A Modified Preconditioned Conjugate Gradient Method for Approximating the Scattering Amplitude

<p>In this thesis, we look at an iterative method for approximating the scattering amplitude that involves solving two linear systems: a forward system A<strong>x</strong>=<strong>b</strong> and an adjoint system A^T<strong>y</strong>=<strong>g</strong>. Once these two systems are solved, the scattering amplitude, defined by <strong>g</strong>^T<strong>x</strong>=<strong>y</strong>^T<strong>b</strong> is easily obtained.</p> <p>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.</p>

Name thesis:degree_name

Master of Science (MS)

Level thesis:degree_level

Masters Thesis

Year dc:date.available

2021

Author dc:creator

• Ayo, Samson

Contributors dc:contributor

• James Lambers
• C.S. Chen
• Huiqing Zhu

• linear systems
• adjoint systems
• nonsymmetric saddle point matrix
• conjugate gradient method
• scattering amplitude
• preconditioning
• Numerical Analysis and Computation

Repository record dc:identifier

https://aquila.usm.edu/masters_theses/850

OAI identifier oai:identifier

oai:aquila.usm.edu:masters_theses-1911