Ian H. Sloan

Multilevel lattice-based kernel approximation for elliptic PDEs with random coefficients

Abstract This paper introduces a multilevel kernel-based approximation method to estimate efficiently solutions to elliptic partial differential equations (PDEs) with periodic random coefficients. Building upon the work of Kaarnioja, Kazashi, Kuo, Nobile, Sloan (Numerische Mathem...

Quasi-Monte Carlo Methods for Uncertainty Quantification of Tumor Growth Modeled by a Parametric Semilinear Parabolic Reaction-diffusion Equation

Abstract. We study the application of a quasi-Monte Carlo (QMC) method to a class of semilinear parabolic reaction-diffusion partial differential equations used to model tumor growth. Mathematical models of tumor growth are largely phenomenological in nature, capturing infiltrati...