Rapid Approximation of Bilinear Forms Involving Matrix Functions Through Asymptotic Analysis of Gaussian Node Placement

<p>Technological advancements have allowed computing power to generate high resolution model s. As a result, greater stiffness has been introduced into systems of ordinary differential equations (ODEs) that arise from spatial discreti zation of partial differential equations (PDEs). The components of the solutions to these systems are coupled and changing at widely varying rates, which present problems for time-stepping methods. Krylov Subspace Spectral methods, developed by Dr. James Lambers, bridge the gap between explicit and implicit methods for stiff problems by computing each Fouier coefficient from an individualized approximation of the solution operator. KSS methods demonstrate a high order of accuracy, but their efficiency needs to be improved. We will carry out an asymptotic study to determine how these approximations behave at high frequencies to develop a formula to reduce the computation of each node while still achieving a high level of accuracy. Our numerical results will reveal that our method does prove to increase the efficiency as well as the accuracy of KSS methods.</p>

Name thesis:degree_name

Master of Science (MS)

Level thesis:degree_level

Masters Thesis

Discipline thesis:degree_discipline

Mathematics

Year dc:date.available

2012

Author dc:creator

• Palchak, Elisabeth Marie

Contributors dc:contributor

• James Lambers
• Joseph Kalibal
• Haiyan Tian

• Mathematics
• Physical Sciences and Mathematics

Repository record dc:identifier

https://aquila.usm.edu/masters_theses/510

OAI identifier oai:identifier

oai:aquila.usm.edu:masters_theses-1587