A finite element-boundary integral formulation for scattering by three-dimensional cavity-backed apertures

A numerical technique is proposed for the electromagnetic characterization of the scattering by a three-dimensional cavity-backed aperture in an infinite ground plane. The technique combines the finite element and boundary integral methods to formulate a system of equations for the solution of the aperture fields and those inside the cavity. Specifically, the finite element method is employed to formulate the fields in the cavity region and the boundary integral approach is used in conjunction with the equivalence principle to represent the fields above the ground plane. Unlike traditional approaches, the proposed technique does not require knowledge of the cavity's Green's function and is, therefore, applicable to arbitrary shape depressions and material fillings. Furthermore, the proposed formulation leads to a system having a partly full and partly sparse as well as symmetric and banded matrix which can be solved efficiently using special algorithms

GMRES using pseudoinverse for range symmetric singular systems

Consider solving large sparse range symmetric singular linear systems $A {\bf x}= {\bf b}$ which arise, for instance, in the discretization of convection diffusion equations with periodic boundary conditions, and partial differential equations for electromagnetic fields using the edge-based finite element method. In theory, the Generalized Minimal Residual (GMRES) method converges to the least squares solution for inconsistent systems if the coefficient matrix $A$ is range symmetric, i.e. ${\rm R}(A)= {\rm R}(A^{ \rm T } )$, where ${\rm R}(A)$ is the range space of $A$. We derived the necessary and sufficient conditions for GMRES to determine a least squares solution of inconsistent and consistent range symmetric systems assuming exact arithmetic except for the computation of the elements of the Hessenberg matrix. In practice, GMRES may not converge due to numerical instability. In order to improve the convergence, we propose using the pseudoinverse for the solution of the severely ill-conditioned Hessenberg systems in GMRES. Numerical experiments on inconsistent systems indicate that the method is effective and robust. Finally, we further improve the convergence of the method by reorthogonalizing the Modified Gram-Schmidt procedure.Comment: Sentence at end of Section 1 when rhs contains discretization, measurement errors. Section 2 on motivation. Theorem 4.1: necessary, sufficient conditions for inconsistent, consistent cases. After Theorem 4.1, difference between theory and experiments explained. Modified Definition 2. Eliminated results for plat1919, saylr3. Modified Conclusions. References 1,2,3 on application

Nonconforming tetrahedral mixed finite elements for elasticity

This paper presents a nonconforming finite element approximation of the space of symmetric tensors with square integrable divergence, on tetrahedral meshes. Used for stress approximation together with the full space of piecewise linear vector fields for displacement, this gives a stable mixed finite element method which is shown to be linearly convergent for both the stress and displacement, and which is significantly simpler than any stable conforming mixed finite element method. The method may be viewed as the three-dimensional analogue of a previously developed element in two dimensions. As in that case, a variant of the method is proposed as well, in which the displacement approximation is reduced to piecewise rigid motions and the stress space is reduced accordingly, but the linear convergence is retained.Comment: 13 pages, 2 figure

Practical analysis of 3-D dynamic nonlinear magnetic field using time-periodic finite element method

A practical 3-D finite element method using edge elements for analyzing stationary nonlinear magnetic fields with eddy currents in electric apparatus, in which the flux interlinking the voltage winding is given, has been proposed. The method is applied to the analysis of magnetic fields in the Epstein frame </p

Free-energy-dissipative schemes for the Oldroyd-B model

In this article, we analyze the stability of various numerical schemes for differential models of viscoelastic fluids. More precisely, we consider the prototypical Oldroyd-B model, for which a free energy dissipation holds, and we show under which assumptions such a dissipation is also satisfied for the numerical scheme. Among the numerical schemes we analyze, we consider some discretizations based on the log-formulation of the Oldroyd-B system proposed by Fattal and Kupferman, which have been reported to be numerically more stable than discretizations of the usual formulation in some benchmark problems. Our analysis gives some tracks to understand these numerical observations

Computer Analysis of Dielectric Waveguides: A Finite-Difference Method

A method for computing the modes of dielectric guiding structures based on finite differences is described. The numerical computation program is efficient and can be applied to a wide range of problems. We report here solutions for circular and rectangular dielectric waveguides and compare our solutions with those obtained by other methods. Limitations in the commonly used approximate formulas developed by Marcatili are discussed