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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)
An application of formal model reduction to generate a boundary condition independent compact thermal model is discussed. A new method to find a lowdimensional 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 while keeping the accuracy(More)
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)
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 parameterized 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 modeling 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 = bj , j = 1, 2, . . . , i − 1, such that a lot of computational work can be saved when(More)
The variational analysis [11] has been employed in [7] for order reduction of weakly nonlinear systems. For a relatively strong nonlinear system, this method will mostly lose efficiency because of the exponentially increased number of inputs in higher order variational equations caused by the individual reduction process of the variational systems.(More)