This tutorial intoduces the use of FEniCS for solving differentiable variational problems in PyMC3. Automatic adjoint solvers for FEniCS programs are generated with ...

which essential conditions that are set. -Laplace(u) = f on the unit square. u = 1 + 2y^2 on x=0. u = 2 + 2y^2 on x=1. -du/dn = g on y=0 and y=1. u = 1 + x^2 + 2y^2, f = -6, g = -4y.

Using a series of examples, including the Poisson equation, the equations of linear elasticity, the incompressible Navier–Stokes equations, and systems of nonlinear advection–diffusion–reaction ...

ABSTRACT: In shape optimization, we often seek to optimize the shape of a domain in order to achieve a goal. For example, the sound of a drum depends on the shape of its membrane, via the eigenvalues ...