<div class="csl-bib-body">
<div class="csl-entry">Scaglioni, A., An, X., Dick, J., Feischl, M., & Tran, T. (2024, March 21). <i>Sparse grid approximation of nonlinear SPDEs: The Landau–Lifshitz–Gilbert problem</i> [Presentation]. Annaul retreat CRC Wave phenomena, Bad Herrenalb, Germany. http://hdl.handle.net/20.500.12708/196648</div>
</div>
-
dc.identifier.uri
http://hdl.handle.net/20.500.12708/196648
-
dc.description
Presentation of results obtained in the last year in the context of the CRC wave phenomena
-
dc.description.abstract
We show convergence rates for a sparse grid approximation of the distribution of solutions of the stochastic Landau-Lifshitz-Gilbert equation. Beyond being a frequently studied equation in engineering and physics, the stochastic Landau-Lifshitz-Gilbert equation poses many interesting challenges that do not appear simultaneously in previous works on uncertainty quantification: The equation is strongly non-linear, time-dependent, and has a non-convex side constraint. Moreover, the parametrization of the stochastic noise features countably many unbounded parameters and low regularity compared to other elliptic and parabolic problems studied in uncertainty quantification. We use a novel technique to establish uniform holomorphic regularity of the parameter-to-solution map based on a Gronwall-type estimate and the implicit function theorem. This method is very general and based on a set of abstract assumptions. Thus, it can be applied beyond the Landau-Lifshitz-Gilbert equation as well. We demonstrate numerically the feasibility of approximating with sparse grid and show a clear advantage of a multi-level sparse grid scheme.
en
dc.language.iso
en
-
dc.subject
Stochastic and parametric PDEs
en
dc.subject
stochastic Landau-Lifshitz-Gilbert problem
en
dc.subject
Doss-Sussmann transform
en
dc.subject
Lévy-Ciesielski expansion
en
dc.subject
regularity of sample paths solution
en
dc.subject
curse of dimensionality
en
dc.subject
implicit function theorem
en
dc.subject
holomorphy and sparsity of parameter-to-solution map
en
dc.subject
piecewise polynomials
en
dc.subject
sparse high-dimensional approximation
en
dc.subject
sparse grid
en
dc.subject
stochastic collocation
en
dc.subject
dimension independent convergence
en
dc.subject
multilevel sparse grid
en
dc.title
Sparse grid approximation of nonlinear SPDEs: The Landau–Lifshitz–Gilbert problem
