A Numerical Study Of The Coefficient Matrix Of The Boundary Element Method Near Characteristic Frequencies

✍ Scribed by P. Juhl

• Publisher: Elsevier Science
• Year: 1994
• Tongue: English
• Weight: 446 KB
• Volume: 175
• Category: Article
• ISSN: 0022-460X
• DOI: 10.1006/jsvi.1994.1309

✦ Synopsis

In this paper the well-known failure in numerical computations of the exterior surface Helmholtz integral equation at certain characteristic frequencies is investigated. The problem of characteristic frequencies is numerically reflected in an ill-conditioning of the coefficient matrix arising from the transformation of the integral equation to a linear set of equations. By means of a rank revealing factorization the rank deficiency of the coefficient matrix is determined, and thereby the necessary number of equations to be added to the original system of equations can be found. One of the most popular methods to overcome this "non-uniqueness" problem is the Combined Helmholtz Integral Equation Formulation (CHIEF) proposed by Schenck [1]. However, CHIEF points placed on or near a nodal surface of the corresponding interior problem do not provide a linearly independent constraint, and the problem of selecting "good" CHIEF points is still a topic of considerable interest. In this paper the CHIEF is used with a rank revealing factorization, and it is shown that the necessary number of "good" CHIEF points can be predicted; furthermore, a method of determining whether a CHIEF point is "good" is presented. The new approach has been tested on an axisymmetric BEM formulation with one or several CHIEF points.