The following paper compares a consistent Newton-Raphson and fixed-point iteration based solution strategy for a variational multiscale finite element formulation for incompress-ible Navier–Stokes. The main contributions of this work include a consistent linearization of the Navier–Stokes equations, which provides an avenue for advanced algorithms that require origins in a consistent method. We...

The stability analysis of islanded inverter-based microgrids (IBMGs) is increasingly an important and challenging topic due to the nonlinearity of IBMGs. In this paper, a new linear model for such microgrids as well as an iterative method to correct the linear model is proposed. Using the linear model makes it easy to analyze the eigenvalues and stability of IBMGs due to the fact that it derive...

We extend a recently developed numerical code to obtain stationary, axisymmetric solutions that describe rotating black hole spacetimes in wide class of modified theories gravity. The utilizes relaxed Newton-Raphson method solve the full nonlinear Einstein's equations on two-dimensional grid with Newton polynomial finite difference scheme. validate this by considering static and holes general r...

Goldschmidt’s Algorithms for division and square root are often characterized as being useful for hardware implementation, and lacking self-correction. A reexamination of these algorithms show that there are good software counterparts that retain the speed advantage of Goldschmidt’s Algorithm over the Newton-Raphson iteration. A final step is needed, however, to get the last bit rounded correctly.

Digital image correlation (DIC) has become a well-established approach for the calculation of full-field displacement and strains within the field of experimental mechanics. Since their introduction, DIC methods have been relying on only two images to measure the displacements and strains that materials undergo under load. It can be foreseen that the use of additional image information for the ...