The goal of this work is to derive and justify a multilevel preconditioner of optimal arithmetic complexity for symmetric interior penalty discontinuous Galerkin finite element approximations of second order elliptic problems. Our approach is based on the following simple idea given in [R.D. Lazarov, P.S. Vassilevski, L.T. Zikatanov, Multilevel preconditioning of second order elliptic discontin...

We consider an exponentially fitted discontinuous Galerkin method for advection dominated problems and propose a block solver for the resulting linear systems. In the case of strong advection the solver is robust with respect to the advection direction and the number of unknowns.

For the last three decades, a large scale integration of distributed generation (DG) is beginning to change the electrical distribution network from passive to active. Consequently, technical difficulties are created by significant impacts generated by DGs with voltage variation being the dominant effect. This paper presents a comprehensive review of voltage control techniques on electrical dis...