445 research outputs found
A course space construction based on local Dirichlet-to-Neumann maps
Coarse-grid correction is a key ingredient of scalable domain decomposition methods. In this work we construct coarse-grid space using the low-frequency modes of the subdomain Dirichlet-to-Neumann maps and apply the obtained two-level preconditioners to the extended or the original linear system arising from an overlapping domain decomposition. Our method is suitable for parallel implementation, and its efficiency is demonstrated by numerical examples on problems with large heterogeneities for both manual and automatic partitionings
Abstract robust coarse spaces for systems of PDEs via generalized eigenproblems in the overlaps
Coarse spaces are instrumental in obtaining scalability for domain decomposition methods for partial differential equations (PDEs). However, it is known that most popular choices of coarse spaces perform rather weakly in the presence of heterogeneities in the PDE coefficients, especially for systems of PDEs. Here, we introduce in a variational setting a new coarse space that is robust even when there are such heterogeneities. We achieve this by solving local generalized eigenvalue problems in the overlaps of subdomains that isolate the terms responsible for slow convergence. We prove a general theoretical result that rigorously establishes the robustness of the new coarse space and give some numerical examples on two and three dimensional heterogeneous PDEs and systems of PDEs that confirm this property
Multispace and Multilevel BDDC
BDDC method is the most advanced method from the Balancing family of
iterative substructuring methods for the solution of large systems of linear
algebraic equations arising from discretization of elliptic boundary value
problems. In the case of many substructures, solving the coarse problem exactly
becomes a bottleneck. Since the coarse problem in BDDC has the same structure
as the original problem, it is straightforward to apply the BDDC method
recursively to solve the coarse problem only approximately. In this paper, we
formulate a new family of abstract Multispace BDDC methods and give condition
number bounds from the abstract additive Schwarz preconditioning theory. The
Multilevel BDDC is then treated as a special case of the Multispace BDDC and
abstract multilevel condition number bounds are given. The abstract bounds
yield polylogarithmic condition number bounds for an arbitrary fixed number of
levels and scalar elliptic problems discretized by finite elements in two and
three spatial dimensions. Numerical experiments confirm the theory.Comment: 26 pages, 3 figures, 2 tables, 20 references. Formal changes onl
Wer bremst verliert - Antimon in Straßenrandböden
Seit dem weitreichenden Verbot von Asbest in den 1980er Jahren wurde verstärkt das Halbmetall Antimon (Sb) in Bremsbelägen von PKW und LKW verwendet. Im Zuge des Bremsvorganges wird dieses in Form von Feinstaub freigesetzt und straßennah in die Böden eingetragen. Grundsätzlich sind Antimoneinträge in Böden negativ zu bewerten, da das Halbmetall toxische Wirkungen hervorrufen kann. Um die räumliche Verteilung von Antimon und seinen Bindungsformen in Straßenrandböden zu untersuchen, wurden 5 parallele Transekte mit jeweils 7 Entfernungen und 4 Probentiefen entlang einer Kölner Kreisstraße (Verkehrsaufkommen ca. 9.600 Fahrzeuge pro Tag) beprobt. Neben einer allgemeinen physikochemischen Charakterisierung der Bodenproben wurden ihre königswasser-löslichen Antimongehalte bestimmt. Zusätzlich wurde an einem Transekt eine sequentielle Extraktion nach Wenzel et al. 2001 durchgeführt, um die Bindungsformen von Antimon zu ermitteln. Die Antimongehalte nahmen von bis zu 6,18 g kg–1 unmittelbar am Straßenrand bis auf 0,513 g kg–1 in 10 m Entfernung ab. Ebenfalls konnte eine deutliche Abnahme mit der Bodentiefe (0 bis 30 cm) festgestellt werden. Dieses Verteilungsmuster deutet auf den Verkehr als Antimoneintragsquelle hin. Als Hinweis auf einen durch den Bremsabrieb metallener Bremsscheiben dominierten Eintrag wurde die magnetische Suszeptibilität gemessen. Allerdings lieferte der Korrelationskoeffizient (Spearman) von Antimon gegenüber der magnetischen Suszeptibilität 0,423 (p = 0,023) nur einen eher schwachen