Silent Boundary Methods for Transient Wave Analysis

Citation

Cohen, Martin (1981) Silent Boundary Methods for Transient Wave Analysis. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/xrgh-ag46. https://resolver.caltech.edu/CaltechThesis:08132021-221014507

Abstract

This thesis sets forth a dynamic model, designed to absorb infinitely radiating waves in a finite, computational grid. The analysis is primarily directed toward the problem of soil-structure interaction, where energy propagates from a region near a structure, outward toward the boundaries.

The proposed method, called the extended-paraxial boundary, is derived from one-directional, wave theories that have been propounded by other authors. In this thesis, the theory is presented from a more general viewpoint and is studied for its stability properties. This work suggests some modifications to the method as it was first presented. Innovations are also put forward in the boundary's implementation for finite element calculations. These alterations render the boundary an effective wave absorber.

The extended-paraxial boundary is then compared, both analytically and numerically, with two other transmitting (or silent) boundaries currently available -- the standard-viscous and unified-viscous methods. The analytical results indicate that the extended-paraxial boundary enjoys a distinct advantage in cancelling wave reflections; actual numerical tests revealed a small superiority over the viscous approaches.

Various issues are also discussed as they relate to the silent boundaries. These include Rayleigh waves, spherically symmetric and axially symmetric waves, nonlinear waves, anisotropic media, and numerical stability.

Thesis Files