Quadrature Over a Pyramid or Cube of Integrands with a Singularity at a Vertex

Previous article Next article Quadrature Over a Pyramid or Cube of Integrands with a Singularity at a VertexMichael G. DuffyMichael G. Duffyhttps://doi.org/10.1137/0719090PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAboutAbstractA simple transformation is introduced which facilitates the evaluation of integrals over certain square based pyramids or cubes in cases where the integrand has a singularity at a vertex.1 J. N. Lyness, An error functional expansion for N-dimensional quadrature with an integrand function singular at a point, Math. Comp., 30 (1976), 1–23 53:11976 0343.65007 CrossrefISIGoogle Scholar2 J. N. Lyness, Applications of extrapolation techniques to multidimensional quadrature of some integrand functions with a singularity, J. Computational Phys., 20 (1976), 346–364 10.1016/0021-9991(76)90087-5 52:15972 0336.65015 CrossrefISIGoogle Scholar Previous article Next article FiguresRelatedReferencesCited ByDetails Static and dynamic analysis of plane elasticity using complex Fourier manifold method based on numerical improvement of Gauss–Legendre quadrature techniquesEngineering Analysis with Boundary Elements, Vol. 143 | 1 Oct 2022 Cross Ref Arbitrarily high-order trapezoidal rules for functions with fractional singularities in two dimensionsApplied Mathematics and Computation, Vol. 429 | 1 Sep 2022 Cross Ref A computational framework for well production simulation: Coupling steady state Darcy flow and channel flow by SGBEM–FEMComputer Methods in Applied Mechanics and Engineering, Vol. 399 | 1 Sep 2022 Cross Ref A Wavelet-Based Approach for the Simulation and Optimal Control of NonLocal Operator EquationsStephan Dahlke, Helmut Harbrecht, and Thomas M. 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