TIES675 COM1: Fast Boundary Element Methods (3–4 cr)
How to solve field problems numerically on the computer? The Boundary Element Method (BEM) has developed into an important alternative to domain-oriented approaches (like Finite Elements),ever since fast implementations are available. The BEM reduces the dimensionality of the problem and can easily take into account unbounded domains.
Starting from the representation formulas of Kirchhoff and Stratton-Chu boundary integral equations are derived. Next, their discretization by collocation and Galerkin methods is discussed.
The resulting fully populated matrices have to be compressed for practical applications, by Fast Multipole or Adaptive Cross Approximation methods.
Industrial examples for application of the BEM are considered, for instance acoustic and electromagnetic scattering problems,and thermal analysis.
Programming homework will be assigned, to deepen the students’ understanding of the contents.