positive definite banded solution of Ax=b

I'm writing code for a finite element solver for the poisson equation.
 The problem I'm having is that I can't find a routine that will
decompose my banded matrix effieciently. The equation is Ax=b to solve
for x where A is a sysmmetric banded matrix.  I wish to decompose it
once, and then solve for different vectors b many times.  The matrix
is ~10,000x10,000 with a bandwidth of ~100.  The dense lu
decomposittion for this will take about 56 hours by my reckoning. 
Please can someone let me know of a better way.

Leon.
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