13,008 research outputs found
A Fast Algorithm for Parabolic PDE-based Inverse Problems Based on Laplace Transforms and Flexible Krylov Solvers
We consider the problem of estimating parameters in large-scale weakly
nonlinear inverse problems for which the underlying governing equations is a
linear, time-dependent, parabolic partial differential equation. A major
challenge in solving these inverse problems using Newton-type methods is the
computational cost associated with solving the forward problem and with
repeated construction of the Jacobian, which represents the sensitivity of the
measurements to the unknown parameters. Forming the Jacobian can be
prohibitively expensive because it requires repeated solutions of the forward
and adjoint time-dependent parabolic partial differential equations
corresponding to multiple sources and receivers. We propose an efficient method
based on a Laplace transform-based exponential time integrator combined with a
flexible Krylov subspace approach to solve the resulting shifted systems of
equations efficiently. Our proposed solver speeds up the computation of the
forward and adjoint problems, thus yielding significant speedup in total
inversion time. We consider an application from Transient Hydraulic Tomography
(THT), which is an imaging technique to estimate hydraulic parameters related
to the subsurface from pressure measurements obtained by a series of pumping
tests. The algorithms discussed are applied to a synthetic example taken from
THT to demonstrate the resulting computational gains of this proposed method
Semi-analytical description of the modulator section of the coherent electron cooling
In the coherent electron cooling, the modern hadron beam cooling technique,
each hadron receives an individual kick from the electric field of the
amplified electron density perturbation created in the modulator by this hadron
in a co-propagating electron beam. We developed a method for computing the
dynamics of these density perturbations in an infinite electron plasma with any
equilibrium velocity distribution -- a possible model for the modulator. We
derived analytical expressions for the dynamics of the density perturbations in
the Fourier-Laplace domain for a variety of 1D, 2D, and 3D equilibrium
distributions of the electron beam. To obtain the space-time dynamics, we
employed the fast Fourier transform (FFT) algorithm. We also found an
analytical solution in the space-time domain for the 1D Cauchy equilibrium
distribution, which serves as a benchmark for our general approach based on
numerical evaluation of the integral transforms and as a fast alternative to
the numerical computations. We tested the method for various distributions and
initial conditions.Comment: 11 pages, 5 figure
Transform methods for precision continuum and control models of flexible space structures
An open loop optimal control algorithm is developed for general flexible structures, based on Laplace transform methods. A distributed parameter model of the structure is first presented, followed by a derivation of the optimal control algorithm. The control inputs are expressed in terms of their Fourier series expansions, so that a numerical solution can be easily obtained. The algorithm deals directly with the transcendental transfer functions from control inputs to outputs of interest, and structural deformation penalties, as well as penalties on control effort, are included in the formulation. The algorithm is applied to several structures of increasing complexity to show its generality
Frequency response modeling and control of flexible structures: Computational methods
The dynamics of vibrations in flexible structures can be conventiently modeled in terms of frequency response models. For structural control such models capture the distributed parameter dynamics of the elastic structural response as an irrational transfer function. For most flexible structures arising in aerospace applications the irrational transfer functions which arise are of a special class of pseudo-meromorphic functions which have only a finite number of right half place poles. Computational algorithms are demonstrated for design of multiloop control laws for such models based on optimal Wiener-Hopf control of the frequency responses. The algorithms employ a sampled-data representation of irrational transfer functions which is particularly attractive for numerical computation. One key algorithm for the solution of the optimal control problem is the spectral factorization of an irrational transfer function. The basis for the spectral factorization algorithm is highlighted together with associated computational issues arising in optimal regulator design. Options for implementation of wide band vibration control for flexible structures based on the sampled-data frequency response models is also highlighted. A simple flexible structure control example is considered to demonstrate the combined frequency response modeling and control algorithms
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