Computationally efficient modeling and simulation of large scale systems
A method of simulating operation of a VLSI interconnect structure having capacitive and inductive coupling between nodes thereof. A matrix X and a matrix Y containing different combinations of passive circuit element values for the interconnect structure are obtained where the element values for each matrix include inductance L and inverse capacitance P. An adjacency matrix A associated with the interconnect structure is obtained. Numerical integration is used to solve first and second equations, each including as a factor the product of the inverse matrix X 1 and at least one other matrix, with first equation including X 1 Y, X 1 A, and X 1 P, and the second equation including X 1 A and X 1 P.
1. A method of simulating operation of a VLSI interconnect structure having capacitive and inductive coupling between nodes thereof, comprising:
obtaining a matrix X and a matrix Y containing different combinations of passive circuit element values for said interconnect structure, said element values for each matrix including inductance L and inverse capacitance P;
obtaining an adjacency matrix A associated with said interconnect structure;
using a processor to perform numerical integration to solve first and second equations each including as a factor the product of the inverse matrix X −1 and at least one other matrix, said first equation including X −1 Y, X −1 A, and X −1 P, and said second equation including X −1 A and X −1 P.
2. The method of claim 1 , wherein matrices X and Y each contain resistance values R in addition to L and P.
3. The method of claim 2 , wherein said first equation is substantially of the form
i
l
k
+
1
=
X
-
1
Yi
l
k
+
X
-
1
Av
n
k
+
h
4
X
-
1
AP
(
I
s
k
+
1
+
I
s
k
)
,
where v n and i l are node voltages and inductor currents, respectively, A is an adjacency matrix for the circuit, and I s is a current source vector, and
wherein said second equation is substantially of the form
X
-
1
Av
n
k
+
1
=
X
-
1
Av
n
k
-
h
2
X
-
1
APA
T
(
i
l
k
+
1
+
i
l
k
)
+
h
2
X
-
1
AP
(
I
s
k
+
1
+
I
s
k
)
.