A finite-element capacitance matrix method for exterior Helmholtz problems (Q1358124)

The paper proposes an efficient finite element method to solve exterior Helmholtz problems. Firstly, by introducing an exact boundary condition on a circular artificial boundary, the problem is reformulated as an equivalent one on a bounded domain and its mathematical properties are carefully studied. Then, a finite-dimensional version of the variational problem is considered. The author extends to this problem class an iterative finite element capacitance matrix method and obtains in this way a fast solver for which the convergence rate of the iteration is mesh independent; finally some numerical experiments validate the efficiency of the method. A very interesting paper, nicely written.