Abstract
We present algorithms for computing weakly singular and near-singular integrals arising when solving the 3D Helmholtz equation with curved boundary elements. These are based on the computation of the preimage of the singularity in the reference element's space using Newton's method, singularity subtraction, the continuation approach, and transplanted Gauss quadrature. We demonstrate the accuracy of our method for quadratic basis functions and quadratic triangles with several numerical experiments, including the scattering by two half-spheres.
| Original language | English |
|---|---|
| Pages (from-to) | A3728-A3753 |
| Journal | SIAM Journal on Scientific Computing |
| Volume | 44 |
| Issue number | 6 |
| DOIs | |
| Publication status | Published - 1 Dec 2022 |
Keywords
- Gauss quadrature
- Helmholtz equation
- Taylor series
- boundary element method
- continuation approach
- homogeneous functions
- integral equations
- near-singular integrals
- singular integrals