Abstract
The modified biharmonic equation is encountered in a variety of application areas, including streamfunction formulations of the Navier–Stokes equations. We develop a separation of variables representation for this equation in polar coordinates, for either the interior or exterior of a disk, and derive a new class of special functions which makes the approach stable. We discuss how these functions can be used in conjunction with fast algorithms to accelerate the solution of the modified biharmonic equation or the “bi-Helmholtz” equation in more complex geometries.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 1674-1697 |
| Number of pages | 24 |
| Journal | Journal of Scientific Computing |
| Volume | 76 |
| Issue number | 3 |
| DOIs | |
| State | Published - Sep 1 2018 |
| Externally published | Yes |
All Science Journal Classification (ASJC) codes
- Software
- Theoretical Computer Science
- Numerical Analysis
- General Engineering
- Computational Theory and Mathematics
- Computational Mathematics
- Applied Mathematics
Keywords
- Fast multipole method
- Integral equation
- Modified biharmonic equation
- Separation of variables
- Special functions