T-Spline based analysis for waveform inversion in frequency domain

Abstract

This work focuses on implementation of Isogeometric Analysis (IGA) to solve the Helmholtz equation for acoustic problem in unbounded domain which is the first step for problem of waveform inversion in frequency domain. In this work, T-spline is preferable to Non-Uniform Rational B-spline (NURBS) because of its flexibility which allows local refinement in a specific region as well as modeling complicated curved geometry by only one patch. Those properties of T-spline offer many choices to examine the problem. Because the physical domain is infinite and the computational domain is finite, problem of truncation error appears. In order to deal with it, Perfectly Matched Layer (PML) method is chosen. This work is restricted in two dimensional problems. In addition, the results in some numerical examples from IGA is compared with High Order Finite Element Method (HOFEM) which are provided by Prof. Matthias Baitsch and MSc. Khayal Musayev and validated by analytical solutions. Then, local refinement property of T-spline is examined in details. All of this work have been done on the foundation of Finite Element Software which is written in java by Prof. Matthias Baitsch. MSc. Khayal Musayev contributed his work related to the Perfectly Matched Layer method later.