Stochastic Fractional PDEs: Random Field Generation and Topology Optimization - MFEM Workshop 2022

Explore stochastic fractional PDEs and their applications in a 19-minute conference talk from the MFEM Workshop 2022. Dive into the numerical solution of these complex equations using MFEM's WhiteNoiseIntegrator and rational approximation techniques. Discover how to generate Matérn-type Gaussian random fields and apply them to model geometric uncertainties in additive manufacturing processes. Learn about the SPDE method for spatial statistics and its implementation in topology optimization under uncertainty. Gain insights into the power of fractional PDEs in describing complicated systems and the importance of incorporating randomness in various scientific disciplines.

Introduction
Gaussian Random Fields
Overview
Fractional PDEs
Rational Approximation
Serious Expansion
Stochastic PDEs
SPD Method
Results
Recap