A Pollution Effect in the Boundary Element Method for Acoustic Problems

Abstract

The pollution effect is a well-known and well-investigated phenomenon of the finite element method for wave problems in general and for acoustic problems in particular. It is understood as the problem that a local mesh refinement cannot compensate the numerical error which is generated and accumulated in other regions of the model. This is the case for the phase error of the finite element method which leads to dispersion resulting in very large numerical errors for domains with many waves in them and is of particular importance for low order elements. Former investigations have shown that a pollution effect resulting from dispersion is unlikely for the boundary element method. However, numerical damping in the boundary element method can account for a pollution effect. A further investigation of numerical damping reveals that it has similar consequences as the phase error of the finite element method. One of these consequences is that the number of waves within the domain may be controlling the discretization error in addition to the size and the order of the boundary elements. This will be demonstrated in computational examples discussing traveling waves in rectangular ducts. Different lengths, element types and mesh sizes are tested for the boundary element collocation method. In addition to the amplitude error which is due to numerical damping, a rather small phase error is observed. This may indicate numerical dispersion.