Computationally efficient modeling and simulation of large scale systems
A system for simulating operation of a VLSI interconnect structure having capacitive and inductive coupling between nodes thereof, including a processor, and a memory, the processor configured to perform obtaining a matrix X and a matrix Y containing different combinations of passive circuit element values for the interconnect structure, the element values for each matrix including inductance L and inverse capacitance P, obtaining an adjacency matrix A associated with the interconnect structure, storing the matrices X, Y, and A in the memory, and performing numerical integration to solve first and second equations.
1. A system for simulating operation of a VLSI interconnect structure having capacitive and inductive coupling between nodes thereof, comprising:
a processor; and
a memory, said processor configured to:
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,
storing said matrices X, Y, and A in said memory, and
performing numerical integration to solve first and second equations each including as a factor product of inverse said matrix X (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 system of claim 1 , wherein said matrices X and Y each contain resistance values in addition to L and P.
3. The system of claim 2 , wherein said first equation is substantially of the form,
i
l
k
+
1
=
X
-
1
Y
i
l
k
+
X
-
1
A
v
n
k
+
h
4
X
-
1
A
P
(
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
A
v
n
k
+
1
=
X
-
1
A
v
n
k
-
h
2
X
-
1
A
P
A
T
(
i
l
k
+
1
+
i
l
k
)
+
h
2
X
-
1
A
P
(
I
s
k
+
1
+
I
s
k
)
.