摘要 工程師能夠在ANSYS開發(fā)的有限元模型中運用現(xiàn)有的軟件實現(xiàn)現(xiàn)代模型降階技術(shù)。我們著于一個人如何獨立的從在ANSYS和C ++上實現(xiàn)的執(zhí)行模型中提取所需的信息，而不用依靠特別的專業(yè)人士，我們將利用與結(jié)構(gòu)力學(xué)和熱力學(xué)有限元模型相關(guān)的實例來討論計算成本。
1.介紹
大型線性動態(tài)系統(tǒng)模型降階已經(jīng)是相當(dāng)成熟的領(lǐng)域[1]。許多論文（見參考文獻(xiàn)[2]）指出，模型降價的優(yōu)勢已在各種科學(xué)和工程應(yīng)用上被證實。我們目前的工作是集中討論工程師如何將該技術(shù)與現(xiàn)有的商業(yè)有限元軟件相結(jié)合，以達(dá)到如下目的：
— 加快對瞬變電壓、諧波的分析；
— 自動生成系統(tǒng)級仿真的緊湊模型；
— 在設(shè)計階段納入有限元程序包。
通常大規(guī)模動態(tài)系統(tǒng)模型降階第一步如下
Ex˙=Ax+Bu (1.1)
y=Cx
其中A和E是系統(tǒng)矩陣，B是輸入矩陣，C是輸出矩陣。模型降階的目的是產(chǎn)生一個低維式以逼近（1.1）， Erz=Arz.+Bru


Abstract. We present the software mor4ansysthat allows engineers to employ modern model reduction techniques to finite element models developed in ANSYS. We focus on how one extracts the required information from ANSYS and performs model reduction in a C++ implementation that is not dependent on a particular sparse solver. We discuss the computational cost with examples related to structural mechanics and thermal finite element models.
1.Introduction
The model order reduction of linear large-scale dynamic systems is already quite an established area [1]. In many papers (see references in [2]), advantages of model reduction have been demonstrated for a variety of scientific and engineering applications. In the present work, we focus on how engineers can combine this technique with existing commercial finite element software in order to
– Speed up a transient or harmonic analysis,
– Generate automatically compact models for system-level simulation,
– Incorporate finite element packages during the design phase.
Model reduction is conventionally applied to a large-scale dynamic system of the first order as follows
Ex˙=Ax+Bu (1.1)
y=Cx
where Aand E are system matrices, Bis the input matrix, Cis the output matrix. The aim of model reduction is to generate a low-dimensional approximation to (1.1) in a similar form
Erz=Arz.+Bru (1.2)
Y=Crz.