The code looks good, but not the math. Am I missing some plugin? -- Anders
--- Begin Message --------------------------------------------------------------- revno: 9 committer: Garth N. Wells <[email protected]> branch nick: fenics-doc timestamp: Tue 2010-04-27 12:12:29 +0100 message: Add some source code. Looks nice. modified: source/demos/common/pde/poisson.txt source/demos/cpp/pde/cpp_poisson.rst-- lp:fenics-doc https://code.launchpad.net/~fenics-core/fenics-doc/main You are subscribed to branch lp:fenics-doc. To unsubscribe from this branch go to https://code.launchpad.net/~fenics-core/fenics-doc/main/+edit-subscription=== modified file 'source/demos/common/pde/poisson.txt' --- source/demos/common/pde/poisson.txt 2010-04-27 10:34:48 +0000 +++ source/demos/common/pde/poisson.txt 2010-04-27 11:12:29 +0000 @@ -1,7 +1,9 @@ Explain what the Poisson demo does and how. Link to download code. -Strong: +The Poisson equation is the cannonical elliptic partial differential equation. +For a domain :math:`\Omega \in \mathbb{R}^{n}`, the Poisson equation with +particular boundary conditions reads: .. math:: - \nabla^{2} u &= f \quad {\rm in} \ \Omega \\ @@ -9,10 +11,21 @@ \nabla u \cdot \boldsymbol{n} &= h \quad {\rm on} \ \Gamma_{N} \\ -Variational: +Find :math:`u \in V` such that + +.. math:: + a(u, v) = L(v) \quad \forall v \in V, + +where .. math:: a(u, v) &= \int_{\Omega} \nabla u \cdot \nabla v \, d\Omega \\ L(v) &= \int_{\Omega} f v \, d\Omega + \int_{\Gamma_{N}} h v \, d\Omega +The expression :math:`a(u, v)` is the bilinear form and :math:`L(v)` +is the linear form. + +In the demo :math:`f = 10\exp(-((x - 0.5)^2 + (y - 0.5)^2) / 0.02)` +and :math:`h = -\sin(5x)`. + === modified file 'source/demos/cpp/pde/cpp_poisson.rst' --- source/demos/cpp/pde/cpp_poisson.rst 2010-04-27 10:34:48 +0000 +++ source/demos/cpp/pde/cpp_poisson.rst 2010-04-27 11:12:29 +0000 @@ -9,3 +9,65 @@ .. include:: ../../common/pde/poisson.txt This text is C++ specific + +Some UFL code in ``Poisson.h`` + +.. code-block:: python + + element = FiniteElement("Lagrange", triangle, 1) + + v = TestFunction(element) + u = TrialFunction(element) + f = Coefficient(element) + g = Coefficient(element) + + a = inner(grad(v), grad(u))*dx + L = v*f*dx + v*h*ds + + +Some C++ + +.. code-block:: c++ + + #include <dolfin.h> + #include "Poisson.h" + + using namespace dolfin; + +Some more C++ + +.. code-block:: c++ + + // Source term (right-hand side) + class Source : public Expression + { + void eval(Array<double>& values, const Array<double>& x) const + { + double dx = x[0] - 0.5; + double dy = x[1] - 0.5; + values[0] = 10*exp(-(dx*dx + dy*dy) / 0.02); + } + }; + + // Boundary flux (Neumann boundary condition) + class Flux : public Expression + { + void eval(Array<double>& values, const Array<double>& x) const + { + values[0] = -sin(5*x[0]); + } + }; + +Yet more C++ + +.. code-block:: c++ + + // Sub domain for Dirichlet boundary condition + class DirichletBoundary : public SubDomain + { + bool inside(const Array<double>& x, bool on_boundary) const + { + return x[0] < DOLFIN_EPS or x[0] > 1.0 - DOLFIN_EPS; + } + }; +
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