Edge Element Methods for Maxwell's Equations with Strong Convergence for Gauss' Laws

Edge Element Methods for Maxwell's Equations with Strong Convergence for Gauss' Laws

In this paper we propose and investigate some edge element approximations for three Maxwell systems in three dimensions: the stationary Maxwell equations, the time-harmonic Maxwell equations and the time-dependent Maxwell equations. These approximations have three novel features. First, the resulting discrete edge element systems can be solved by some existing preconditioned solvers with optima...

islanding detection methods for microgrids

امروزه استفاده از منابع انرژی پراکنده کاربرد وسیعی یافته است . اگر چه این منابع بسیاری از مشکلات شبکه را حل می کنند اما زیاد شدن آنها مسائل فراوانی برای سیستم قدرت به همراه دارد . استفاده از میکروشبکه راه حلی است که علاوه بر استفاده از مزایای منابع انرژی پراکنده برخی از مشکلات ایجاد شده توسط آنها را نیز منتفی می کند . همچنین میکروشبکه ها کیفیت برق و قابلیت اطمینان تامین انرژی مشترکان را افزایش ...

Convergence of Adaptive Edge Element Methods for the 3d Eddy Currents Equations

Abstract. We consider an Adaptive Edge Finite Element Method (AEFEM) for the 3D eddy currents equations with variable coefficients using a residual-type a posteriori error estimator. Both the components of the estimator and certain oscillation terms, due to the occurrence of the variable coefficients, have to be controlled properly within the adaptive loop which is taken care of by appropriate ...

Convergence and optimality of adaptive edge finite element methods for time-harmonic Maxwell equations

We consider a standard Adaptive Edge Finite Element Method (AEFEM) based on arbitrary order Nédélec edge elements, for three-dimensional indefinite time-harmonic Maxwell equations. We prove that the AEFEM gives a contraction for the sum of the energy error and the scaled error estimator, between two consecutive adaptive loops provided the initial mesh is fine enough. Using the geometric decay, ...

New family of Two-Parameters Iterative Methods for Non-Linear Equations with Fourth-Order Convergence