New least squares method with geometric conservation law (GC-LSM) for compressible flow computation in meshless method

2018 ◽  
Vol 172 ◽  
pp. 122-146 ◽  
Author(s):  
Jin Young Huh ◽  
Jae Sang Rhee ◽  
Kyu Hong Kim ◽  
Suk Young Jung
Keyword(s):  
Least Squares ◽  
Compressible Flow ◽  
Conservation Law ◽  
Meshless Method ◽  
Least Squares Method ◽  
Flow Computation ◽  
Geometric Conservation Law

A Meshless Method Based on the Improved Interpolating Moving Least-Squares Method for the Regularized Long Wave Equation

2011 ◽  
Vol 101-102 ◽  
pp. 467-470
Author(s):  
Ju Feng Wang ◽  
Feng Xin Sun
Keyword(s):  
Least Squares ◽  
Meshless Method ◽  
Least Squares Method ◽  
Equation System ◽  
Moving Least Squares ◽  
Weak Nonlinearity ◽  
Orthogonal Functions ◽  
Long Wave ◽  
Regularized Long Wave Equation ◽  
Moving Least Squares Method

This paper presents an improved interpolating moving least-squares (IIMLS) method, in which orthogonal functions system is used as the basis functions. In the IIMLS method, the final algebra equation system is not ill-conditioned, and can be solved without obtaining the inverse matrix. Hence, the computing speed and efficiency are improved. Then based on the IIMLS method, a meshless method is presented for the numerical solution of the regularized long wave (RLW) equation, which can be used to describe phenomena with weak nonlinearity and dispersion waves. And a numerical example is given to confirm the IMLS method.

‘Least squares’ method—theorem or law?

1980 ◽  
Vol 59 (9) ◽  
pp. 8
Author(s):  
D.E. Turnbull
Keyword(s):  
Least Squares ◽  
Least Squares Method

An Augmented Iteratively Re-weighted and Refined Least Squares Method for lp Minimization Problem in Inverse Modeling of Potential Field Magnetic Data

2020 ◽  
Vol 1 (3) ◽  
Author(s):  
Maysam Abedi
Keyword(s):  
Magnetic Field ◽  
Magnetic Susceptibility ◽  
Least Squares ◽  
Minimization Problem ◽  
Potential Field ◽  
Field Data ◽  
Least Squares Method ◽  
Porphyry Copper ◽  
Magnetic Data ◽  
Magnetic Field Data

The presented work examines application of an Augmented Iteratively Re-weighted and Refined Least Squares method (AIRRLS) to construct a 3D magnetic susceptibility property from potential field magnetic anomalies. This algorithm replaces an lp minimization problem by a sequence of weighted linear systems in which the retrieved magnetic susceptibility model is successively converged to an optimum solution, while the regularization parameter is the stopping iteration numbers. To avoid the natural tendency of causative magnetic sources to concentrate at shallow depth, a prior depth weighting function is incorporated in the original formulation of the objective function. The speed of lp minimization problem is increased by inserting a pre-conditioner conjugate gradient method (PCCG) to solve the central system of equation in cases of large scale magnetic field data. It is assumed that there is no remanent magnetization since this study focuses on inversion of a geological structure with low magnetic susceptibility property. The method is applied on a multi-source noise-corrupted synthetic magnetic field data to demonstrate its suitability for 3D inversion, and then is applied to a real data pertaining to a geologically plausible porphyry copper unit.  The real case study located in  Semnan province of  Iran  consists  of  an arc-shaped  porphyry  andesite  covered  by  sedimentary  units  which  may  have  potential  of  mineral  occurrences, especially  porphyry copper. It is demonstrated that such structure extends down at depth, and consequently exploratory drilling is highly recommended for acquiring more pieces of information about its potential for ore-bearing mineralization.

Theoretical accuracy of the last squares method in the isotope dilution analysis

1984 ◽  
Vol 49 (4) ◽  
pp. 805-820
Author(s):  
Ján Klas
Keyword(s):  
Least Squares ◽  
Isotope Dilution ◽  
Least Squares Method ◽  
Isotope Dilution Analysis ◽  
Straight Line ◽  
The One ◽  
Two Parameter ◽  
Theoretical Accuracy

The accuracy of the least squares method in the isotope dilution analysis is studied using two models, viz a model of a two-parameter straight line and a model of a one-parameter straight line.The equations for the direct and the inverse isotope dilution methods are transformed into linear coordinates, and the intercept and slope of the two-parameter straight line and the slope of the one-parameter straight line are evaluated and treated.

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