DOLFIN User Manual - FEniCS Project

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DOLFIN User ManualHoffman, Jansson, Logg, WellsNext, we initialize the pair of bilinear and linear forms that we have previouslycompiled with FFC:Poisson::BilinearForm a;Poisson::LinearForm L(f);We may now define a PDE from the pair of forms, the mesh and the boundaryconditions:PDE pde(a, L, mesh, bc);To solve the PDE, we now just need to call the solve function as follows:Function U = pde.solve();Finally, we export the solution u to a file for visualization. Here, we chooseto save the solution in VTK format for visualization in ParaView or MayaVi,which we do by specifying a file name with extension .pvd:File file(‘‘poisson.pvd’’);file
DOLFIN User ManualHoffman, Jansson, Logg, Wellsclass : public Function{real eval(const Point& p, unsigned int i){return p.x*sin(p.y);}} f;// Boundary conditionclass : public BoundaryCondition{void eval(BoundaryValue& value, const Point& p, unsigned int i){if ( std::abs(p.x - 1.0) < DOLFIN_EPS )value = 0.0;}} bc;// Set up problemUnitSquare mesh(16, 16);Poisson::BilinearForm a;Poisson::LinearForm L(f);PDE pde(a, L, mesh, bc);// Compute solutionFunction U = pde.solve();// Save solution to fileFile file("poisson.pvd");file
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Page 3 and 4: ContentsAbout this manual 91 Introd
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Page 25 and 26: Chapter 3Linear algebra◮ Develope
Page 29 and 30: Chapter 4The mesh◮ Developer’s
Page 33 and 34: Chapter 5Functions◮ Developer’s
Page 43: Chapter 6Ordinary differential equa
Page 53 and 54: Chapter 8Nonlinear solver◮ Develo
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Page 65 and 66: Chapter 10The log systemDOLFIN prov
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Bibliography[1] Cygwin, 2005. http:
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v 2 v 0 = (0, 0)DOLFIN User ManualH
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Appendix CContributing codeIf you h
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Appendix DLicenseDOLFIN is licensed
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