Nested Iteration and First-Order Systems Least Squares for a Two-Fluid Electromagnetic Darwin Model

2015 ◽  
Vol 37 (5) ◽  
pp. S314-S333 ◽  
Author(s):  
C. A. Leibs ◽  
T. A. Manteuffel
Keyword(s):  
Least Squares ◽  
First Order ◽  
Nested Iteration ◽  
Two Fluid

scholarly journals Nested Iteration and First-Order System Least Squares for Incompressible, Resistive Magnetohydrodynamics

2010 ◽  
Vol 32 (3) ◽  
pp. 1506-1526 ◽  
Author(s):  
J. H. Adler ◽  
T. A. Manteuffel ◽  
S. F. McCormick ◽  
J. W. Ruge ◽  
G. D. Sanders
Keyword(s):  
Least Squares ◽  
Order System ◽  
First Order ◽  
Nested Iteration

scholarly journals Breaking the cosmological background degeneracy by two-fluid perturbations in f(R) gravity

2015 ◽  
Vol 24 (07) ◽  
pp. 1550053 ◽  
Author(s):  
Amare Abebe
Keyword(s):  
General Relativity ◽  
Exact Solutions ◽  
Structure Formation ◽  
Background Level ◽  
Cosmological Perturbations ◽  
Gauge Invariant ◽  
First Order ◽  
Cosmological Background ◽  
Theories Of Gravity ◽  
Two Fluid

One of the exact solutions of f(R) theories of gravity in the presence of different forms of matter exactly mimics the ΛCDM solution of general relativity (GR) at the background level. In this work we study the evolution of scalar cosmological perturbations in the covariant and gauge-invariant formalism and show that although the background in such a model is indistinguishable from the standard ΛCDM cosmology, this degeneracy is broken at the level of first-order perturbations. This is done by predicting different rates of structure formation in ΛCDM and the f(R) model both in the complete and quasi-static regimes.

Q least-squares reverse time migration based on the first-order viscoacoustic quasidifferential equations

Geophysics ◽  
2021 ◽  
pp. 1-65
Author(s):  
Yingming Qu ◽  
Yixin Wang ◽  
Zhenchun Li ◽  
Chang Liu
Keyword(s):  
Wave Equation ◽  
Least Squares ◽  
Surface Topography ◽  
Density Perturbation ◽  
Second Order ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
First Order ◽  
Time Migration ◽  
Grid Scheme

Seismic wave attenuation caused by subsurface viscoelasticity reduces the quality of migration and the reliability of interpretation. A variety of Q-compensated migration methods have been developed based on the second-order viscoacoustic quasidifferential equations. However, these second-order wave-equation-based methods are difficult to handle with density perturbation and surface topography. In addition, the staggered grid scheme, which has an advantage over the collocated grid scheme because of its reduced numerical dispersion and enhanced stability, works in first-order wave-equation-based methods. We have developed a Q least-squares reverse time migration method based on the first-order viscoacoustic quasidifferential equations by deriving Q-compensated forward-propagated operators, Q-compensated adjoint operators, and Q-attenuated Born modeling operators. Besides, our method using curvilinear grids is available even when the attenuating medium has surface topography and can conduct Q-compensated migration with density perturbation. The results of numerical tests on two synthetic and a field data sets indicate that our method improves the imaging quality with iterations and produces better imaging results with clearer structures, higher signal-to-noise ratio, higher resolution, and more balanced amplitude by correcting the energy loss and phase distortion caused by Q attenuation. It also suppresses the scattering and diffracted noise caused by the surface topography.

scholarly journals Analytical quality assessment of iteratively reweighted least-squares (IRLS) method

2014 ◽  
Vol 20 (1) ◽  
pp. 132-141 ◽  
Author(s):  
Jianfeng Guo
Keyword(s):  
Least Squares ◽  
Order Approximation ◽  
Diagnostic Tools ◽  
Iteratively Reweighted Least Squares ◽  
First Order ◽  
Iterative Reweighting ◽  
First Order Approximation ◽  
Detectable Bias ◽  
Theoretical Analyses ◽  
Exact Analytical Method

The iteratively reweighted least-squares (IRLS) technique has been widely employed in geodetic and geophysical literature. The reliability measures are important diagnostic tools for inferring the strength of the model validation. An exact analytical method is adopted to obtain insights on how much iterative reweighting can affect the quality indicators. Theoretical analyses and numerical results show that, when the downweighting procedure is performed, (1) the precision, all kinds of dilution of precision (DOP) metrics and the minimal detectable bias (MDB) will become larger; (2) the variations of the bias-to-noise ratio (BNR) are involved, and (3) all these results coincide with those obtained by the first-order approximation method.

A note on some factors influencing muscle pH values in commercial pig carcasses

1978 ◽  
Vol 26 (2) ◽  
pp. 229-232 ◽  
Author(s):  
W. C. Smith ◽  
A. Wilson
Keyword(s):  
Least Squares ◽  
Practical Significance ◽  
Longissimus Dorsi ◽  
Post Mortem ◽  
First Order ◽  
Commercial Grade ◽  
Ph Values ◽  
Factors Influencing ◽  
Muscle Ph ◽  
Pig Carcasses

ABSTRACTMeasurements of longissimus dorsi pH at 45 min post mortem (pH1) were taken in 27 727 pig carcasses at four bacon factories. The overall least squares mean pH1 was 6·26 and 15·5% of carcasses had pHi values of 5·9 or less. Sex and commercial grade of carcass had little influence on muscle pHi or the incidence of values below pH 6·0. Factory differences were recorded in the distribution of muscle and within each there were marked producer effects in mean and the incidence of values below pH 6·0. Carcasses of Large Whites had fewer muscle pH1 values below 6·0 (12·4%) than those of British Landrace (18·7%), this being mainly due to a large breed effect at one factory. Although breed and testing background of sires of the carcasses examined and the first order interactions with factory had significant effects on muscle pHi and the incidence of values below pH 6·0, they were of little practical significance.

scholarly journals Further results on a space-time FOSLS formulation of parabolic PDEs

2020 ◽  
Author(s):  
Gregor Gantner ◽  
Rob Stevenson
Keyword(s):  
Finite Element Method ◽  
Least Squares ◽  
Parabolic Equations ◽  
Space Time ◽  
Adaptive Finite Element Method ◽  
Order System ◽  
Well Posedness ◽  
Adaptive Finite Element ◽  
Parabolic Pdes ◽  
First Order

In [2019, Space-time least-squares finite elements for parabolic equations, arXiv:1911.01942] by Führer&Karkulik, well-posedness of a space-time First-Order System Least-Squares formulation of the heat equation was proven.  In the present work, this result is generalized to general second order parabolic PDEs with possibly inhomogenoeus boundary conditions, and plain convergence of a standard adaptive finite element method driven by the least-squares estimator is demonstrated.  The proof of the latter easily extends to a large class of least-squares formulations.

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