20,737 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
Transmission properties in waveguides: An optical streamline analysis
A novel approach to study transmission through waveguides in terms of optical
streamlines is presented. This theoretical framework combines the computational
performance of beam propagation methods with the possibility to monitor the
passage of light through the guiding medium by means of these sampler paths. In
this way, not only the optical flow along the waveguide can be followed in
detail, but also a fair estimate of the transmitted light (intensity) can be
accounted for by counting streamline arrivals with starting points
statistically distributed according to the input pulse. Furthermore, this
approach allows to elucidate the mechanism leading to energy losses, namely a
vortical dynamics, which can be advantageously exploited in optimal waveguide
design.Comment: 8 pages, 4 figure
Kinetic Solvers with Adaptive Mesh in Phase Space
An Adaptive Mesh in Phase Space (AMPS) methodology has been developed for
solving multi-dimensional kinetic equations by the discrete velocity method. A
Cartesian mesh for both configuration (r) and velocity (v) spaces is produced
using a tree of trees data structure. The mesh in r-space is automatically
generated around embedded boundaries and dynamically adapted to local solution
properties. The mesh in v-space is created on-the-fly for each cell in r-space.
Mappings between neighboring v-space trees implemented for the advection
operator in configuration space. We have developed new algorithms for solving
the full Boltzmann and linear Boltzmann equations with AMPS. Several recent
innovations were used to calculate the discrete Boltzmann collision integral
with dynamically adaptive mesh in velocity space: importance sampling,
multi-point projection method, and the variance reduction method. We have
developed an efficient algorithm for calculating the linear Boltzmann collision
integral for elastic and inelastic collisions in a Lorentz gas. New AMPS
technique has been demonstrated for simulations of hypersonic rarefied gas
flows, ion and electron kinetics in weakly ionized plasma, radiation and light
particle transport through thin films, and electron streaming in
semiconductors. We have shown that AMPS allows minimizing the number of cells
in phase space to reduce computational cost and memory usage for solving
challenging kinetic problems
Segmentation of Myocardial Boundaries in Tagged Cardiac MRI Using Active Contours: A Gradient-Based Approach Integrating Texture Analysis
The noninvasive assessment of cardiac function is of first importance for the diagnosis of cardiovascular diseases. Among all medical scanners only a few enables radiologists to evaluate the local cardiac motion. Tagged cardiac MRI is one of them. This protocol generates on Short-Axis (SA) sequences a dark grid which is deformed in accordance with the cardiac motion. Tracking the grid allows specialists a local estimation of cardiac geometrical parameters within myocardium. The work described in this paper aims to automate the myocardial contours detection in order to optimize the detection and the tracking of the grid of tags within myocardium. The method we have developed for endocardial and epicardial contours detection is based on the use of texture analysis and active contours models. Texture analysis allows us to define energy maps more efficient than those usually used in active contours methods where attractor is often based on gradient and which were useless in our case of study, for quality of tagged cardiac MRI is very poor
Non-equilibrium dissociating nitrogen flow over spheres and circular cylinders
Theoretical results based on the methods of Freeman and Garr & Marrone show that the stand-off distance and flow pattern of non-equilibrium dissociating flow of nitrogen over the front part of a blunt body can be correlated in terms of a single reaction rate parameter ω taking account of parameters describing the speed, density, dissociation and temperature of the free stream. The density pattern, which is sensitive to the reaction rate, consists of two distinct regions dominated by the effects of reaction and pressure respectively. The shape and size of these regions depend on Q. Experimental results obtained by optical interferometry in a free-piston shock tunnel confirm the theoretical results. A scale effect consistent with the induction time phenomenon suggested by Shui, Appleton & Keck modifies the theoretical results considerably in the case of small models
Combinatorial Continuous Maximal Flows
Maximum flow (and minimum cut) algorithms have had a strong impact on
computer vision. In particular, graph cuts algorithms provide a mechanism for
the discrete optimization of an energy functional which has been used in a
variety of applications such as image segmentation, stereo, image stitching and
texture synthesis. Algorithms based on the classical formulation of max-flow
defined on a graph are known to exhibit metrication artefacts in the solution.
Therefore, a recent trend has been to instead employ a spatially continuous
maximum flow (or the dual min-cut problem) in these same applications to
produce solutions with no metrication errors. However, known fast continuous
max-flow algorithms have no stopping criteria or have not been proved to
converge. In this work, we revisit the continuous max-flow problem and show
that the analogous discrete formulation is different from the classical
max-flow problem. We then apply an appropriate combinatorial optimization
technique to this combinatorial continuous max-flow CCMF problem to find a
null-divergence solution that exhibits no metrication artefacts and may be
solved exactly by a fast, efficient algorithm with provable convergence.
Finally, by exhibiting the dual problem of our CCMF formulation, we clarify the
fact, already proved by Nozawa in the continuous setting, that the max-flow and
the total variation problems are not always equivalent.Comment: 26 page
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