The Galerkin Lumped Parameter Method for Thermal Problems

2012 ◽  
Author(s):  
Alfredo Bermúdez ◽  
Francisco Pena
Keyword(s):  
Reduction Method ◽  
Order Reduction ◽  
Parameter Method ◽  
The Finite Element Method ◽  
Reduced Basis ◽  
Model Order ◽  
Lumped Parameter ◽  
Lumped Parameter Models ◽  
Order Reduction Method ◽  
Lumped Parameter Method

In this contribution, we present a method called Galerkin lumped parameter (GLP) method, as a generalization of the lumped parameter models used in engineering. This method can also be seen as a model-order reduction method. Similarities and differences are discussed. In the GLP method, introduced in [1], domain is decomposed into several sub-domains and a time-independent adapted reduced basis is calculated solving elliptic problems in each sub-domain. The method seeks a global solution in the space spanned by this basis, by solving an ordinary differential system. This approach is useful for electric motors, since the decomposition into several pieces is natural. Numerical results concerning heat equation are presented. Firstly, the comparison with an analytic solution is shown to check the implementation of the numerical algorithm. Secondly, the thermal behavior of an electric motor is simulated, assuming that the electric losses are known. A comparison with the solution obtained by the finite element method is shown.

scholarly journals Analysis and Application of Screens for Acoustic Impedance in a Speaker Box with a Passive Radiator to Decrease Standing-Wave Influence

2020 ◽  
Vol 10 (3) ◽  
pp. 866
Author(s):  
Yuan-Wu Jiang ◽  
Dan-Ping Xu ◽  
Zhi-Xiong Jiang ◽  
Jun-Hyung Kim ◽  
Ki-Hong Park ◽  
...  
Keyword(s):  
Standing Wave ◽  
Acoustic Resonance ◽  
Experimental Result ◽  
Parameter Method ◽  
Analysis Tool ◽  
Analysis Method ◽  
The Finite Element Method ◽  
Lumped Parameter ◽  
Acoustic Domain ◽  
Lumped Parameter Method

Micro speakers are playing an increasingly important role with the development of multimedia devices. This study applies the lumped-parameter method, which uses an equivalent circuit to model the electromagnetic and mechanical domains. The acoustic domain is modeled using the finite element method. Based on the analysis tool, the use of a screen is analyzed, and the screen is designed to depress the acoustic resonance in the sound-pressure-level curve and improve the performance. The samples are fabricated, and the experiment verifies the analysis method. The experimental result shows that the peak and dip due to the standing wave are cancelled, and the frequency response is smooth when the screen is used.

scholarly journals AN ITERATIVE MODEL ORDER REDUCTION METHOD FOR LARGE-SCALE DYNAMICAL SYSTEMS

2017 ◽  
Vol 59 (1) ◽  
pp. 115-133
Author(s):  
K. MOHAMED ◽  
A. MEHDI ◽  
M. ABDELKADER
Keyword(s):  
Dynamical Systems ◽  
Model Order Reduction ◽  
Large Scale ◽  
Reduction Method ◽  
Linear Time ◽  
Order Reduction ◽  
Lyapunov Equation ◽  
Model Order ◽  
Iterative Model ◽  
Order Reduction Method

We present a new iterative model order reduction method for large-scale linear time-invariant dynamical systems, based on a combined singular value decomposition–adaptive-order rational Arnoldi (SVD-AORA) approach. This method is an extension of the SVD-rational Krylov method. It is based on two-sided projections: the SVD side depends on the observability Gramian by the resolution of the Lyapunov equation, and the Krylov side is generated by the adaptive-order rational Arnoldi based on moment matching. The use of the SVD provides stability for the reduced system, and the use of the AORA method provides numerical efficiency and a relative lower computation complexity. The reduced model obtained is asymptotically stable and minimizes the error ($H_{2}$and$H_{\infty }$) between the original and the reduced system. Two examples are given to study the performance of the proposed approach.

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