Computer Simulations and Thermal Design 381
(14.111)
This is the general form of the matrix equation that is solved by computer simulation
tools. If N is the number of nodes in the domain, the coefcient matrix [A] is an
N × N matrix, and [T] and [C] are vectors with N elements.
If [A]
–1
is the inverse of matrix [A] such that [A]
–1
[A] = [I] where [I] is the unity
matrix, the solution of this matrix equation will be
(14.112)
However, obtaining the inverse of a matrix is not a trivial task. There are many
numerical techniques such as Gauss–Seidel and incomplete LU decomposition that
are used to approximate the inverse of a matrix. These methods will not be described
here and the interested readers are referre ...