The way which is leading toward bem
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The document outlines the 7 stages of the boundary element method (BEM) for solving boundary value problems: 1) Find the fundamental solution of the governing equation, 2) Derive a formula converting domain integrals to boundary integrals, 3) Obtain the boundary integral equation (BIE) for a domain point, 4) Let the domain point approach the boundary to obtain the BIE for a boundary point, 5) Discretize the BIEs for boundary points into a matrix equation, 6) Solve the matrix equation using prescribed boundary conditions, 7) Solve for domain points using the BIE for a domain point.
The way which is leading toward bem
- 1. The Way which is Leading toward BEM To gaina feeling of transforming adifferential formulationtoits corresponding boundary integral formulation, andtohave a rough knowledge of how the boundary element methodworks. Sevenstages are to be identifiedinworking out the example. Sevenstages are tobe identifiedinworking out the example of problem. Stage 1:Find the fundamental solutionof the governing equation. Stage 2:Derive a formulaof two fieldvariables whichconvertsdomain integrals into boundary integrals. Stage 3:Obtainthe BIE for a domain point. Stage 4:Let x approach to the boundary and obtain the BIE for a boundary point. Stage 5:Choose a finite number of boundary points discritizethe BIEs for the boundary points, and put the discreditedBIE's inmatrix form. Stage 6:With the aid of the prescribedboundary conditions solve the matrix equation. Stage 7: Solve for the domain points by using the BIE for a domain point. A boundary value problemis a problem, givensome data on the boundary B, to solve for the rest of informationonthe boundary B and in the domain D.
- 4. Differential equation and Boundary Conditions
- 5. Step by Step Solution Using BEM/BIE