[PDF] Top 20 Optimized Schwarz methods for Maxwell's equations

... convergent Schwarz method for the Helmholtz equation, where the classical overlapping Schwarz algorithm is not ...classical Schwarz method is rather slow and too strongly dependent on the size of the ... See full document

... (DG) methods have seen rapid growth and are widely used in various application domains (see [13] for an historical intro- ...volume methods. For the time-harmonic Maxwell equations, once the ... See full document

... the optimized Schwarz methods corresponding to Theorem 5 have an iteration number that is independent of the mesh size, whereas the optimized Schwarz methods based on Theorem 3 ... See full document

... of optimized Schwarz methods, provided that the co- efficient jumps are aligned with the interfaces, and the jumps are taken into account in an appropriate way in the transmission ...Maxwell’s ... See full document

... 20, 40, and 80 subdomains is shown in Table 2, again for a random initial guess, and then in parentheses with the TEM mode as excitation, and a zero initial guess. In this study, the propagating modes are of pre-dominant ... See full document

... here optimized Schwarz methods for Maxwell’s equations in hetero- geneous media with discontinuous coefficients, and show that the discontinuities need to be taken into account in the ... See full document

... decomposition methods based on well chosen transmission ...Maxwell’s equations, can be written and optimized in the com- mon framework of optimized Schwarz methods, independently ... See full document

... differential equations and Lie pseudogroups in order to revisit the mathe- matical foundations of general ...structure equations” must not be identified with the quadratic terms appearing in the well known ... See full document

... In this report, it will be shown how discontinuous Galerkin (DG) finite element methods can be used to compute time-harmonic electric and magnetic fields in periodic media. A periodic medium is a medium which ... See full document

... element methods for the approximation of the time- harmonic Maxwell equations at moderately high wave numbers, and provide quantitative information on the level of mesh refinement and order of ... See full document

... on Maxwell and Transport equations, that can be applied for simplified transport model for an ionized gaseous species in a PECVD ...discretization methods for each separate equation. Splitting ... See full document

... time-harmonic Maxwell equations using high order methods such as discontinuous Galerkin formulations require efficient ...on optimized Schwarz methods applied to the first order ... See full document

... Optimized Schwarz methods have been analyzed thoroughly for the positive definite Helmholtz equation at the continuous level in Gander [2006], and extensive numerical tests have been presented which ... See full document

... We now illustrate graphically the improvement of the optimized Schwarz method over the classical one in 2D. We show in Figure 1 in red the divergence regions and in blue the convergence regions for ... See full document

... field equations with reference to the general relativistic prediction of gravitational ...field equations for static ball of charged coherent perfect has received wide ... See full document

... For overlapping domain decomposition preconditioners, a similar idea was introduced in the case of Darcy equations in [GE10a, GE10b]. The authors of [NXD10] consider also the hetero- geneous Darcy equation and ... See full document

... This paper is structured as follows. In Section 2. we introduce the basic theory of the Vlasov equa- tion and the equations of Vlasov-Maxwell equilibria. We discuss the two distinct approaches to calculat- ... See full document

... our equations, this provides a full explanation why Blackett’s formula is sometimes valid and why this occurs only for a range of ...the equations derived from the exact global solution of the ... See full document

... The solution of the AS problem has been obtained in the form of a simple–layer source term in the general non- stationary formulation. The solution only requires the knowledge of the total field (desirable and ... See full document

... However, in general cases like multi-ion systems, such manipulation is not easily possible and then φ is not explicitly defined. When the method of lines is applied the system might be described by a series of small ... See full document