Gregory A. Kriegsmann

Bio: Gregory A. Kriegsmann is an academic researcher from University of Nebraska–Lincoln. The author has contributed to research in topics: Bessel function & Spherical shell. The author has an hindex of 3, co-authored 3 publications receiving 54 citations.

The axisymmetric branching behavior of complete spherical shells

Abstract: : The purpose of the paper is to describe the axisymmetric branching behavior of complete spherical shells subjected to either external pressure or a centrally directed (dead) loading. By means of an asymptotic integration technique (based on the smallness of the ratio of the shell thickness to the shell radius) applied directly to a differential equation formulation, the authors are able to continue the solution branches from the immediate neighborhood of the branch points, where the solution has the functional form predicted by the linear buckling theory, to the region where the solution consists of either one or two dimples with the remainder of the shell remaining nearly spherical. The latter deflection states are the ones usually observed in experiments. The authors also deduce a number of results for the branching of solutions from the multiple eigenvalues. Finally, a boundary layer analysis is performed to determine the possible form of large deflection states. (Author)

Numerical solutions of exterior problems with the reduced wave equation

Abstract: A new technique for numerically solving the reduced wave equation on exterior domains is presented. The method is basically a relaxation scheme. It is general enough to handle both inhomogeneous and nonlinear indices of refraction. Although the convergence is slow, the technique is tested on two classical problems: the scattering of a plane wave off a metal cylinder and off a metal sphere. The results are in good qualitative agreement with previously calculated values. In particular, the numerical solutions exhibit the correct diffractive effects at moderate frequencies.

On large axisymmetrical deflection states of spherical shells

Abstract: A boundary layer analysis is carried out to determine the possible form of large axisymmetrical deflection states for thin elastic spherical shells subjected to uniform external pressure. For the case of complete spheres it is shown that the governing equations admit boundary layer solutions corresponding to large deflections provided the pressure is sufficiently small. However, such solutions are found to exist for nonshallow clamped spherical caps for a much wider range of pressure. Numerical results are presented for the latter case.

Radiation boundary conditions for wave-like equations

Abstract: In the numerical computation of hyperbolic equations it is not practical to use infinite domains; instead, the domain is truncated with an artificial boundary. In the present study, a sequence of radiating boundary conditions is constructed for wave-like equations. It is proved that as the artificial boundary is moved to infinity the solution approaches the solution of the infinite domain as O(r exp -m-1/2) for the m-th boundary condition. Numerical experiments with problems in jet acoustics verify the practical nature of the boundary conditions.

Boundary conditions for the numerical solution of elliptic equations in exterior regions

Abstract: Elliptic equations in exterior regions frequently require a boundary condition at infinity to ensure the well-posedness of the problem. Examples of practical applications include the Helmholtz equation and Laplace's equation. Computational procedures based on a direct discretization of the elliptic problem require the replacement of the condition on a finite artificial surface. Direct imposition of the condition at infinity along the finite boundary results in large errors. A sequence of boundary conditions is developed which provides increasingly accurate approximations to the problem in the infinite domain. Estimates of the error due to the finite boundary are obtained for several cases. Computations are presented which demonstrate the increased accuracy that can be obtained by the use of the higher order boundary conditions. The examples are based on a finite element formulation but finite difference methods can also be used.

Theory and application of radiation boundary operators

Abstract: A succinct unified review is provided of the theory of radiation boundary operators. With the recent introduction of the on-surface radiation condition (OSRC) method and the continued growth of finite-difference and finite-element techniques for modeling electromagnetic wave scattering problems, the understanding and use of radiation boundary operators has become increasingly important. Results are presented to illustrate the application of radiation boundary operators in both these areas. Recent OSRC results include analysis of the scattering behavior of both electrically small and large cylinders, a reactively loaded acoustic sphere, and a simple reentrant duct. Radiation boundary operator results include the demonstration of the effectiveness of higher-order operators in truncating finite-difference time-domain grids. >

A new formulation of electromagnetic wave scattering using an on-surface radiation boundary condition approach

Abstract: A new formulation of electromagnetic wave scattering by convex, two-dimensional conducting bodies is reported. This formulation, called the on-surface radiation condition (OSRC) approach, is based upon an expansion of the radiation condition applied directly on the surface of a scatterer. Past approaches involved applying a radiation condition at some distance from the scatterer in order to achieve a nearly reflection-free truncation of a finite-difference time-domain lattice. However, it is now shown that application of a suitable radiation condition directly on the surface of a convex conducting scatterer can lead to substantial simplification of the frequency-domain integral equation for the scattered field, which is reduced to just a line integral. For the transverse magnetic (TM) case, the integrand is known explicitly. For the transverse electric (TE) case, the integrand can be easily constructed by solving an ordinary differential equation around the scatterer surface contour. Examples are provided which show that OSRC yields computed near and far fields which approach the exact results for canonical shapes such as the circular cylinder, square cylinder, and strip. Electrical sizes for the examples are ka = 5 and ka = 10 . The new OSRC formulation of scattering may present a useful alternative to present integral equation and uniform high-frequency approaches for convex cylinders larger than ka = 1 . Structures with edges or corners can also be analyzed, although more work is needed to incorporate the physics of singular currents at these discontinuities. Convex dielectric structures can also be treated using OSRC. These will be the subject of a forthcoming paper.

Solving the Helmholtz Equation for Exterior Problems with Variable Index of Refraction

Abstract: A new technique for numerically solving the reduced wave equation on exterior domains is presented. The method is basically a relaxation scheme which exploits the limiting amplitude principle. A modified boundary condition at “infinity” is also given. The technique is tested on several model problems: the scattering of a plane wave off a metal cylinder, a metal strip, a Helmholtz resonator, an inhomogeneous cylinder (lens), and a nonlinear plasma column. The results are in good qualitative agreement with previously calculated values. In particular, the numerical solutions exhibit the correct refractive and diffractive effects at moderate frequencies.