DOLFIN User Manual - FEniCS Project

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DOLFIN User ManualHoffman, Jansson, Logg, WellsThe right-hand side f of (7.1) is similarly specified by defining a new subclassof Function, which we here will name MyFunction, and overloading theevaluation operator:class MyFunction : public Function{real operator() (const Point& p) const{return p.x*p.z*sin(p.y);}};with the source f(x, y, z) = xz sin(y).7.8 Initial value problemsA time dependent problem has to be discretized in time manually, and theresulting variational form is then discretized in space using FFC similarly toa stationary problem, with the solution at previous time steps provided asdata to the form file.For example, the form file Heat.form for the heat equation discretized intime with the implicit Euler method, takes the form:v = BasisFunction(scalar) # test functionU1 = BasisFunction(scalar) # value at next time stepU0 = Function(scalar) # value at previous time stepf = Function(scalar) # source termk = Constant() # time stepa = v*U1*dx + k*v.dx(i)*U1.dx(i)*dxL = v*U0*dx + v*f*dx50
DOLFIN User ManualHoffman, Jansson, Logg, Wellswhich generates a file Heat.h when compiled with FFC. To initializationsthe corresponding forms we write:real k;Vector x0;Function U0(x0, mesh);// time step// vector containing dofs for u0// solution at previous time stepHeat::BilinearForm a(k);Heat::LinearForm L(U0, f, k);51
Page 1 and 2: DOLFIN User ManualFebruary 24, 2006
Page 3 and 4: ContentsAbout this manual 91 Introd
Page 5 and 6: DOLFIN User ManualHoffman, Jansson,
Page 7: DOLFIN User ManualHoffman, Jansson,
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
Page 65 and 66: Chapter 10The log systemDOLFIN prov
Page 85: Bibliography[1] Cygwin, 2005. http:
Page 88 and 89: v 2 v 0 = (0, 0)DOLFIN User ManualH
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DOLFIN User ManualHoffman, Jansson,
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Appendix CContributing codeIf you h
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Appendix DLicenseDOLFIN is licensed
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