Partial inversion of elliptic operator to speed up computation of likelihood in Bayesian inference

##### Type

Technical Report##### Authors

Litvinenko, Alexander##### KAUST Department

Extreme Computing Research CenterCenter for Uncertainty Quantification in Computational Science and Engineering (SRI-UQ)

##### Date

2017-08-09##### Abstract

In this paper, we speed up the solution of inverse problems in Bayesian settings. By computing the likelihood, the most expensive part of the Bayesian formula, one compares the available measurement data with the simulated data. To get simulated data, repeated solution of the forward problem is required. This could be a great challenge. Often, the available measurement is a functionalThe main ingredients of the developed approach are the hierarchical domain decomposition technique, the finite element method and the Schur complements. To speed up computations and to reduce the storage cost, we approximate the forward operator and the
Schur complement in the hierarchical matrix format.
Applying the hierarchical
matrix technique, we reduced the computing cost to

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