A weighted residual formulation for the CHIEF method in acoustics

In this article, the combined Helmholtz integral equation formulation (CHIEF) proposed by Schenck is greatly improved so that it will alleviate the annoying nodal surface problem. The constraint provided by each CHIEF equation and its first-order derivatives is enforced in a weighted residual sense over a small interior region rather than only at a single point. Consequently, “CHIEF blocks” rather than CHIEF points are used in the numerical implementation. Although the corresponding interior problem may have nodal surfaces at characteristic frequencies, it has no such things as “nodal blocks.” Therefore, the “CHIEF-block” (CHIEF-B) method is expected to work even if all of the CHIEF blocks fall on the intersection of several nodal surfaces. This new formulation is implemented in an isoparametric element environment. Numerical examples in spherical radiation and scattering at intermediate frequencies are given to test the new formulation.