[PDF] Top 20 DG discretization of optimized Schwarz methods for Maxwell's equations

... (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, ... See full document

... classical Schwarz methods have been extended to systems of hyperbolic partial differential equations, using characteristic transmission conditions, and it has been observed that the classical ... 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

... iterative methods. Domain decomposition methods are currently most promising: following the first provably convergent method in [4], various optimized Schwarz methods were developed ... See full document

... an optimized Schwarz method for Maxwell’s equations with convergence factor that does not deteriorate when the mesh parameter h goes to zero, even without ... See full document

... Cauchy-Riemann equations, they were also observed when the classical Schwarz method is applied to Maxwell’s equations, see Dolean et ...differential equations such differences can ... See full document

... the DG methods, the design of efficient algorithms for the resulting sparse linear system has to be ...on optimized Schwarz methods [5], [7], ...the discretization of the problem ... See full document

... Maxwell’s equations by using nodal finite elements ...a Schwarz technique with total recovery by Ben Belgacem et ...and S. Lanteri have used in [11] discontinuous Galerkin methods to solve the ... See full document

... Optimized Schwarz methods have been developed for Maxwell equations in first order form without conductivity in [8], and with conductivity in [5, ...sical Schwarz methods. ... See full document

... From (2.6), we may take B 0 = 0, and equation ∇ × E 0 = 0 in (2.5) implies the exis- tence of a potential function j 0 such that E 0 = - ∇ j 0 . Then Equations 2.2-2.5 become a non-isentropic compressible ... See full document

... Vlasov Maxwell system and we try to show the solutions of inhomogeneous wave equations with initial conditions in  3 and Gronwall’s lemma is stated and ... See full document

... adding the absorption into the preconditioner (as in the theory) allows good parallel scaling. 6.1. Details of the computations and notation. All the computations are done in FreeFem++, an open source domain specific ... See full document

... element discretization of the Darcy problem can be efficiently solved by applying the penalty ...of equations with uncoupled ...element discretization of the Darcy ... See full document

... , s = ...number s < 8 , two-step, s -stage TSRK methods of order 7 ...HB methods shows that HB methods of order 7 with only 4 stages ...HB methods of order 7 are ... See full document

... and then it is usually difficult to prove that a minimizing sequence or a sequence that satisfies the (PS) condition, briefly a Palais-Smale sequence, is strongly convergent if we seek solutions of () by variational ... See full document

... of discretization for all continuous variables and continue the process using discrete Bayesian ...networks. Discretization methods commonly used include equal-width [23] and equal frequency [24, ... See full document

... (DD) methods decompose Ω into subdomains and then reduce the second order elliptic problem (1) to smaller problems on each ...A. Schwarz [47] who used such an idea to prove existence and uniqueness of the ... See full document

... In this paper a slightly different approach to the use of the domain decomposition method of the Schwarz type is proposed. Instead of the standard coarse space construction we propose to use a recursive solution ... See full document

... these methods however sound really similar to the procedure followed by Microwave ...the Maxwell Equations and end with an expression for the values of the domain in terms of values on the ... See full document