arXiv subjects

Andrew J Wathen

Publications and source records attributed to Andrew J Wathen.

3 recordsLinked to original sources

arXiv2020

A constrained pressure-temperature residual (CPTR) method for non-isothermal multiphase flow in porous media

For both isothermal and thermal petroleum reservoir simulation, the Constrained Pressure Residual (CPR) method is the industry-standard preconditioner. This method is a two-stage process involving the solution of a restricted pressure system. While initially designed for the isothermal case, CPR is also the standard for thermal cases. However, its treatment of the energy conservation equation does not incorporate heat diffusion, which is often dominant in thermal cases. In this paper, we present an extension of CPR: the Constrained Pressure-Temperature Residual (CPTR) method, where a restricted pressure-temperature system is solved in the first stage. In previous work, we introduced a block preconditioner with an efficient Schur complement approximation for a pressure-temperature system. Here, we extend this method for multiphase flow as the first stage of CPTR. The algorithmic performance of different two-stage preconditioners is evaluated for reservoir simulation test cases.

math.NA↗

arXiv2019

Sparse inversion for derivative of log determinant

Algorithms for Gaussian process, marginal likelihood methods or restricted maximum likelihood methods often require derivatives of log determinant terms. These log determinants are usually parametric with variance parameters of the underlying statistical models. This paper demonstrates that, when the underlying matrix is sparse, how to take the advantage of sparse inversion---selected inversion which share the same sparsity as the original matrix---to accelerate evaluating the derivative of log determinant.

stat.CO↗

arXiv2018

Essential formulae for restricted maximum likelihood and its derivatives associated with the linear mixed models

The restricted maximum likelihood method enhances popularity of maximum likelihood methods for variance component analysis on large scale unbalanced data. As the high throughput biological data sets and the emerged science on uncertainty quantification, such a method receives increasing attention. Estimating the unknown variance parameters with restricted maximum likelihood method usually requires an nonlinear iterative method. Therefore proper formulae for the log-likelihood function and its derivatives play an essential role in practical algorithm design. It is our aim to provide a mathematical introduction to this method, and supply a self-contained derivation on some available formulae used in practical algorithms. Some new proof are supplied.

stat.CO↗