1,721,149 research outputs found
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 Hybrid CM-BEM Formulation for Solving Large-Scale 3D Eddy-Current Problems Based on H-Matrices and Randomized Singular Value Decomposition for BEM Matrix Compression
Full text linkWe present a novel a, v -q hybrid method for solving large-scale time-harmonic eddy-current problems. This method combines a hybrid unsymmetric formulation based on the cell method and the boundary element method with a hierarchical matrix-compression technique based on randomized singular value decomposition. The main advantage is that the memory requirements are strongly reduced compared to the corresponding hybrid method without matrix compression while retaining the same robust solution strategy consisting of a simple construction of the preconditioner. In addition, the matrix-compression accuracy and efficiency are enhanced compared to traditional compression methods, such as adaptive cross approximation. The numerical results show that the proposed hybrid approach can also be effectively used to analyze large-scale eddy-current problems of engineering interest
Coupling the cell method with the boundary element method in static and quasi–static electromagnetic problems
Full text linkA unified discretization framework, based on the concept of augmented dual grids, is proposed for devising hybrid formulations which combine the Cell Method and the Boundary Element Method for static and quasi-static electromagnetic field problems. It is shown that hybrid approaches, already proposed in literature, can be rigorously formulated within this framework. As a main outcome, a novel direct hybrid approach amenable to iterative solution is derived. Both direct and indirect hybrid approaches, applied to an axisymmetric model, are compared with a reference third-order 2D FEM solution. The effectiveness of the indirect approach, equivalent to the direct approach, is finally tested on a fully 3D benchmark with more complex topology
Domain Decomposition with Non-Conforming Polyhedral Grids
Full text linkA novel mortar approach for the domain decomposition of field problems discretized in terms of nodal variables by the cell method is here proposed. This approach allows the use of both arbitrary polyhedral meshes and non-conforming discretizations, without limitations or complications due to the mesh type or the model geometry. Therefore, it provides a new domain decomposition method that can be practically used in engineering applications for coupling different parts of a model, which can be independently discretized and then reassembled together. More precisely: 1) Any part of the computational domain is first separately modeled in order to assess the mesh type and size that are best suited for ensuring an accurate local field reconstruction; 2) The different discretized parts can be combined together in order to obtain an accurate solution of a composite problem, while maintaining the local discretizations already determined. As a main advantage over existing mortar approaches, the algebraic structure of the final matrix system - derived by the cell method discretization - is not altered by the introduction of mortar interface conditions. As a result, the same preconditioning and iterative solver strategy can be extended as is to the proposed mortar method. This approach is validated by a convergence analysis on an analytical test case and its effectiveness for practical applications is assessed on a real-sized engineering problem
Enforcing Lumped Parameter Excitations in Edge-Element Formulations by Using a Fast Iterative Approach
No full textIn order to couple external circuits to edge-element discretized electromagnetic models, with full field equations, global constraints involving voltages or currents need to be enforced. There is no canonical way to impose a voltage or a current without additional modeling information on the distribution of field sources that rely on topological concepts. In this article, a fast solution of field sources within massive conductors in static and dynamic problems is proposed. Global basis functions, required to cope with non-trivial coil topologies, are directly generated by an iterative solver rather than pre-computing source fields, e.g., by tree-cotree decomposition
A New Set of Basis Functions for the Discrete Geometric Approach
No full textBy exploiting the geometric structure behind Maxwell’s equations, the so called discrete
geometric approach allows to translate the physical laws of electromagnetism into discrete
relations, involving circulations and fluxes associated with the geometric elements of a pair
of interlocked grids: the primal grid and the dual grid.
To form a finite dimensional system of equations, discrete counterparts of the constitutive
relations must be introduced in addition. They are referred to as constitutive matrices
which must comply with precise properties (symmetry, positive definiteness, consistency)
in order to guarantee the stability and consistency of the overall finite dimensional system
of equations.
The aim of this work is to introduce a general and efficient set of vector functions associated
with the edges and faces of a polyhedral primal grids or of a dual grid obtained from
the barycentric subdivision of the boundary of the primal grid; these vector functions comply
with precise specifications which allow to construct stable and consistent discrete constitutive
equations for the discrete geometric approach in the framework of an energetic
method
Subgridding to Solving Magnetostatics within Discrete Geometric Approach
No full textWe propose a recipe to construct a symmetric positive definite and consistent reluctance constitutive matrix to be used within discrete geometric approaches when the primal grid is generated by an enhanced subgridding of a generic hexahedral grid. We focus on a magnetostatic problem as working example
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