Coupled structural, thermal, phase-change and electromagnetic analysis for superconductors, volume 2

Two families of parametrized mixed variational principles for linear electromagnetodynamics are constructed. The first family is applicable when the current density distribution is known a priori. Its six independent fields are magnetic intensity and flux density, magnetic potential, electric intensity and flux density and electric potential. Through appropriate specialization of parameters the first principle reduces to more conventional principles proposed in the literature. The second family is appropriate when the current density distribution and a conjugate Lagrange multiplier field are adjoined, giving a total of eight independently varied fields. In this case it is shown that a conventional variational principle exists only in the time-independent (static) case. Several static functionals with reduced number of varied fields are presented. The application of one of these principles to construct finite elements with current prediction capabilities is illustrated with a numerical example

Dispersion and dissipation error in high-order Runge-Kutta discontinuous Galerkin discretisation of the Maxwell eqations

Different time-stepping methods for a nodal high-order discontinuous Galerkin discretisation of the Maxwell equations are discussed. A comparison between the most popular choices of Runge-Kutta (RK) methods is made from the point of view of accuracy and computational work. By choosing the strong-stability-preserving Runge-Kutta (SSP-RK) time-integration method of order consistent with the polynomial order of the spatial discretisation, better accuracy can be attained compared to fixed-order schemes. This comes without a significant increase in the computation work. A numerical Fourier analysis is performed for this Runge-Kutta discontinuous Galerkin (RKDG) discretisation to gain insight into the dispersion and dissipation properties of the complete scheme. The analysis also provides practical information on the convergence of the dissipation and dispersion error, which is important when studying wave propagation phenomena

Two conjectures on the Stokes complex in three dimensions on Freudenthal meshes

In recent years, a great deal of attention has been paid to discretizations of the incompressible Stokes equations that exactly preserve the incompressibility constraint. These are of substantial interest because these discretizations are pressure-robust; i.e., the error estimates for the velocity do not depend on the error in the pressure. Similar considerations arise in nearly incompressible linear elastic solids. Conforming discretizations with this property are now well understood in two dimensions but remain poorly understood in three dimensions. In this work, we state two conjectures on this subject. The first is that the Scott–Vogelius element pair is inf-sup stable on uniform meshes for velocity degree k≥4; the best result available in the literature is for k≥6. The second is that there exists a stable space decomposition of the kernel of the divergence for k≥5. We present numerical evidence supporting our conjectures

A Least-Squares Finite Element Method for Electromagnetic Scattering Problems

The least-squares finite element method (LSFEM) is applied to electromagnetic scattering and radar cross section (RCS) calculations. In contrast to most existing numerical approaches, in which divergence-free constraints are omitted, the LSFF-M directly incorporates two divergence equations in the discretization process. The importance of including the divergence equations is demonstrated by showing that otherwise spurious solutions with large divergence occur near the scatterers. The LSFEM is based on unstructured grids and possesses full flexibility in handling complex geometry and local refinement Moreover, the LSFEM does not require any special handling, such as upwinding, staggered grids, artificial dissipation, flux-differencing, etc. Implicit time discretization is used and the scheme is unconditionally stable. By using a matrix-free iterative method, the computational cost and memory requirement for the present scheme is competitive with other approaches. The accuracy of the LSFEM is verified by several benchmark test problems

Coupled structural, thermal, phase-change and electromagnetic analysis for superconductors, volume 1

This research program has dealt with the theoretical development and computer implementation of reliable and efficient methods for the analysis of coupled mechanical problems that involve the interaction of mechanical, thermal, phase-change and electromagnetic subproblems. The focus application has been the modeling of superconductivity and associated quantum-state phase-change phenomena. In support of this objective the work has addressed the following issues: (1) development of variational principles for finite elements; (2) finite element modeling of the electromagnetic problem; (3) coupling of thermal and mechanical effects; and (4) computer implementation and solution of the superconductivity transition problem. The research was carried out over the period September 1988 through March 1993. The main accomplishments have been: (1) the development of the theory of parametrized and gauged variational principles; (2) the application of those principled to the construction of electromagnetic, thermal and mechanical finite elements; and (3) the coupling of electromagnetic finite elements with thermal and superconducting effects; and (4) the first detailed finite element simulations of bulk superconductors, in particular the Meissner effect and the nature of the normal conducting boundary layer. The grant has fully supported the thesis work of one doctoral student (James Schuler, who started on January 1989 and completed on January 1993), and partly supported another thesis (Carmelo Militello, who started graduate work on January 1988 completing on August 1991). Twenty-three publications have acknowledged full or part support from this grant, with 16 having appeared in archival journals and 3 in edited books or proceedings

Analog hardware for detecting discontinuities in early vision

The detection of discontinuities in motion, intensity, color, and depth is a well-studied but difficult problem in computer vision [6]. We discuss the first hardware circuit that explicitly implements either analog or binary line processes in a deterministic fashion. Specifically, we show that the processes of smoothing (using a first-order or membrane type of stabilizer) and of segmentation can be implemented by a single, two-terminal nonlinear voltage-controlled resistor, the “resistive fuse”; and we derive its current-voltage relationship from a number of deterministic approximations to the underlying stochastic Markov random fields algorthms. The concept that the quadratic variation functionals of early vision can be solved via linear resistive networks minimizing power dissipation [37] can be extended to non-convex variational functionals with analog or binary line processes being solved by nonlinear resistive networks minimizing the electrical co-content. We have successfully designed, tested, and demonstrated an analog CMOS VLSI circuit that contains a 1D resistive network of fuses implementing piecewise smooth surface interpolation. We furthermore demonstrate the segmenting abilities of these analog and deterministic “line processes” by numerically simulating the nonlinear resistive network computing optical flow in the presence of motion discontinuities. Finally, we discuss various circuit implementations of the optical flow computation using these circuits