We explain and justify a path-following algorithm for solving the equations Af^ix) = a, where A is a. linear transformation from R" to R", C is a polyhedral convex subset of R", and Ac is the associated normal map. When A^ is coherently oriented, we are able to prove that the path following method terminates at the unique solution of A^ix) = a, which is a generalization of the weU known fact th...

Exact solution and variational approximation of eigenmodes in high gain FELs are presented. These eigenmodes specifi transverse profiles and exponential growth rates of the laser field before saturation. They are self-consistent-solutions of coupled Maxwell-Vlasov equations describing FEL interaction taking into account the effects due to energy spread, emittance and betatron oscillations of th...

The variational multi-scale (VMS) method for large-eddy simulation (LES) is a promising new approach that employs variational projection to achieve a priori scale separation in lieu of traditional spatial filtering. However, depending on the numerical method used, VMS may not be practicable in all spatial directions. We apply the VMS methodology to a numerical method that does not support expli...

We prove sufficient conditions for the monotonicity and the strong monotonicity of fixed point and normal maps associated with variational inequality problem over a general closed convex set. Sufficient conditions for the strong monotonicity of their perturbed versions are also shown. These results include some known ones in the literature as particular instances. Inspired by these results, we ...