140 research outputs found
Convergence of iterative split-operator approaches for approximating nonlinear reactive transport problems
Abstract Numerical solutions to nonlinear reactive solute transport problems (NRTPs) are often computed using split-operator (SO) approaches, which separate the transport and reaction processes. This uncoupling introduces an additional source of numerical error, known as the splitting error. The iterative split-operator (ISO) algorithm removes the splitting error through iteration. Although the ISO algorithm is often used, there has been very little analysis of its convergence behavior. This work uses theoretical analysis and numerical experiments to investigate the convergence rate of the ISO approach for solving NRTPs. We show that under certain assumptions regarding smoothness, the convergence rate of the ISO algorithm applied NRTPs is O(Î ). We demonstrate that the theoretical convergence rate can be achieved in practice if the numerical solution of the transport and reaction steps are carried out with sufficient accuracy. We also show that accurate estimation of the lagged operator in each step is crucial to obtaining the theoretical convergence rate
Optimal design for problems involving flow and transport phenomena in saturated subsurface systems
Abstract Estimation problems arise routinely in subsurface hydrology for applications that range from water resources management to water quality protection to subsurface restoration. Interest in optimal design of such systems has increased over the last two decades and this area is considered an important and active area of research. In this work, we review the state of the art, assess important challenges that must be resolved to reach a mature level of understanding, and summarize some promising approaches that might help meet some of the challenges. While much has been accomplished to date, we conclude that more work remains before comprehensive, efficient, and robust solution methods exist to solve the most challenging applications in subsurface science. We suggest that future directions of research include the application of direct search solution methods, and developments in stochastic and multi-objective optimization. We present a set of comprehensive test problems for use in the research community as a means for benchmarking and comparing optimization approaches
Efficient steady-state solution techniques for variably saturated groundwater flow
We consider the simulation of steady-state variably saturated groundwater flow using Richards' equation (RE). The difficulties associated with solving RE numerically
are well known. Most discretization approaches for RE lead to nonlinear systems
that are large and difficult to solve. The solution of nonlinear systems for steady-
state problems can be particularly challenging, since a good initial guess for the
steady-state solution is often hard to obtain, and the resulting linear systems may
be poorly scaled. Common approaches like Picard iteration or variations of Newton's method have their advantages but perform poorly with standard globalization
techniques under certain conditions.
Pseudo-transient continuation has been used in computational fluid dynamics for some time to obtain steady-state solutions for problems in which Newton's method
with standard line-search strategies fails. It combines aspects of backward Euler time
integration and Newton's method to select intermediate estimates of the steady-state solution. Here, we examine the use of pseudo-transient continuation as well as
Newton's method combined with standard globalization techniques for steady-state
problems in heterogeneous domains. We investigate the methods' performance with
direct and preconditioned Krylov iterative linear solvers. We then make recommendations for robust and efficient approaches to obtain steady-state solutions for RE
under a range of conditions
Magnetic Resonance Detection of Gas Microbubbles via HyperCEST: A Path Toward Dual Modality Contrast Agent
Gas microbubbles are an established clinical ultrasound contrast agent. They could also become a powerful magnetic resonance (MR) intravascular contrast agent, but their low susceptibility-induced contrast requires high circulating concentrations or the addition of exogenous paramagnetic nanoparticles for MR detection. In order to detect clinical in vivo concentrations of raw microbubbles via MR, an alternative detection scheme must be used. HyperCEST is an NMR technique capable of indirectly detecting signals from very dilute molecules (concentrations well below the NMR detection threshold) that exchange hyperpolarized 129Xe. Here, we use quantitative hyperCEST to show that microbubbles are very efficient hyperCEST agents. They can accommodate and saturate millions of 129Xe atoms at a time, allowing for their indirect detection at concentrations as low as 10 femtomolar. The increased MR sensitivity to microbubbles achieved via hyperCEST can bridge the gap for microbubbles to become a dual modality contrast agent
Constrained dogleg methods for nonlinear systems with simple bounds
