On Sampling Spatially-Correlated Random Fields for Complex Geometries

International audienceExtracting spatial heterogeneities from patient-specific datais challenging. In most cases, it is unfeasible to achieve an arbitrary levelof detail and accuracy. This lack of perfect knowledge can be treatedas an uncertainty associated with the estimated parameters and thus bemodeled as a spatially-correlated random field superimposed to them. Inorder to quantify the effect of this uncertainty on the simulation outputs,it is necessary to generate several realizations of these random fields.This task is far from trivial, particularly in the case of complex geometries.Here, we present two different approaches to achieve this. In thefirst method, we use a stochastic partial differential equation, yieldinga method which is general and fast, but whose underlying correlationfunction is not readily available. In the second method, we propose ageodesic-based modification of correlation kernels used in the truncatedKarhunen-Loève expansion with pivoted Cholesky factorization, whichrenders the method efficient even for complex geometries, provided thatthe correlation length is not too small. Both methods are tested on a fewexamples and cardiac applications