First-passage time statistics on surfaces of general shape: Surface PDE solvers using Generalized Moving Least Squares (GMLS)

•Computational approaches for First Passage Times (FPTs) and other path-dependent statistics for surfaces of general shape.•Development of high-order surface PDE solvers using meshless methods / Generalized Moving Least Squares (GMLS) approximation.•Methods for general stochastic drift-diffusion dyn...

Ausführliche Beschreibung

Gespeichert in:
Bibliographische Detailangaben
Veröffentlicht in:Journal of computational physics 2022-03, Vol.453, p.110932, Article 110932
Hauptverfasser: Gross, B.J., Kuberry, P., Atzberger, P.J.
Format: Artikel
Sprache:eng
Schlagworte:
Online-Zugang:Volltext
Tags: Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
Beschreibung
Zusammenfassung:•Computational approaches for First Passage Times (FPTs) and other path-dependent statistics for surfaces of general shape.•Development of high-order surface PDE solvers using meshless methods / Generalized Moving Least Squares (GMLS) approximation.•Methods for general stochastic drift-diffusion dynamics on surfaces and associated Backward-Kolmogorov PDEs.•Methods for handling surfaces with general geometry and topology.•Results for FPTs investigating the roles of surface geometry, drift dynamics, and spatially-dependent diffusivity. We develop numerical methods for computing statistics of stochastic processes on surfaces of general shape with drift-diffusion dynamics dXt=a(Xt)dt+b(Xt)dWt. We formulate descriptions of Brownian motion and general drift-diffusion processes on surfaces. We consider statistics of the form u(x)=Ex[∫0τg(Xt)dt]+Ex[f(Xτ)] for a domain Ω and the exit stopping time τ=inft⁡{t>0|Xt∉Ω}, where f,g are general smooth functions. For computing these statistics, we develop high-order Generalized Moving Least Squares (GMLS) solvers for associated surface PDE boundary-value problems based on Backward-Kolmogorov equations. We focus particularly on the mean First Passage Times (FPTs) given by the case f=0,g=1 where u(x)=Ex[τ]. We perform studies for a variety of shapes showing our methods converge with high-order accuracy both in capturing the geometry and the surface PDE solutions. We then perform studies showing how statistics are influenced by the surface geometry, drift dynamics, and spatially dependent diffusivities.
ISSN:0021-9991
1090-2716
DOI:10.1016/j.jcp.2021.110932