A Modified Preconditioned Conjugate Gradient Method for Approximating the Scattering Amplitude

Author

Samson AyoFollow

Date of Award

Summer 8-2021

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 A^Ty=g. Once these two systems are solved, the scattering amplitude, defined by g^Tx=y^Tb 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.

Copyright

Samson Ayo

Recommended Citation

Ayo, Samson, "A Modified Preconditioned Conjugate Gradient Method for Approximating the Scattering Amplitude" (2021). Master's Theses. 850.
https://aquila.usm.edu/masters_theses/850