Fast Numerical Methods for Stochastic Partial Differential Equations
Abstract
Uncertainty quantification has been an active research area in the past 15 years because of its potential of significant applications ranging from signal processing to aircraft wing designs. It is well understood that effective numerical methods for stochastic partial differential equations (SPDES) are essential for uncertainty quantification. In the last decade much progress has been made in the construction of numerical algorithms to efficiently solve SPDES with random coefficients and white noise perturbations. However, high dimensionality and low regularity are still the bottleneck in solving real world applicable SPDES with efficient numerical methods. This research is intended to address the numerical analysis as well as algorithm aspects of SPDES. Three major contributions are made in this project: i) Construction and convergence analysis of Quasi Monte Carlo based Particle Swarm Optimization (PSO) method; ii) Efficient adaptive domain sparse grid method for SPDES; iii) High order methods of SPDES via systems of forward backward stochastic differential equations. Our work contains algorithm constructions, rigorous error analysis, and extensive numerical experiments to demonstrate our algorithm efficiency and validity of our theoretical analysis.
Document Details
- Document Type
- Technical Report
- Publication Date
- Apr 15, 2016
- Accession Number
- AD1008313
Entities
People
- Hongmei Chi
- Yanzhao Cao
Organizations
- Florida A&M University