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5.3.9. Technical Reference

Both OM2p and OM3p solve for eigenpairs of the following equation

subject to boundary conditions and the attributes applied to the materials in the geometry.

The solvers use the Lanczos algorithm to solve the eigenproblem, by default. The application of the finite-element method yields the following matrix equation that is solved for the specified number of eigenpairs:

where A and B are sparse Hermitian matrices in the lossless case. The solvers use either direct (LU decomposition), or iterative techniques such as the preconditioned conjugate gradient method (PCG), for the linear solve of the finite-element matrix that is required at each Lanczos iteration. The iterative Lanczos process converges the extremal eigenpairs first (typically those with the largest eigenvalues), and since it is often the lowest frequency modes of a resonant structure that are of interest, you transform the matrix equation so that the eigenpairs near a given frequency, or "shift point", have the largest eigenvalues.

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