FEniCS Course - FEniCS Project

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Implementing the variational problemdt = 0.3u0 = project (g, V)u1 = Function (V)u = TrialFunction (V)v = TestFunction (V)f = Constant ( beta - 2 - 2* alpha )a = u*v*dx + dt* inner ( grad (u), grad (v))*dxL = u0*v*dx + dt*f*v*dxbc = DirichletBC (V, g, " on_boundary ")# assemble only once , before time - steppingA = assemble (a)11 / 13

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A closer look at solveFor linear problems, this codesolve (a == L, u, bcs )is equivalent to this# Assembling a bilinear form yields a matrixA = assemble (a)# Assembling a linear form yields a vectorb = assemble (L)# Applying boundary condition info to systemfor bc in bcs :bc. apply (A, b)# Solve Ax = bsolve (A, u. vector () , b)10 / 13

Page 5 and 6: Naive FEniCS code for the heat equa
Page 12 and 13: Implementing the time-stepping loop

FEniCS Course - FEniCS Project

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