Elements of MATLAB and Simulink - Lecture 7 - PERCRO

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Laplace EquationLaplace Equationu_xx + u_yy = 0Poisson Equationu_xx + u_yy = g(x,y,z)Helmholt’s Equationu_xx + u_yy + f(x,y) u = g(x,y,z)Require boundary conditions for resolution
Basics <strong>of</strong> FEMHow we can solve PDE numerically when no analytical solution isavailable?The Finite Element Method is the most common solution1. Decompose the Domain in subspaces2. Approximate the Function with piecewise linear function definedinside each subspace3. Find the numerical solution for every subspace given theconditionsFDM is the Finite Difference Method is possible but it works betterwith rectangular domains
Page 1 and 2: Elements ofMatlab and SimulinkLectu
Page 3 and 4: Introducing PDEOrdinary Differentia
Page 5 and 6: Heat EquationHeat (or diffusion) eq
Page 7 and 8: Heat Equation 2DHeat Equation 2D: d
Page 9: Wave EquationLinear Waveu_tt = c^2
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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