Elements of MATLAB and Simulink - Lecture 7 - PERCRO

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Boundary ProblemThe Dirichlet problem is the general problem of finding a function uwhich solves a PDE for which the values are known on theboundary of a given region• Given a PDE over R N• Given a function f that has values over a boundary region of Ω• Find a function u solving PDE that is differentiable twice in theinterior and once on the boundary and assumes the values of f onthe boundaryThe Neumann problem involves a boundary condition relative to aderivative of the target functionExpressed as u_n
Heat Equation 2DHeat Equation 2D: diffusion of a quantity along the space and timeu_t = u_xx + u_yyThe general formulation isu_t = div grad uExampleMetal block with a rectangular crack. The left side is heated at 100degrees, the right side heat is flowing to air at constant rate. Theothers sides are insulatedu = 100 (Dirichlet condition)u_n = -10 on the right side (Neumann condition)u_n = 0 on the other boundaries (Neumann condition)
Page 1 and 2: Elements ofMatlab and SimulinkLectu
Page 3 and 4: Introducing PDEOrdinary Differentia
Page 5: Heat EquationHeat (or diffusion) eq
Page 9 and 10: Wave EquationLinear Waveu_tt = c^2
Page 11 and 12: Basics of FEMHow we can solve PDE n
Page 13 and 14: FEM 2DAirSiliconGeneralized approac
Page 15 and 16: MATLAB Partial Differential Equatio
Page 17 and 18: Geometry as Mesh• The FEM resolut
Page 19 and 20: Resolution of PDE• Solver functio
Page 21 and 22: PDE for Simulink• Simulink Solves
Page 23 and 24: Matrix Form of the FEMBasic Matrix
Page 25 and 26: Thermal Regulation PDE• Geometry
Page 27: References• Books• An Introduct

Elements of MATLAB and Simulink - Lecture 7 - PERCRO

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