Model Reduction for Power Electronics Systems with Multiple Heat Sources

Fast transient analysis of electronic systems thermal behavior is a vital tool for the examination of integrated circuits during the development. In an operational as well as in failure mode, this kind of analysis is needed to verify that operation conditions will remain safe for complex mixed signal electronic systems. Many of the questions, which have to be evaluated, are coming up in the last stages of the development, when the time to take a decision has to be short, and the designers need fast and accurate answers. A formal model reduction approach allows us to take a high dimensional finite element model and generate its low-dimensional approximation formally. As such, it is an ideal candidate for the goal above. Several research groups have already documented its successful application to a thermal problem with a single heat source. In the paper, we present the application of model reduction to a thermal problem with many independent heat sources. We demonstrate that the block Arnoldi process allows us to automatically build accurate compact dynamic thermal models while preserving independent heat sources in the reduced model. We discuss computational time necessary to perform model reduction. We show that a simple approach based on local error indicators allows us to choose automatically the dimension of the reduced system. We present the complete flow of using the method in engineering environment : Modeling in ANSYS the original problem, Model reduction with MOR for ANSYS, Evaluation of results using Mathematica

4 AS DETERMINED BY ION-MOLECULE EQUILIBRIA METHOD

Admixture of potassium chromate to manganese oxide has allowed us to generate measurable concentration of negative ions Mn

Abstract STATISTICAL MODEL OF SYSTEMATIC ERRORS: AN ASSESSMENT OF THE BA-CU AND CU-Y PHASE DIAGRAM

In a series of experimental measurements, the difference among values obtained in several experiments (between-errors) quite often are greater than the reproducibility scatter within an experiment (within-errors). This is typically explained in terms of systematic experimental errors. The application of a method devised in mathematical statistics, i.e., The Estimation of Variance Components, allows us to treat this problem. In the present work, the use of this method is considered for the non-linear thermodynamic model pertaining to the assessment of the BaCu and Cu-Y phase diagrams. The linear error model comprising a reproducibility error with the shift and tilt systematic errors was employed to describe the scatter observed. Special attention is paid to visualizing the quality of the fit. Keywords random factor, mixed model, estimation of variance components, maximum likelihood

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Efficient harmonic simulation of a trabecular bone finite element model by means of model reduction

Three-dimensional serial reconstruction techniques allow us to develop very detailed microfinite element (micro-FE) model of bones that can very accurately represent the porous bone micro-architecture. However, such models are of very high dimension and, at present, simulation is limited to a linear elastic analysis only. In the present paper, we suggest to use model reduction in order to enable harmonic simulation for micro-FE models. We take two bone models of dimensions 130 000 and 900 000 and report results for implicit moment matching based via the Arnoldi process. We demonstrate that for the fist model a low-dimensional subspace of dimension 10 allows us to accurately describe frequency response up to 190 Hz. For the second model, a low-dimensional subspace of dimension 25 is enough to accurately describe frequency response up to 30 Hz. We show that the time to perform model reduction and then to simulate the low-dimensional model is orders of magnitude less than that needed for harmonic simulation of the original model