149 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
Stochastic PEEC Method Based on Polynomial Chaos Expansion
No full textThe new stochastic partial element equivalent circuit (PEEC) method is proposed for uncertainty quantification in electromagnetic
problems when material parameters are considered as random variables. The proposed formulation is derived using polynomial
chaos expansion (PCE) and Galerkin projection. For the first time, the well-known advantages of PEEC are combined with those
of PCE techniques, which can tackle also large variations in the random parameters. Volume conductive media are first considered
in the formulation, which is then extended to dielectric, magnetic, and surface conductive media
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
Galerkin's Projection Framework for BCI CTMs - Part I: Extended FANTASTIC Approach
No full textA general Galerkin's projection framework is proposed for the definition of boundary condition independent (BCI) compact thermal models (CTMs). First, it is shown how the proposals of BCI CTMs, deriving from the works of Bar-Cohen and Sabry, can be straightforwardly reinterpreted within this framework. Then, following such reinterpretation, the approach due to Lasance, nowadays widely adopted for the extraction of BCI CTMs, is generalized into a novel approach, based on the extension of the previous FAst Novel Thermal Analysis Simulation Tool for Integrated Circuits (FANTASTIC) method, from the fixed boundary conditions case to the BCI case. Such an approach allows widely enlarging the set of boundary conditions for which a BCI CTM ensures accuracy and allows overcoming the main limitations of previous approaches, e.g., with multisource problems and dynamic models
Trefftz Co-chain Calculus
No full textWe propose a comprehensive approach to obtain systems of equations that discretize linear stationary or time-harmonic elliptic problems in unbounded domains. This is achieved by coupling any numerical method that fits co-chain calculus with a Trefftz method. The framework of co-chain calculus accommodates both finite element exterior calculus and discrete exterior calculus. It encompasses methods based on volume meshes: its application is therefore confined to bounded domains.
Conversely, Trefftz methods are based on functions that solve the homogeneous equations exactly in the unbounded complement of the meshed domain, while satisfying suitable conditions at infinity. An example of a Trefftz method is the Multiple Multipole Program (MMP), which makes use of multipoles, i.e. solutions spawned by point sources with central singularities that are placed outside the domain of approximation. In our approach the degrees of freedom describing these sources can be eliminated by computing the Schur complement of the system for the coupling, therefore leading to a boundary term for co-chain calculus that takes into account the exterior problem. As a concrete example, we specialize this general framework for the cell method, a particular variant of discrete exterior calculus, coupled with MMP to solve frequency-domain eddy-current problems. A numerical experiment shows the effectiveness of this approach
Discrete geometric formulation of admittance boundary conditions for frequency domain problems over tetrahedral dual grids
No full textIn this communication it is shown how admittance boundary
conditions for electromagnetic boundary value problems in the frequency
domain can be formulated for the Discrete Geometric Approach. The details
are presented for primal grids composed of tetrahedra and barycentric
dual grids
A geometric frequency-domain wave propagation formulation for fast convergence of iterative solvers
No full textThe frequency-domain wave propagation problem is notoriously difficult to solve through iterative methods, because of the huge nullspace of the curl-curl operator. Direct methods are then usually employed, at the expense of great memory usage. Accelerated convergence of iterative methods can be obtained by a modification of the wave equation. In this paper, we introduce the modified wave equation in the Discrete Geometric Approach (DGA) framework. Moreover, the impedance boundary condition in the formulation is presented, together with a smart assembly technique that allows to greatly reduce the memory requirements
GPU Accelerated Time-Domain Discrete Geometric Approach Method for Maxwell's Equations on Tetrahedral Grids
No full textA recently introduced time-domain method for the numerical solution of Maxwell's equations on unstructured grids is reformulated in a novel way, with the aim of implementation on graphical processing units (GPUs). Numerical tests show that the GPU implementation of the resulting scheme yields correct results, while also offering an order of magnitude in speedup and still preserving all of the main properties of the original finite-difference time-domain algorithm
A Geometric Frequency-Domain Wave Propagation Formulation for Fast Convergence of Iterative Solvers
No full textThe frequency-domain wave propagation problem is notoriously difficult to solve through iterative methods because it leads to a symmetric but indefinite linear system. For this reason, direct methods are usually employed at the expense of great memory usage. Convergence of iterative methods, however, could be obtained by regularizing the wave equation. We introduce such regularization in discrete geometric approach framework on polyhedral grids. Moreover, we extend the regularization to the impedance boundary condition
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