Galerkin boundary integral formulation for the 3D Helmholtz equation
Event details
| Date | 29.08.2011 |
| Hour | 11:00 |
| Speaker | L. J. Gray, Bergen Software Services International, Norway |
| Location | |
| Category | Conferences - Seminars |
A Galerkin boundary integral analysis for the three-dimensional Helmholtz equation will be presented. The target application involves acoustic scattering by an open (crack) surface and thus both the standard (singular) and normal derivative (hypersingular) boundary integral equations are considered. The key task is the evaluation of the Galerkin singular integrals and the boundary limit technique has been employed. The advantages of this direct approach are that the procedures are the same for all kernel functions (the Green's function and its first or second order derivatives) and as a reformulation of the integrals is not needed the methods are generally applicable. Moreover in the limit analysis the divergent terms in the hypersingular integrals are explicitly identified leading to the numerical evaluation of finite integrals. The analytic integrations
that are required for the limit evaluation are carried out by employing a Taylor series expansion for the exponential factor in the Helmholtz fundamental solutions. All of the calculus work can be automated using symbolic manipulation codes.
Practical information
- General public
- Free
Contact
- Michael Mattes