The boundary-residual method for three-dimensional homogeneous field problems with boundaries of arbitrary geometry

Cavity resonances by the boundary residual method versus experiment

“…The boundary residual method has already been discussed (Bunch 1990, Bunch and Grow 1989, 1990, Davies 1973. For a cavity with a perfectly conducting boundary, this method forces the tangential electric fields to zero:…”

“…A is the vector of unknown coefficients in (I). A minimum boundary residual, and thus the problem solution, is given by the minimum eigenvalue of the matrix product MtM (Bunch 1990, Bunch andGrow 1989). Bunch and Grow (1990) have shown a method to solve a direct form of the matrix equation (4):…”

“…Thai (1979) has measured the cavity resonances of several different geometries. A scalar wave expansion complete to represent the fields has been given by Bunch and Grow (1989) …”

Numerical aspects of the boundary residual method

“…This set of equations is called 'normal equations', l2 and the matrix product Mt M will be called the 'normal' matrix. Using the matrix defined in equation (2), the elements of equation (5) (6) and (7) become integrals so that…”

High Order Representations for Singular Currents at Corners

“…(For approach 4 will be larger in corner cells than in other cells.) Since the equations are obtained at quadrature nodes and weighted by the square root of quadrature weights, the numerical solution minimizes the integrated square error of the residual on the scatterer surface, as explained by Bunch and Grow [34], [35].…”