sfepy.homogenization.convolutions module¶

class sfepy.homogenization.convolutions.ConvolutionKernel(name, times, kernel, decay=None, exp_coefs=None, exp_decay=None)[source]¶

The convolution kernel with exponential synchronous decay approximation approximating the original kernel represented by the array $c[i]$ , $i = 0, 1, \dots$ .

$\begin{split} & c_0 \equiv c[0] \;, c_{e0} \equiv c_0 c^e_0 \;, \\ & c(t) \approx c_0 d(t) \approx c_0 e(t) = c_{e0} e_n(t) \;, \end{split}$

where $d(0) = e_n(0) = 1$ , $d$ is the synchronous decay and $e$ its exponential approximation, $e = c^e_0 exp(-c^e_1 t)$ .

diff_dt(use_exp=False)[source]¶: The derivative of the kernel w.r.t. time.

get_exp()[source]¶: Get the exponential synchronous decay kernel approximation.

get_full()[source]¶: Get the original (full) kernel.

int_dt(use_exp=False)[source]¶: The integral of the kernel in time.

sfepy.homogenization.convolutions.approximate_exponential(x, y)[source]¶

Approximate $y = f(x)$ by $y_a = c_1 exp(- c_2 x)$ .

Initial guess is given by assuming y has already the required exponential form.

sfepy.homogenization.convolutions.compute_mean_decay(coef)[source]¶: Compute mean decay approximation of a non-scalar fading memory coefficient.

sfepy.homogenization.convolutions.eval_exponential(coefs, x)[source]¶

sfepy.homogenization.convolutions.fit_exponential(x, y, return_coefs=False)[source]¶: Evaluate $y = f(x)$ after approximating $f$ by an exponential.