.. _diffusion-poisson_parametric_study: diffusion/poisson_parametric_study.py ===================================== **Description** Poisson equation. This example demonstrates parametric study capabilities of Application classes. In particular (written in the strong form): .. math:: c \Delta t = f \mbox{ in } \Omega, t = 2 \mbox{ on } \Gamma_1 \;, t = -2 \mbox{ on } \Gamma_2 \;, f = 1 \mbox{ in } \Omega_1 \;, f = 0 \mbox{ otherwise,} where :math:\Omega is a square domain, :math:\Omega_1 \in \Omega is a circular domain. Now let's see what happens if :math:\Omega_1 diameter changes. Run:: $./simple.py and then look in 'output/r_omega1' directory, try for example::$ ./resview.py output/r_omega1/circles_in_square*.vtk -2 Remark: this simple case could be achieved also by defining :math:\Omega_1 by a time-dependent function and solve the static problem as a time-dependent problem. However, the approach below is much more general. Find :math:t such that: .. math:: \int_{\Omega} c \nabla s \cdot \nabla t = 0 \;, \quad \forall s \;. :download:source code  .. literalinclude:: /../sfepy/examples/diffusion/poisson_parametric_study.py