Chandrashekar, Praveen (2001) Some results on the least squares formula. 2001-FM-05.
In this report, we establish some interesting invariance properties of the first order least squares formula. It is shown that it is consistent with the transformation properties of the exact derivatives, both in the case of a scalar and a vector field variable. This leads to the result that when the full stencil is used (i.e. no upwinding), there are no optimum coordinate directions which will minimize some relevant norm of the error vector. A numerical example with upwinding shows the existence of optimum coordinate directions. Finally, some length scales are derived based on the eigenvalues of the least squares matrix which help in characterizing the connectivity for LSKUM.
|Item Type:||Departmental Technical Report|
|Keywords:||Least squares;kinetic schemes;meshless methods;LSKUM|
|Department/Centre:||Division of Physical & Mathematical Sciences > Mathematics
Division of Mechanical Sciences > Aerospace Engineering (Formerly, Aeronautical Engineering)
|Date Deposited:||04 Jun 2004|
|Last Modified:||19 Sep 2010 04:12|
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