Beleg. Die ursprünglich für Arsen entwickelte sequentielle Extraktion ließ sich reproduzierbar ebenfalls für Antimon anwenden. Anhand dieser konnten im Wesentlichen drei Trends der Bindungsformen erfasst werden: i) spezifisch gebundenes Antimon (Fraktion 2: 0,05 mol l–1 (NH4)H2P2O4) konnte lediglich innerhalb 1 m Entfernung zur Straße und mit der Bodentiefen abnehmenden Gehalten nachgewiesen werden, ii) der Anteil an schwachkristallinen Eisenoxiden gebundenem Antimon (Fraktion 3: 0,2 mol l–1 (NH4)2-Oxalatpuffer; pH 3,25) nahm signifikant mit steigender Entfernung zur Straße ab, während iii) die prozentualen Gehalte in den starkkristallinen Eisenoxiden (Fraktion 4: 0,2 mol l–1 (NH4)2-Oxalatpuffer + 0,1 mol l–1 Ascorbinsäure; pH 3,25) und in der Residualphase (Fraktion 5: Königswasser) zunahmen
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Self-repairing control for damaged robotic manipulators
Algorithms have been developed allowing operation of robotic systems under damaged conditions. Specific areas addressed were optimal sensor location, adaptive nonlinear control, fault-tolerant robot design, and dynamic path-planning. A seven-degree-of-freedom, hydraulic manipulator, with fault-tolerant joint design was also constructed and tested. This report completes this project which was funded under the Laboratory Directed Research and Development program
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Structural dynamics modeling and testing of the Department of Energy tractor/trailer combination
This study presents a combined analytical and experimental effort to characterize and improve the ride quality of the Department of Energy tractor/trailer combination. The focus is to augment the experimental test results with the use of a high quality computer model. The discussion includes an overview of the finite element model of the vehicle and experimental modal test results. System identification techniques are employed to update the mathematical model. The validated model is then used to illustrate the benefits of incorporating two major design changes, namely the switch from a separate cab/sleeper configuration to an integrated cab, and the use of a cab suspension system
Cross Section Measurement of Charged Pion Photoproduction from Hydrogen and Deuterium
We have measured the differential cross section for the gamma n --> pi- p and
gamma p --> pi+ n reactions at center of mass angle of 90 degree in the photon
energy range from 1.1 to 5.5 GeV at Jefferson Lab (JLab). The data at photon
energies greater than 3.3 GeV exhibit a global scaling behavior for both pi-
and pi+ photoproduction, consistent with the constituent counting rule and the
existing pi+ photoproduction data. Possible oscillations around the scaling
value are suggested by these new data The data show enhancement in the scaled
cross section at a center-of-mass energy near 2.2 GeV. The cross section ratio
of exclusive pi- to pi+ photoproduction at high energy is consistent with the
prediction based on one-hard-gluon-exchange diagrams
Nucleon-nucleon elastic scattering analysis to 2.5 GeV
A partial-wave analysis of NN elastic scattering data has been completed.
This analysis covers an expanded energy range, from threshold to a laboratory
kinetic energy of 2.5 GeV, in order to include recent elastic pp scattering
data from the EDDA collaboration. The results of both single-energy and
energy-dependent analyses are described.Comment: 23 pages of text. Postscript files for the figures are available from
ftp://clsaid.phys.vt.edu/pub/said/n
A versatile method for simulating pp -> ppe+e- and dp -> pne+e-p_spec reactions
We have developed a versatile software package for the simulation of
di-electron production in and collisions at SIS energies. Particular
attention has been paid to incorporate different descriptions of the Dalitz
decay via a common interface. In addition, suitable
parameterizations for the virtual bremsstrahlung process
based on one-boson exchange models have been implemented. Such simulation tools
with high flexibility of the framework are important for the interpretation of
the di-electron data taken with the HADES spectrometer and the design of
forthcoming experiments
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