Implicit integration methods
Now that we have our implicit scheme, we must solve the linear system.
While the resolution itself is not that difficult, the problem is that
the system is very large : suppose our cloth is defined by 2500 nodes.
The system then has 7500 equations. That means we have to store a 7500x7500
matrix, and then solve the system !
Fortunately, the matrix is sparse. That is, only few values are not zero.
This property is very important. First, we can save some memory space
by storing only the non-zero values, and secondly we can use a special
iterative method to solve the linear system : the conjugate gradient.
This iterative method is designed to exploit the sparsity property. It
uses only vector-matrix products. Obviously, the matrix-vector product
implementation exploit the sparsity described before.
To resume
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