Professor Eckart Schnack visited Ashurst Lodge recently to give a Seminar on “FEM-BEM coupling using Neumann series for high gradient problems”. He is Head of the Institute of Solid Mechanics at the University of Karlsruhe and Adjunct Professor at WIT.
During his lecture, he explained how the domain of interest can be split into a FEM and BEM region. He applied hybrid boundary element to combine with FEM using discontinuous elements of the type he called Mortar elements. These are boundary element meshes which are independent of FEM discretisation.
The numerical problems related to the domain discretisation were studied in detail using :
- Collocation Method
- Galerkin Methods
- Iterative Solution using Neumann series
While the first two approaches had some problems, including in the case of Galerkin, the need to compute multiple integrals, the new technique using Neumann’s series proposed by Eckart gives accurate and convergent results.
In these problems, one can use coarse finite element meshes while the BEM region can be discretised after using discontinuous elements.
Neumann’s series allows the satisfaction of continuity at the corner nodes which is an added advantage as well as the incorporation of rigid boundary motions. The process is iterative for the points in the interface between the finite and boundary element regions.
Eckart presented some interesting applications for cases of stress concentration problems.
He concluded by pointing out that solving linear systems is not required when using Neumann’s series. The method presents good stability and rapid convergence. It can also easily handle discontinuities.
The talk was followed by a lively discussion, in part due to the many questions of some of the researchers at WIT who are working on the combination of BEM and FEM.
Wessex Institute