DRUM Community: UMIACS Technical Reports
http://hdl.handle.net/1903/2277
Thu, 02 Apr 2015 03:10:03 GMT2015-04-02T03:10:03ZA Stochastic Approach to Uncertainty in the Equations of MHD Kinematics
http://hdl.handle.net/1903/15523
Title: A Stochastic Approach to Uncertainty in the Equations of MHD Kinematics
Authors: Phillips, Edward G.; Elman, Howard C.
Abstract: The magnetohydodynamic (MHD) kinematics model describes the
electromagnetic behavior of an electrically conducting fluid when its
hydrodynamic properties are assumed to be known. In particular, the MHD
kinematics equations can be used to simulate the magnetic field induced
by a given velocity field. While prescribing the velocity field leads to
a simpler model than the fully coupled MHD system, this may introduce
some epistemic uncertainty into the model. If the velocity of a physical
system is not known with certainty, the magnetic field obtained from the
model may not be reflective of the magnetic field seen in experiments.
Additionally, uncertainty in physical parameters such as the magnetic
resistivity may affect the reliability of predictions obtained from this
model. By modeling the velocity and the resistivity as random variables
in the MHD kinematics model, we seek to quantify the effects of
uncertainty in these fields on the induced magnetic field. We develop
stochastic expressions for these quantities and investigate their impact
within a finite element discretization of the kinematics equations. We
obtain mean and variance data through Monte-Carlo simulation for several
test problems. Toward this end, we develop and test an efficient block
preconditioner for the linear systems arising from the discretized
equations.Thu, 10 Jul 2014 00:00:00 GMThttp://hdl.handle.net/1903/155232014-07-10T00:00:00ZPreconditioning Techniques for Reduced Basis Methods for Parameterized Partial Differential Equations
http://hdl.handle.net/1903/15078
Title: Preconditioning Techniques for Reduced Basis Methods for Parameterized Partial Differential Equations
Authors: Elman, Howard C.; Forstall, Virginia
Abstract: The reduced basis methodology is an efficient approach to solve
parameterized discrete partial differential equations when the solution
is needed at many parameter values. An offline step approximates the
solution space and an online step utilizes this approximation, the
reduced basis, to solve a smaller reduced problem, which provides an
accurate estimate of the solution. Traditionally, the reduced problem is
solved using direct methods. However, the size of the reduced system
needed to produce solutions of a given accuracy depends on the
characteristics of the problem, and it may happen that the size is
significantly smaller than that of the original discrete problem but
large enough to make direct solution costly. In this scenario, it may be
more effective to use iterative methods to solve the reduced problem. We
construct preconditioners for reduced iterative methods which are
derived from preconditioners for the full problem. This approach permits
reduced basis methods to be practical for larger bases than direct
methods allow. We illustrate the effectiveness of iterative methods for
solving reduced problems by considering two examples, the steady-state
diffusion and convection-diffusion-reaction equations.Tue, 27 May 2014 00:00:00 GMThttp://hdl.handle.net/1903/150782014-05-27T00:00:00ZAnomaly Detection for Symbolic Representations
http://hdl.handle.net/1903/15073
Title: Anomaly Detection for Symbolic Representations
Authors: Cox, Michael T.; Paisner, Matt; Oates, Tim; Perlis, Don
Abstract: A fully autonomous agent recognizes new problems, explains what causes
such problems, and generates its own goals to solve these problems. Our
approach to this goal-driven model of autonomy uses a methodology called
the Note-Assess-Guide procedure. It instantiates a monitoring process in
which an agent notes an anomaly in the world, assesses the nature and
cause of that anomaly, and guides appropriate modifications to behavior.
This report describes a novel approach to the note phase of that
procedure. A-distance, a sliding-window statistical distance metric, is
applied to numerical vector representations of intermediate states from
plans generated for two symbolic domains. Using these representations,
the metric is able to detect anomalous world states caused by
restricting the actions available to the planner.Tue, 25 Mar 2014 00:00:00 GMThttp://hdl.handle.net/1903/150732014-03-25T00:00:00ZRecursive computation of spherical harmonic rotation coefficients of large degree
http://hdl.handle.net/1903/15013
Title: Recursive computation of spherical harmonic rotation coefficients of large degree
Authors: Gumerov, Nail A.; Duraiswami, Ramani
Abstract: Computation of the spherical harmonic rotation coefficients or elements
of Wigner's d-matrix is important in a number of quantum mechanics and
mathematical physics applications. Particularly, this is important for
the Fast Multipole Methods in three dimensions for the Helmholtz,
Laplace and related equations, if rotation-based decomposition of
translation operators are used. In these and related problems related to
representation of functions on a sphere via spherical harmonic
expansions computation of the rotation coefficients of large degree n
(of the order of thousands and more) may be necessary. Existing
algorithms for their computation, based on recursions, are usually
unstable, and do not extend to n. We develop a new recursion and study
its behavior for large degrees, via computational and asymptotic
analyses. Stability of this recursion was studied based on a novel
application of the Courant-Friedrichs-Lewy condition and the von Neumann
method for stability of finite-difference schemes for solution of PDEs.
A recursive algorithm of minimal complexity O(n^2) for degree n and
FFT-based algorithms of complexity O(n^2 log n) suitable for computation
of rotation coefficients of large degrees are proposed, studied
numerically, and cross-validated. It is shown that the latter algorithm
can be used for n <~ 10^3 in double precision, while the former
algorithm was tested for large n (up to 10^4 in our experiments) and
demonstrated better performance and accuracy compared to the FFT-based
algorithm.Fri, 28 Mar 2014 00:00:00 GMThttp://hdl.handle.net/1903/150132014-03-28T00:00:00Z