The BEM for solving the nonhomogeneous Helmholtz equation with variable coefficients
The authors consider the nonhomogeneous equation \(\nabla^2 \cdot u + Eu = F\), where \(E\) is not a constant. They suggest that it should be solved by using an iterative process \(\nabla^2 u^{(n)} = F - Eu^{(n - 1)}\) and then applying the boundary element method (BEM) in this iterative process. This method it is thought involves less computation than using the coupled method of BEM. They illustrate the method by comparing the results on the boundary obtained for a 20-node solution with the exact results there for the equation \[ \nabla^2 u - {2u \over (x + y) t + 2t^2} = - {(x + y) \over 2t} \] with given boundary conditions for a particular rectangular domain and the two values \(e\) and \(\pi\) for \(t\). It is not stated what particular type of boundary elements is used nor is any formula given for the exact solution of the differential equation nor any explanation of how it arises.
scientific article; zbMATH DE number 862652