We focus on the numerical solution of medium scale bound-constrained systems of nonlinear equations. In this context, we consider an affine-scaling trust region approach that allows a great flexibility in choosing the scaling matrix used to handle the bounds. The method is based on a dogleg procedure tailored for constrained problems and so, it is named Constrained Dogleg method. It generates only strictly feasible iterates. Global and locally fast convergence is ensured under standard assumptions. The method has been implemented in the Matlab solver CoDoSol that supports several diagonal scalings in both spherical and elliptical trust region frameworks. We give a brief account of CoDoSol and report on the computational experience performed on a number of representative test problem
Reduced Basis Method for the Stokes Equations in Decomposable Parametrized Domains Using Greedy Optimization
Flow simulations in pipelined channels and several kinds of parametrized configurations have a growing interest in many life sciences and industrial applications. Applications may be found in the analysis of the blood flow in specific compartments of the circulatory system that can be represented as a combination of few deformed vessels from reference ones, e.g. pipes. We propose a solution approach that is particularly suitable for the study of internal flows in hierarchical parametrized geometries. The main motivation is for applications requiring rapid and reliable numerical simulations of problems in domains involving parametrized complex geometries. The classical reduced basis (RB) method is very effective to address viscous flows equations in parametrized geometries (see, e.g., [10]). An interesting alternative foresees a combination of RB with a domain decomposition approach. In this respect, preliminary efforts to reduce the global parametrized problem to local ones have led to the introduction of the so-called reduced basis element method to solve the Stokes problem [6], and more recently to the reduced basis hybrid method [3] and to the static condensation method [7]. In general, we are interested in defining a method able to maintain the flexibility of dealing with arbitrary combinations of subdomains and several geometrical deformations of the latter. A further new contribution to this field is the computation of the reduced basis functions through an optimization greedy algorithm
Bottom-Tau Unification in SUSY SU(5) GUT and Constraints from b to s gamma and Muon g-2
An analysis is made on bottom-tau Yukawa unification in supersymmetric (SUSY)
SU(5) grand unified theory (GUT) in the framework of minimal supergravity, in
which the parameter space is restricted by some experimental constraints
including Br(b to s gamma) and muon g-2. The bottom-tau unification can be
accommodated to the measured branching ratio Br(b to s gamma) if superparticle
masses are relatively heavy and higgsino mass parameter \mu is negative. On the
other hand, if we take the latest muon g-2 data to require positive SUSY
contributions, then wrong-sign threshold corrections at SUSY scale upset the
Yukawa unification with more than 20 percent discrepancy. It has to be
compensated by superheavy threshold corrections around the GUT scale, which
constrains models of flavor in SUSY GUT. A pattern of the superparticle masses
preferred by the three requirements is also commented.Comment: 21pages, 6figure
Neutralino Dark Matter, b-tau Yukawa Unification and Non-Universal Sfermion Masses
We study the implications of minimal non-Universal Boundary Conditions in the
sfermion Soft SUSY Breaking (SSB) masses of mSUGRA. We impose asymptotic b-tau
Yukawa coupling Unification and we resort to a parameterization of the
deviation from Universality in the SSB motivated by the multiplet structure of
SU(5) GUT. A set of cosmo-phenomenological constraints, including the recent
results from WMAP, determines the allowed parameter space of the models under
consideration. We highlight a new coannihilation corridor where
neutralino-sbottom and neutralino-tau sneutrino-stau coannihilations
significantly contribute to the reduction of the neutralino relic density.Comment: 38 pages, 27 Figures, Latex; Version accepted for publication in PR
On the selection of AGN neutrino source candidates for a source stacking analysis with neutrino telescopes
The sensitivity of a search for sources of TeV neutrinos can be improved by
grouping potential sources together into generic classes in a procedure that is
known as source stacking. In this paper, we define catalogs of Active Galactic
Nuclei (AGN) and use them to perform a source stacking analysis. The grouping
of AGN into classes is done in two steps: first, AGN classes are defined, then,
sources to be stacked are selected assuming that a potential neutrino flux is
linearly correlated with the photon luminosity in a certain energy band (radio,
IR, optical, keV, GeV, TeV). Lacking any secure detailed knowledge on neutrino
production in AGN, this correlation is motivated by hadronic AGN models, as
briefly reviewed in this paper.
The source stacking search for neutrinos from generic AGN classes is
illustrated using the data collected by the AMANDA-II high energy neutrino
detector during the year 2000. No significant excess for any of the suggested
groups was found.Comment: 43 pages, 12 figures, accepted by Astroparticle Physic
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