Research On Reduced-Order Algorithm For Large Scale Interconnecting Model

With the increasing size of the integrated circuit,the current integrated circuit interconnects have reached the scale of hundreds of thousands,such a large interconnection circuit network has been unable to use the traditional circuit simulation tools for effective analysis,interconnection problems has become one of the main problems restricting the development of integrated circuits.Therefore,the use of model reduction technology to reduce the order of such a high-order model has become the key to the development of integrated circuits.Firstly,in this paper we study the modeling algorithm of large-scale interconnection model,and use the improved node voltage method(MNA)to model the interconnection network given by the international test library.It is a four-input,four-output and 980-order model,and the nature of the model were analyzed through the simulation.In this paper,the following three kinds of model reduction algorithm are used to reduce the model,that is,1.SVD model reduction method;2.Rational Krylov model reduction method;3.SVD-Krylov model reduction method.To obtain the reduction nature of two kinds of traditional reduction algorithms which are balanced truncation method based on SVD(BR)and moment matching method(RK)based on Krylov,in the paper the the two algorithms are respectively used to reduce for the CDPLayer model and the Iss model.And the order of the two algorithms is obtained.Based on the characteristics and advantages of these two algorithms,this paper presents an least squares(LS)method,which can be said to be an SVD-Krylov algorithm.On the basis of the least squares method,by introducing the translation operator,the equation constrained least squares(ECLS)method is proposed.The ECLS algorithm can make the reduced-order model accurately match the former r +i mode of the original high-order model,and also use the least squares approximation to the other high-order terms,thus greatly improving the degenerate accuracy(where r is the order of the reduction model,i is a nonnegative integer,1 ?i <r).The above four algorithms are used to reduce the interconnection model to 30 respectively,through the simulation and comparison,the ECLS algorithm proposed in this paper is used to reduce the scale of the large-scale interconnection model,which can make the reduced-order model better match with the original model,reduce the error caused by the reduced order,and greatly reduce the time,Confirming the effectiveness of the method.