Fast Algorithms for Elliptic PDEs With Gaussian Boundary Noise

Paul Beckman, New York University

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Recent years have brought numerous advances in statistical modeling and data integration methods for problems involving partial differential equation (PDE) operators, relying primarily on finite element discretizations. At the same time, fast algorithms for integral equation representations of these PDE operators have demonstrated advantages over finite elements in some deterministic settings, namely homogeneous linear constant coefficient elliptic problems, for example the Laplace and Helmholtz equations. However, work at the intersection of these fields, which would allow statistical modeling using integral equation formulations of the PDE remain relatively undeveloped. We present work here for efficient statistical modeling of homogeneous elliptic boundary value problems where the boundary data is assumed to follow a Gaussian process.

Abstract Author(s): Paul G. Beckman, Michael O'Neil