The webinars will take place on Zoom and a link to the virtual room will be sent out to all those who registered at the registration page.
Speaker: Andreas Petersson (University of Oslo)
Title: Noise Simulation in Finite Element Methods for SPDE Approximation
Abstract: In this presentation, we give a brief introduction to finite element methods for parabolic stochastic partial differential equations (SPDEs) on general domains, with applications. Our focus is on equations driven by multiplicative space-time Gaussian noise, white in time and possibly correlated in space. This is modeled as a cylindrical Wiener process in a suitable Hilbert space. More often than not, the noise simulation consumes the largest portion of computational resources. With this in mind, we review some common simulation methods, discussing their respective advantages and disadvantages. Then, we introduce a novel and computationally cheap approach that combines circulant embedding with piecewise linear interpolation between spatial domains. This leads to a new error source, which we analyze in the context of a semilinear stochastic reaction-advection-diffusion equation. The presentation concludes with key findings from the analysis: interpolation of noise with Matérn kernels typically does not cause an additional error, there exist kernels where the interpolation error dominates, and generation of noise on a coarser mesh than that of the SPDE discretization does not always result in a loss of accuracy.
This is joint work with Gabriel J. Lord, Radboud University.
This series of webinars addresses all interested people in probability, stochastic analysis, control, risk evaluation, statistics, with a view towards applications, in particular to renewable energy markets and production. This series brings together the major research themes of the projects STORM, SCROLLER, and SPATUS.