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FFT matvec doc
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otvam committed Jan 22, 2025
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9 changes: 7 additions & 2 deletions docs/content/method.rst
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Expand Up @@ -90,8 +90,13 @@ Hence, the computational cost and memory requirement for generating and storing
Fig. 6 - Illustration of the remapping of the inductance matrix coefficients.

With all the repeated coefficients, the inductance matrix is a a block-Toeplitz Toeplitz-block matrix.
For such matrices, the matrix-vector multiplications can be done with Fast Fourier Transforms.
Hence, the computational complexity of multiplications is reduced from O(n^2) to O(n*log(n)).
For such matrices, the matrix-vector multiplications can be done with Fast Fourier Transforms (:ref:`Fig. 7 <fig_7>`).
Hence, the Fast Fourier Transforms are reducing the computational complexity of multiplications from O(n^2) to O(n*log(n)).

.. _fig_7:
.. figure:: ../method/peec_7.png

Fig. 7 - Toeplitz matrix-vector multiplication with FFT.

In summary, with a voxel structure, the PEEC method features the following advantages:

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