Geometrically Graded h-p Quadrature Applied to the Complex Boundary Integral Equation Method for the Dirichlet Problem with Corner Singularities

摘要: Boundary integral methods for the solution of boundary value PDEs are an alternative to `interior' methods, such as finite difference and element methods. They attractive on domains with corners, particularly when has singularities at these corners. In cases, interior can become excessively expensive, they require a finely discretised 2D mesh in vicinity whilst typically only one dimension, that arc length. Consider Dirichlet problem. Traditional applied problems corner involve (real) equation kernel containing logarithmic singularity. This is both tedious code computationally inefficient. The CBIEM different it involves complex smooth kernel. approximated using collocation technique, then discretisation Cauchy's formula, combined singularity subtraction. A high order quadrature rule required equation. Typical square root type, `geometrically graded h-p' composite used. yields efficient, equation, thence Implementation experimental results \textsc{matlab} presented.