117,602 research outputs found
The Time-Domain Cell Method Is a Coupling of Two Explicit Discontinuous Galerkin Schemes with Continuous Fluxes
No full textThe cell method (CM) or discrete geometric approach (DGA) in the time domain, already introduced by Codecasa et al. in 2008 for the coupled Ampere-Maxwell and Faraday equations, is here recast as a Galerkin Method similar to the finite-element method (FEM). In particular, it is shown to be a mixed method comprising an explicit scheme and two discontinuous Galerkin (DG) FEM spaces formulated on dual meshes, in which each of the two function spaces provides a continuous numerical flux choice for its dual mesh counterpart. The implemented version is shown to compare favorably in terms of accuracy and efficiency with respect to the classic conforming FEM scheme using Whitney elements. When tested on the same tetrahedral mesh, the Courant-Friedrichs-Lewy (CFL) condition for the proposed approach is a factor of 2 less restrictive on the time step with respect to the curl-conforming FEM scheme
To the special issue constructed from the selected papers of Thermal investigations of integrated circuits and systems, THERMINIC’17
No full textCompact Electro-Thermal Models for Integrated Systems
No full textA novel approach is here proposed for the extraction of compact electro-thermal models of interconnects, in the static case, from their 3D discretized nonlinear electro-thermal models. It is based on Nonlinear Model Order Reduction and exploits Taylor's series expansion of the discretized equations. Such extraction procedure of compact electro-thermal models is very efficient since it solely requires the alternate solutions of linear electric and linear thermal 3D discretized problems. Compact electro-thermal models with tiny numbers of degrees of freedom are able to be very accurate, as verified on a simple interconnection example
Constitutive equations for discrete electromagnetic problems over polyhedral grids
No full textIn this paper a novel approach is proposed for constructing discrete counterparts of constitutive equations over polyhedral
grids which ensure both consistency and stability of the algebraic equations discretizing an electromagnetic field
problem.
The idea is to construct discrete constitutive equations preserving the thermodynamic relations for constitutive equations.
In this way, consistency and stability of the discrete equations are ensured. At the base, a purely geometric condition
between the primal and the dual grids has to be satisfied for a given primal polyhedral grid, by properly choosing the dual
grid.
Numerical experiments demonstrate that the proposed discrete constitutive equations lead to accurate approximations
of the electromagnetic field
A Bianisotropic FIT Formulation over Polyhedral Grids for Metamaterial Modeling
No full textModeling bianisotropic constitutive equations, i.e. magnetoelectric coupling, in electromagnetics simulation is increasingly important, in particular in
metamaterials applications. This paper introduces for the first time such constitutive relationships in the framework of FIT and, furthermore, does so by allowing full generality in the discretization through arbitrary polyhedral grids. The resulting formulation is consistent, stable and preserves the thermodynamic properties of the bianisotropic constitutive equations thanks to the energetic approach used to construct the interpolating functions
Complementary Energy Bounds in FIT for Magnetostatics
No full textThe existence of complementary energy bounds for magnetostatic problems discretized by the finite integration technique is proved, when material matrices are constructed according to the so-called energetic approach. A numerical example shows that complementarity provides fast and accurate estimates of global quantities such as the inductance
A 3-D Hybrid Cell Boundary Element Method for Time-Harmonic Eddy Current Problems on Multiply Connected Domains
No full textA novel 3-D hybrid formulation for time-harmonic eddy current problems in multiply connected domains is presented. The interior problem (in conductive regions) is discretized by the cell method (CM) in terms of magnetic vector potentials a, whereas the exterior problem (in the unbounded air domain) is discretized by the boundary element method (BEM) in terms of reduced scalar potentials {arphi }-{r}. Novel topological constraints are derived from magnetostatic energy conservation by using a decomposition of the magnetic field which minimizes the support and the number of cohomology generators. A fast algebraic procedure to pre-compute source fields to handle efficiently current-driven coils is also proposed. The final matrix system can be solved in a limited number of iterations by transpose-free quasi-minimal residual method with symmetric successive over-relaxation preconditioning. Convergence tests show that numerical results are in a very good agreement with third-order finite element method (FEM) on a 2-D axisymmetric model. The CM-BEM with piecewise uniform approximation shows also to be very effective when analyzing fully 3-D test cases, since second-order FEM accuracy is attained even with coarse mesh refinements, by using, however, a much lower number of degrees of freedom compared to FEM
Stochastic finite integration technique for magnetostatic problems
No full textBoth non-intrusive and intrusive stochastic approaches based on Polynomial Chaos Expansion are presented for the Finite Integration Technique over generic polyhedral grids for three-dimensional magnetostatic linear problems. Such algorithms outperform Monte Carlo methods (when the number of random parameters is small), both in terms of accuracy and efficiency. A novel algorithm for the intrusive approach is also provided, by which the intrusive approach becomes less computationally expensive than the non-intrusive approach. Validation is carried out by solving a magnetic circuit where the reluctivity is uncertain
UN METODO IBRIDO CELLE – BEM PER LA SOLUZIONE DI PROBLEMI A CORRENTI INDOTTE CON REGIONI A CONNESSIONE MULTIPLA
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