Date of Award

Summer 8-1-2021

Degree Type

Masters Thesis

Degree Name

Master of Science (MS)

School

Mathematics and Natural Sciences

Committee Chair

James Lambers

Committee Chair School

Mathematics and Natural Sciences

Committee Member 2

C.S. Chen

Committee Member 2 School

Mathematics and Natural Sciences

Committee Member 3

Huiqing Zhu

Committee Member 3 School

Mathematics and Natural Sciences

Abstract

In this thesis, we look at an iterative method for approximating the scattering amplitude that involves solving two linear systems: a forward system Ax=b and an adjoint system ATy=g. Once these two systems are solved, the scattering amplitude, defined by gTx=yTb is easily obtained.

We derive a conjugate gradient-like iteration for a nonsymmetric saddle point matrix that is constructed to have a real positive spectrum. We investigate the use of Schur Complement preconditioners with block-diagonal factorization to speed up the convergence of our method and compare the results to our NspcG method without preconditioning.

Available for download on Wednesday, June 22, 2022

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