Numerical solution of ideal MHD equilibrium via radial basis functions collocation and moving least squares approximation methods

A Hybridizable Discontinuous Galerkin solver for the Grad–Shafranov equation

“…In order to deal with the semi-linearity of the problem we will resort to an iterative strategy. Due to their simplicity and effectiveness, straightforward fixed-point iterations (also known as a Picard iterations) of the style −∆ * ψ n = F(r, z, ψ n−1 ) have been preferred in many applications [11,12,17,18,19,20,22]. We choose to follow a similar strategy, but enhance it with two simple yet effective acceleration methods.…”

“…have been preferred in many applications [11,12,17,18,19,20,22]. We choose to follow a similar strategy, but enhance it with two simple yet effective acceleration methods.…”

“…Some other recent alternatives that have attracted attention include the hybrid approach EEC-ESC that couples Hermite elements near the plasma edge with Fourier decomposition methods in the plasma core [20], the use of meshless methods [21,22], the use of approximate particular solutions [23], and the method of fundamental solutions [24].…”

Measuring the 3D motion space of the human ankle

“…5a and b show fitted curves of the maximum rotation angles of adduction and abduction, which changed with the rotation angles of the dorsal flexure or plantar flexion. We used MATLAB to obtain the fitted equations and curves using the least square method to fit the final data, represented by dots [18][19][20][21][22]. From the graphs, we can see that when the rotation angles of the plantar flexion and dorsal flexure decrease, the maximum rotation angles of adduction and abduction increase.…”