A Time Domain Formulation of Inverse Source Problems Using the Transmission-Line Matrix Method

Abstract

<p>p.p1 {margin: 0.0px 0.0px 0.0px 0.0px; font: 11.5px Times; color: #2d2d2d} p.p2 {margin: 0.0px 0.0px 0.0px 0.0px; font: 11.5px Times; color: #4d4d4d} p.p3 {margin: 0.0px 0.0px 0.0px 0.0px; font: 11.5px Times; color: #626262} span.s1 {color: #4d4d4d} span.s2 {color: #2d2d2d} span.s3 {color: #141414} span.s4 {color: #aaaaaa} span.s5 {color: #626262} span.s6 {color: #797979} span.s7 {font: 11.5px Helvetica}</p> <p>The inverse source problem of electromagnetics for homogeneous background medium</p> <p>is investigated numerically using the Transmission-Line Matrix (TLM) method. By transforming all sources and fields into their equivalent link impulses inside a TLM computational domain, a discrete linear inversion formulation is developed. Our approach solves for the unknown source distribution inside a given source region using the near-field measurements on its boundary. Unlike the conventional frequency domain treatments, both our source solution and the field measurements are obtained in the time domain. The non-uniqueness of the inverse source problem is addressed by addit ionally imposing a smoothness prior constraint. First-order time and spatial derivatives of the source distribut ion are minimized. The source reconstruction algorithm introduced in this thesis is illustrated through various two-dimensional numerical examples. It is also shown that our algorithm is robust against the noise from the boundary field measurements.</p>