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Compact thermal models are often used during joint electrothermal simulation of microelectromechanical systems (MEMS) and circuits. Formal model reduction allows generation of compact thermal models automatically from high-dimensional finite-element models. Unfortunately, it requires fixing a film coefficient employed to describe the convection boundary(More)
Several recently developed model order reduction methods for fast simulation of large-scale dynamical systems with two or more parameters are reviewed. Besides, an alternative approach for linear parameter system model reduction as well as a more efficient method for nonlinear parameter system model reduction are proposed in this paper. Comparison between(More)
In this paper we review two recently suggested projection techniques for model order reduction of bilinear systems. The first one is computationally more attractive, but so far it was assumed that this method does not yield a moment-matching approximation. Here we show that the reduced-order models computed by both of the two projection techniques match(More)
In this paper, we reviewed several newly presented nonlinear model order reduction methods, we analyze these methods theoretically and with experiments in detail. We show the problems exists in each method and future work needs to be done. Besides, we propose the two sided projection method which greatly improved the efficiency of the variational equation(More)
— Many model order reduction methods for pa-rameterized systems need to construct a projection matrix V which requires computing several moment matrices of the parameterized systems. For computing each moment matrix, the solution of a linear system with multiple right-hand sides is required. Furthermore, the number of linear systems increases with both the(More)
At present, almost all model order reduction methods assume single-input single-output (SISO) systems or systems with a small number of inputs and outputs. Few methods can deal with systems with a large number of inputs and outputs. Multi-input multi-output (MIMO) systems appear for example in mod-eling of integrated circuits. The number of inputs and(More)
by iterative methods based on recycling Krylov subspaces. We propose two recycling algorithms, which are both based on the generalized conjugate residual (GCR) method. The recycling methods reuse the descent vectors computed while solving the previous linear systems Ax = b j , j = 1, 2,. .. , i − 1, such that a lot of computational work can be saved when(More)
An application of formal model reduction to generate a boundary condition independent compact thermal model is discussed. A new method to find a low-dimensional basis that preserves the convection coefficient as a parameter is presented. Numerical results show that the method allows the convection coefficient to change from 1 to 10 9 while keeping the(More)
Krylov subspace recycling is a process for accelerating the convergence of sequences of linear systems. Based on this technique we have recently developed the recycling BiCG algorithm. We now generalize and extend this recycling theory to BiCGSTAB. Recycling BiCG focuses on efficiently solving sequences of dual linear systems, while the focus here is on(More)