Douglas B. Meade

Comparison of local radiation boundary conditions for the scalar Helmholtz equation with general boundary shapes

The relative accuracy of several local radiation boundary conditions based on the second-order Bayliss-Turkel (1980) condition are evaluated. These boundary conditions permit the approximate solution of the scalar Helmholtz equation in an infinite domain using traditional finite element and finite difference techniques. Unlike the standard Bayliss-Turkel condition, the generalizations considered here are applicable to noncircular solution domains. The accuracy of these conditions are investigated for elliptical and linear/circular boundaries. >

Comparison of Two-Dimensional Conformal Local Adiation Boundary Conditions

ABSTRACT Numerical solutions for openndash;region electromagnetic problems based on differential equations require some means of truncating the computational domain. A number of local Radiation Boundary Conditions (RBCs) for general boundary shapes have been proposed during the past decade. Many are generalizations of the Baylissndash;Turkel RBC for circular truncation boundaries. Tbis paper reviews several twondash;dimensional RBCs for general truncation boundaries. The RBCs are evaluated on the basis of their performance on two separate numerical tests: the annihilation of terms in the Hankel series and the comparison of nearndash;field and radar cross sections for finite element solutions to scattering problems. These tests suggest that the simpler RBCs can be very competitive with RBCs based on more sophisticated derivations.

Analytic evaluation of the accuracy of several conformable local absorbing boundary conditions

A. Bayliss et al. (1982) (BT) have proposed an arbitrary order approximation based upon the Wilcox (1956) spherical wave function far-field expansion, for the case of a circular or spherical boundary with the source located at the center. In the present work, the BT-type representation is generalized to the case of an arbitrary convex boundary, with the curvature explicitly incorporated. Several possible implementations are compared.<<ETX>>

Applications and performance of a local conformal radiation boundary condition

The validity of the second order Bayliss-Turkel (BT) radiation boundary condition (RBC) representation is presented in terms of errors as a function of the order of a wavefunction representation and distance. Results for an aperture in a finite plane, which could be viewed as a wavelength scale optical lithographic mask, are given for the case of a conformal radiation boundary.<<ETX>>

Irreducibility testing of lacunary 0,1-polynomials

A reciprocal polynomial g(x) ∈ Z[x] is such that g(0) ≠ 0 and if g(α) = 0 then g(1/α) = 0. The non-reciprocal part of a monic polynomial f(x) ∈ Z[x] is f(x) divided by the product of its irreducible monic reciprocal factors (to their multiplicity). This paper presents an algorithm for testing the irreducibility of the non-reciprocal part of a 0,1-polynomial (a polynomial having each coefficient either 0 or 1). The algorithm runs in time O(2r r logr logn) where r is the number of non-zero terms of the input polynomial and n is its degree. Thus, the algorithm efficiently handles lacunary (or sparse) 0,1-polynomials.