This paper concerns the electromagnetic scattering by arbitrary shaped three dimensional imperfectly conducting objects modeled with non-constant Leontovitch impedance boundary condition.It has two objectives.Firstly,...This paper concerns the electromagnetic scattering by arbitrary shaped three dimensional imperfectly conducting objects modeled with non-constant Leontovitch impedance boundary condition.It has two objectives.Firstly,the intrinsically wellconditioned integral equation(noted GCSIE)proposed in[30]is described focusing on its discretization.Secondly,we highlight the potential of this method by comparison with two other methods,the first being a two currents formulation in which the impedance condition is implicitly imposed and whose the convergence is quasioptimal for Lipschitz polyhedron,the second being a CFIE-like formulation[14].In particular,we prove that the new approach is less costly in term of CPU time and gives a more accurate solution than that obtained from the CFIE formulation.Finally,as expected,It is demonstrated that no preconditioner is needed for this formulation.展开更多
For the numerical simulation of time harmonic acoustic scattering in a complex geometry,in presence of an arbitrary mean flow,the main difficulty is the coexistence and the coupling of two very different phenomena:aco...For the numerical simulation of time harmonic acoustic scattering in a complex geometry,in presence of an arbitrary mean flow,the main difficulty is the coexistence and the coupling of two very different phenomena:acoustic propagation and convection of vortices.We consider a linearized formulation coupling an augmented Galbrun equation(for the perturbation of displacement)with a time harmonic convection equation(for the vortices).We first establish the well-posedness of this time harmonic convection equation in the appropriatemathematical framework.Then the complete problem,with Perfectly Matched Layers at the artificial boundaries,is proved to be coercive+compact,and a hybrid numerical method for the solution is proposed,coupling finite elements for the Galbrun equation and a Discontinuous Galerkin scheme for the convection equation.Finally a 2D numerical result shows the efficiency of the method.展开更多
文摘This paper concerns the electromagnetic scattering by arbitrary shaped three dimensional imperfectly conducting objects modeled with non-constant Leontovitch impedance boundary condition.It has two objectives.Firstly,the intrinsically wellconditioned integral equation(noted GCSIE)proposed in[30]is described focusing on its discretization.Secondly,we highlight the potential of this method by comparison with two other methods,the first being a two currents formulation in which the impedance condition is implicitly imposed and whose the convergence is quasioptimal for Lipschitz polyhedron,the second being a CFIE-like formulation[14].In particular,we prove that the new approach is less costly in term of CPU time and gives a more accurate solution than that obtained from the CFIE formulation.Finally,as expected,It is demonstrated that no preconditioner is needed for this formulation.
文摘For the numerical simulation of time harmonic acoustic scattering in a complex geometry,in presence of an arbitrary mean flow,the main difficulty is the coexistence and the coupling of two very different phenomena:acoustic propagation and convection of vortices.We consider a linearized formulation coupling an augmented Galbrun equation(for the perturbation of displacement)with a time harmonic convection equation(for the vortices).We first establish the well-posedness of this time harmonic convection equation in the appropriatemathematical framework.Then the complete problem,with Perfectly Matched Layers at the artificial boundaries,is proved to be coercive+compact,and a hybrid numerical method for the solution is proposed,coupling finite elements for the Galbrun equation and a Discontinuous Galerkin scheme for the convection equation.Finally a 2D numerical result shows the efficiency of the method.
