope and Shock Identifications and Locations: Comparison of White Light Data, Graduated Cylindrical Shell Model, and MHD Simulations (2016)
    In:  Other Sources
    Details
    Publication Date: 2017-04-15
    Description: Coronal mass ejections (CMEs) are major transient phenomena in the solar corona that are observed with ground-based and spacecraft-based coronagraphs in white light or with in situ measurements by spacecraft. CMEs transport mass and momentum and often drive shocks. In order to derive the CME and shock trajectories with high precision, we apply the graduated cylindrical shell (GCS) model to fit a flux rope to the CME directed toward STEREO A after about 19:00 UT on 29 November 2013 and check the quality of the heliocentric distance-time evaluations by carrying out a three-dimensional magnetohydrodynamic (MHD) simulation of the same CME with the Block Adaptive Tree Solar-Wind Roe Upwind Scheme (BATS-R-US) code. Heliocentric distances of the CME and shock leading edges are determined from the simulated white light images and magnetic field strength data. We find very good agreement between the predicted and observed heliocentric distances, showing that the GCS model and the BATS-R-US simulation approach work very well and are consistent. In order to assess the validity of CME and shock identification criteria in coronagraph images, we also compute synthetic white light images of the CME and shock. We find that the outer edge of a cloud-like illuminated area in the observed and predicted images in fact coincides with the leading edge of the CME flux rope and that the outer edge of a faint illuminated band in front of the CME leading edge coincides with the CME-driven shock front.
    Keywords: Solar Physics
    Type: GSFC-E-DAA-TN40667 , Journal of Geophysical Research: Space Physics (e-ISSN 2169-9402); Volume 121; Issue 3; 1886-1906
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  • 5
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    Coronal Magnetic Field Profiles from Shock-CME Standoff Distances (2016)
    In:  Other Sources
    Details
    Publication Date: 2019-07-13
    Description: Coronagraphs observe coronal mass ejections (CMEs) and driven shocks in white light images.From these observations the shocks speed and the shocks standoff distance from the CMEs leading edge can be derived. Using these quantities, theoretical relationships between the shocks Alfvenic Mach number MA and standoff distance, and empirical radial profiles for the solar wind velocity and number density, the radial magnetic field profile upstream of the shock can be calculated. These profiles cannot be measured directly. We test the accuracy of this method for estimating the radial magnetic field profile upstream of the shock by simulating a sample CME that occurred on 29 November 2013 using the three-dimensional (3-D) magnetohydrodynamic Block-Adaptive-Tree-Solar wind-Roe-Upwind-Scheme code, retrieving shock-CME standoff distances from the simulation, and comparing the estimated and simulated radial magnetic field profiles. We find good agreement between the two profiles (within +/-30%) between 1.8 and 10R.Our simulations confirm that a linear relationship exists between the standoff distance and the inverse compression ratio at the shock. We also find very good agreement between the empirical and simulated radial profiles of the number density and speed of the solar wind and inner corona.
    Keywords: Solar Physics
    Type: GSFC-E-DAA-TN40820 , Journal of Geophysical Research: Space Physics (ISSN 2169-9380) (e-ISSN 2169-9402); 121; 10; 9299–9315
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  • 6
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    CME Flux Rope and Shock Identifications and Locations: Comparison of White Light Data, Graduated Cylindrical Shell Model, and MHD Simulations (2016)
    In:  Other Sources
    Details
    Publication Date: 2019-07-13
    Description: Coronal mass ejections (CMEs) are major transient phenomena in the solar corona that are observed with ground-based and spacecraft-based coronagraphs in white light or with in situ measurements by spacecraft. CMEs transport mass and momentum and often drive shocks. In order to derive the CME and shock trajectories with high precision, we apply the graduated cylindrical shell (GCS) model to fit a flux rope to the CME directed toward STEREO A after about 19:00 UT on 29 November 2013 and check the quality of the heliocentric distance-time evaluations by carrying out a three-dimensional magnetohydrodynamic (MHD) simulation of the same CME with the Block Adaptive Tree Solar-Wind Roe Upwind Scheme (BATS-R-US) code. Heliocentric distances of the CME and shock leading edges are determined from the simulated white light images and magnetic field strength data. We find very good agreement between the predicted and observed heliocentric distances, showing that the GCS model and the BATS-R-US simulation approach work very well and are consistent. In order to assess the validity of CME and shock identification criteria in coronagraph images, we also compute synthetic white light images of the CME and shock. We find that the outer edge of a cloud-like illuminated area in the observed and predicted images in fact coincides with the leading edge of the CME flux rope and that the outer edge of a faint illuminated band in front of the CME leading edge coincides with the CME-driven shock front.
    Keywords: Solar Physics
    Type: GSFC-E-DAA-TN40667 , GSFC-E-DAA-TN40626 , Journal of Geophysical Research: Space Physics (ISSN 2169-9402) (e-ISSN 2169-9402); 121; 3; 1886-1906
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  • 7
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    High amplitude waves in the expanding solar wind plasma (1995)
    In:  Other Sources
    Details
    Publication Date: 2019-07-17
    Description: We simulated the 1-D nonlinear time-evolution of high-amplitude Alfven, slow and fast magnetoacoustic waves in the solar wind propagating outward at different angles to the mean magnetic (spiral) field, using the expanding box model. The simulation results for Alfven waves and fast magnetoacustic waves fit the observational constraints in the solar wind best, showing decreasing trends for energies and other rms-quantities due to expansion and the appearance of inward propagating waves as minor species in the wind. Inward propagating waves are generated by reflection of Alfven waves propagating at large angles to the magnetic field or they coincide with the occurrence of compressible fluctuations. In our simulations, fast and slow magnetoacoustic waves seem to have a level in the density-fluctuations which is too high when we compare with the observations. Furthermore, the evolution of energies for slow magnetoacoustic waves differs strongly from the evolution of fluctuation energies in situ.
    Keywords: Solar Physics
    Type: ; 77
    Format: text
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