Solution of the Fokker-Planck Equation by Sequentially Optimized Meshfree Approximation

This thesis presents a technique to solve the Fokker-Planck equation by applica- tion of the Sequentially Optimized Meshfree Approximation (SOMA) method. It is well known that numerical solution of the Fokker-Planck equation is made di cult by the challenges of positivity enforcement, in nite domain, and high dimensionality. Through the use of optimization, radial basis functions, and its mesh-free architecture, respectively, the SOMA method attempts to address these challenges and sidestep the exponential growth of dimensionality, which hinders traditional numerical methods. Results are presented for one, two, and four-dimensional Fokker-Planck equations. This work will show that SOMA allows for enforcement of a positivity condition that removes the need for log-transforms, produces a solution domain that does not re- quire arti cial boundary condition enforcement, and provides the capability of solving higher dimensional forms of the Fokker-Planck equation.

Name thesis:degree_name

Master of Science

Level thesis:degree_level

Masters

Discipline thesis:degree_discipline

Engineering

Grantor

Rice University

Year dc:date.issued

2014

Author dc:creator

• Mokhtarzadeh, Arya

Advisor dc:contributor.advisor

• Meade, Andrew J., Jr.

Committee members dc:contributor.committeemember

• Dick, Andrew J.
• Nagarajaiah, Satish

• Fokker-Planck equation
• FPE
• Sequentially optimized meshfree approximation
• SOMA
• Oscillator
• Curse of dimensionality
• Positivity
• Radial basis functions
• Series expansion
• Optimization

Statement dc:rights

• Copyright is held by the author, unless otherwise indicated. Permission to reuse, publish, or reproduce the work beyond the bounds of fair use or other exemptions to copyright law must be obtained from the copyright holder.

Language dc:language.iso

eng

Handle dc:identifier.uri

https://hdl.handle.net/1911/77226

OAI identifier oai:identifier

oai:repository.rice.edu:1911/77226