Patent ID: 7797140

Claim:
A method performed by computer, for reducing the computational complexity and overcoming numerical instability, resulting in faster computation times and less storage space for RLC (Resistor-Inductor-Capacitor) interconnect model-order reduction by performing adjoint networks operations, comprising: i) establishing an MNA (modified nodal analysis) expression of an original system of a RLC circuit; ii) creating a matrix A and a vector R from the MNA expression as a base vector for subspace expansion, wherein the matrix A is obtained through A =−(s 0 M+N) −1 M and the vector R is obtained through R=(s 0 M+N) −1 B ; iii) executing a block Lanczos algorithm between an expansion vector and a system dynamic differences of Krylov subspace to yield first biorthogonal base V q,L and second biorthogonal base W q,L ; iv) establishing an adjoint MNA expression: M ⁢ ⅆ x a ⁡ ( t ) ⅆ t = - N T ⁢ x a ⁡ ( t ) + Du ⁡ ( t ) , y a ⁡ ( t ) = B T ⁢ x a ⁡ ( t ) , ⁢ wherein system moments are represented as X (i) (s 0 ) and X a (i) (s 0 ), with X (i) (s 0 ) εcolsp(V q,L ) and X a (i) (s 0 ) εcolsp((N T +s 0 M) −1 W q,L ); v) creating an equivalent transformation matrix U using the first biorthogonal base V q,L yielded from the block Lanczos algorithm from the Krylov subspace and the second biorthogonal base W q,L yielded from the block Lanczos algorithm from the Krylov subspace, wherein: U=[V q,L ( N T +s 0 M ) −1 W q,L ],since { X (i) (s 0 ), X a (j) (s 0 )}εcolsp( U ); vi) obtaining a reduced order MNA matrix utilizing the equivalent transformation matrix U by a model-order reduction with a one sided projection; vii) obtaining a frequency response waveshape from the reduced order MNA matrix; and viii) outputting the frequency response waveshape by the computer, wherein (1) N and M are MNA network matrixes; (2) S 0 is a frequency expansion point; (3) B is nodes connecting interconnects and inputted signals; and (4) “t” is time, “u(t)” is a function of an input signal, “x” is a system variable, “y” is an output signal, and “a” is a variable of an adjoint network.