Lecture notes

Boundary Element Methods

Lothar Gaul and Matthias Fischer

• Introduction
• BE Formulation of Laplace's Equation
  • Weak formulation of the differential equation
  • Transformation on the boundary
  • Fundamental solution as weighting function
  • Boundary integral equation of the 2-D problem
    • Preparative example for the limit process
    • Calculation of the limit
    • Discretisation of the boundary
  • The collocation method
  • Example: Laplace problem of heat transfer
    • Numerical solution with the collocation method
    • Analytical solution
  • Computation of solution in the domain
    • Calculation of Dirichlet variable in the domain
    • Calculation of flux in the domain
  
  
• BE formulation of Poisson's equation
  • Calculation of domain integrals by integration of cells
  • Calculation of domain integrals by transformation into a boundary integral
  • Calculation of the unknown boundary variables
  
  
• Orthotropic constitutive behaviour in the domain
• Indirect calculation of diagonal elements in
• Concentrated source terms
• Substructure technique
• Example: Orthotropic heat transfer and subregion coupling
• Fundamental solutions
  • Laplace equation
    • Fundamental solution of the 2D Laplace equation
    • Fundamental solution of the 3D Laplace equation
  • Helmholtz equations
    • Fundamental solution of the 3D Helmholtz equation
  
  
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