Analytical Integrations Of The Linearly Interpolated Triangular IBEM Element With The Aid Of The Matlab Symbolic Math Toolbox
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This paper deals with the analytical integration over the linearly interpolated triangular boundary element involved in an indirect boundary element method (IBEM) for solving three dimensional potential problems. The analytical solutions of all the IBEM integrals are derived using the Matlab Symbolic Math Toolbox, with most of the deriving works carried out by computer, and accompanied by a few crucial manual rectifications and integrating techniques. Compared with the presently published kindred analytical solutions, the computer-produced and human-rectified ones take much less tedious manual work and have their own advantages in implementation, such as convenience for programming, and no need to trace the relevant literature for detailed expressions, etc. A calculation test is also carried out to justify the analytical solutions. Keywords: indirect boundary element method, triangular element, analytical integration, Matlab Symbolic Math Toolbox.
indirect boundary element method, triangular element, analytical integration, Matlab Symbolic Math Toolbox