diff --git a/docs/content/method.rst b/docs/content/method.rst index 88326d15..985747bf 100644 --- a/docs/content/method.rst +++ b/docs/content/method.rst @@ -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 `). +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: diff --git a/docs/method/peec_7.png b/docs/method/peec_7.png new file mode 100644 index 00000000..130625a2 Binary files /dev/null and b/docs/method/peec_7.png differ diff --git a/docs/method/peec_7.svg b/docs/method/peec_7.svg new file mode 100644 index 00000000..1898e623 --- /dev/null +++ b/docs/method/peec_7.svg @@ -0,0 +1,5133 @@ + + + +Step 1. - Embedding the Toeplitz matrix in a Circulant matrixStep 2. - Extraction of the Circulant matrix coefficientsStep 3. - Compute the Circulant matrix-vector multiplication with FFTStep 4. - Extract the Toeplitz matrix-vector multiplication result