SLEPc: Scalable Library for Eigenvalue Problem Computations Jose ...
SLEPc: Scalable Library for Eigenvalue Problem Computations Jose ...
SLEPc: Scalable Library for Eigenvalue Problem Computations Jose ...
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<strong>SLEPc</strong><br />
The Algebraic <strong>Problem</strong><br />
• Discretization: Nodal Collocation, with Legendre<br />
polynomials<br />
⎡ L<br />
⎢<br />
⎣−<br />
L<br />
11<br />
21 22<br />
0 ⎤⎡ψ<br />
1 ⎤ M M<br />
i<br />
1 ⎡<br />
L<br />
⎥⎢<br />
⎦⎣ψ<br />
⎥ =<br />
λ<br />
⎢<br />
2i<br />
⎦ i ⎣ 0 0<br />
• Reduced size eigenproblem<br />
Aψ<br />
1 i 1<br />
i<br />
λ ψ<br />
−1<br />
−1<br />
A= L ( M + M L L )<br />
11<br />
Lψ<br />
=<br />
i<br />
1<br />
Mψ<br />
i<br />
λ<br />
=<br />
i<br />
11 12 22<br />
i<br />
21<br />
⎤⎡ψ<br />
⎤<br />
i<br />
⎥⎢<br />
⎦⎣ψ<br />
⎥<br />
2i<br />
⎦<br />
11 12 1
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