Second-order Krylov subspace and arnoldi procedure

Bai, Zhaojun; Su, Yangfeng

doi:10.1007/s11741-004-0048-9

Cited by 9 publications

(3 citation statements)

References 23 publications

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“…The sum and the ratio of the amounts of protein and carbohydrate represented the total amount and the composition of S-EPS and B-EPS. Protein was determined by the Bradford method [5] ,while carbohydrate was measured with the anthrone method [6] .…”

Section: Extraction and Analysis Of Epsmentioning

confidence: 99%

Effects of Sludge Concentration on EPS and Membrane Fouling in Anoxic/Aerobic Membrane Bioreactors

Wang

Zhu

et al. 2014

AMR

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Sludge Concentration (MLSS) is one of major parameters for operation of Anoxic/Aerobic-Membrane Bioreactors（A/O-MBR）and it influences the removal efficiency of pollutants and the rate of membrane fouling as well. This paper focuses on the effects of different MLSS on the treatment of domestic wastewater, the quantity and composition of extracellular polymeric substance (EPS), and the variation of the rate of membrane fouling. It also includes a preliminary analysis of the correlation between EPS and membrane fouling to provide reference for future studies of the mechanism of membrane fouling.

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Section: Extraction and Analysis Of Epsmentioning

confidence: 99%

Effects of Sludge Concentration on EPS and Membrane Fouling in Anoxic/Aerobic Membrane Bioreactors

Wang

Zhu

et al. 2014

AMR

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“…37 The proper orthogonal decomposition (POD) 38,39 is one of the most commonly used MOR techniques, 40 while it depends on the representativeness of the snapshot (or master frequencies) selected in the POD program, and thus cannot guarantee the quality of the simplified model. 41 For two-dimensional linear systems, the second-order Arnoldi (SOAR) algorithm proposed by Bai et al 42,43 has attracted a lot of researchers' attention. In this algorithm, the full-order model (FOM) is first projected onto the projection subspace; then, a reduced-order model (ROM) retaining the basic structure and characteristics of the original model is established; the orthonormal basis of the projection subspace is finally obtained using the SOAR.…”

Section: Introductionmentioning

confidence: 99%

A BEM broadband topology optimization strategy based on Taylor expansion and SOAR method—Application to 2D acoustic scattering problems

Chen,

Zhao,

Lian

et al. 2023

Numerical Meth Engineering

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In this article, an innovative method is proposed for broadband topology optimization of sound‐absorbing materials adhering to the surface of a sound barrier structure. Helmholtz equation for the acoustic problems is solved using the boundary element method, while sensitivities of the objective function with respect to a large number of design variables are calculated via a sensitivity analysis method originated from the adjoint variable method (AVM), and the optimal solution is obtained by the method of moving asymptotes (MMA). Since the traditional single‐frequency topology optimization is frequency dependent, that is, the optimal solution at a certain frequency may not be optimal at other frequencies, broadband topology optimization of sound‐absorbing materials is conducted in this work. To address the problem of tremendous computational cost due to repetitive calculations at each discrete frequency point during broadband optimization, Taylor expansion of the Hankel function is performed to decouple the frequency dependent and independent terms in the BEM equations. For large‐scale problems, a reduced‐order model that retains the essential structures and key properties of the original model is built using the second‐order Arnoldi (SOAR) method. The accuracy and feasibility of the proposed algorithms are finally validated via some two‐dimensional numerical examples.

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“…However, for a complex MEMS device [5], atomic-level partition will cause excessive lumped behavior models used in systemlevel modeling and simulation, which will make the model large-scale and complex and hard to understand. A Krylov subspace projection [6][7][8][9][10] technique, such as the Arnoldi or Lanczos procedure, is another popular macromodeling method.…”

Section: Introductionmentioning

confidence: 99%

Angularly parameterized macromodel extraction for unconstrained microstructures

Xu¹,

Yuan²,

Chang³

et al. 2008

J. Micromech. Microeng.

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In this paper, we present an angularly parameterized model order reduction (APMOR) technique for macromodel extraction of unconstrained microstructures by combining a new, iterated IRS (improved reduced system) method with coordinate transformation theory. The extracted macromodels are encapsulated in the MAST hardware description language and can be exported automatically as components which can be inserted directly into an analog circuit simulator for dynamics simulation. An in-plane micro accelerometer including four variable cross-section folded beams is used to demonstrate the proposed macromodeling method. The folded beams are treated as unconstrained microstructures, and numerical simulation results in a SABER simulator show that the macromodels can dramatically reduce the computation cost while capturing the device behavior faithfully. Compared with FEM results, the relative error is less than 1.4%, while the computational efficiency improves about 22 times. Once the macromodel of one of the folded beams is obtained, the macromodels of all other folded beams can be obtained easily by setting the corresponding angle parameters. With the help of an APMOR technique and the existing model library which is developed in our previous work, the hybrid system-level model of the in-plane micro accelerometer can be constructed rapidly, and the scale factor of the accelerometer is simulated. Compared with experimental results, the relative error is about 8.16%.

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Second-order Krylov subspace and arnoldi procedure

Cited by 9 publications

References 23 publications

Effects of Sludge Concentration on EPS and Membrane Fouling in Anoxic/Aerobic Membrane Bioreactors

Effects of Sludge Concentration on EPS and Membrane Fouling in Anoxic/Aerobic Membrane Bioreactors

A BEM broadband topology optimization strategy based on Taylor expansion and SOAR method—Application to 2D acoustic scattering problems

Angularly parameterized macromodel extraction for unconstrained microstructures

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