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rrsettgast committed May 13, 2024
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Expand Up @@ -10,50 +10,59 @@ authors:
orcid: 0000-0002-2536-7867
corresponding: true
affiliation: 1
- name: Andrea Borio
affiliation: 5
- name: Nicola Castelletto
affiliation: 1
- name: Aurélien Citrain
affiliation: 2
- name: Benjamin C. Corbett
affiliation: 1
- name: James Corbett
affiliation: 1
- name: Francois Hamon
affiliation: 2
- name: Thomas Gazzola
- name: Philippe Cordier
affiliation: 2
- name: Matteo Cusini
affiliation: 1
- name: Chris S. Sherman
- name: Stefano Frambati
affiliation: 2
- name: Andrea Franceschini
affiliation: 3
- name: Thomas Gazzola
affiliation: 2
- name: Herve Gross
affiliation: 2
- name: Francois Hamon
affiliation: 2
- name: Brian M. Han
affiliation: 1
- name: Sergey Klevzoff
affiliation: 3
- name: Nicola Castelletto
affiliation: 1
- name: Alexandre Lapene
affiliation: 2
- name: Victor Paludetto Magri
affiliation: 1
- name: Chris S. Sherman
affiliation: 1
- name: Hamdi Tchelepi
affiliation: 3
- name: William R. Tobin
affiliation: 1
- name: Pavel Tomin
affiliation: 4
- name: Joshua White
affiliation: 1
- name: Brian M. Han
affiliation: 1
- name: Herve Gross
affiliation: 2
- name: Stefano Frambati
affiliation: 2
- name: Aurélien Citrain
affiliation: 2
- name: Andrea Franceschini
affiliation: 2
- name: Andrea Borio
affiliation: 4
- name: Jian Huang
affiliation: 2
affiliations:
- name: Lawrence Livermore National Laboratory, USA
index: 1
- name: TotalEnergies E&P Research & Technology, USA
index: 2
- name: Stanford University, USA
index: 3
- name: Chevron Technical Center, USA
index: 4
- name: Politecnico di Torino, Italy
index: 5
date: 15 December 2023
bibliography: paper.bib

Expand Down Expand Up @@ -90,22 +99,12 @@ The management of distributed memory parallelism is done through a MPI, and the
GEOS is intended to be a generic multi-physics simulation platform.
As such, single physics packages are developed and tested independent of other physics packages.
When coupling one or more single physics capabilities together to create a couple physics package, the strategy can be described as a monolithic linear system with an underlying block structure corresponding where the row/col of the block corresponds with a set of constraint equations/degrees-of-freedom associated with a physics package.
As an example, figure \autoref{fig:matrix} shows a system matrix ($A_{coupled}$) that couples 3 distinct physics packages (1,2,3).
the diagonal blocks result from each single physics package contributions to its own boundary value problem.
The off-diagonal blocks represent the coupling between physics packages and are typically filled through one of several options, such as through the coupled physics package, or through a callback mechanism in the single physics package which adds the off-diagonal contributions to the single-physics kernels.

\begin{equation}
A_{coupled} = \left(\begin{array}{@{}c|c|c@{}}
A_{11} & A_{12} & A_{13} \\ \hline
A_{21} & A_{22} & A_{23} \\ \hline
A_{31} & A_{32} & A_{33} \\
\end{array}\right)
\end{equation}\label{fig:matrix}


To solve linear systems, GEOS maintains a generic linear algebra interface (LAI) capable of wrapping various linear algebra packages.
However as a matter of practice, the primary linear algebra package used for the great majority of GEOS simulations is LLNL's hypre[@hypre].
For multi-physics problems involving the solution of a linear system, GEOS exclusively relies on hypre's implementation a multi-grid reduction preconditioner strategy as presented [@BUI:2020],[@BUI:2021114111].
For multi-physics problems involving the solution of a linear system, GEOS exclusively relies on hypre's implementation a multi-grid reduction preconditioning strategy as presented by [@BUI:2020],[@BUI:2021114111].

In addition to its c++ core, the the GEOS team provides a Python3 interface that allows for the integration of the simulation capabilities into complex python workflows involving components unrelated to GEOS.
The Python3 interface provides data exchange between GEOS simulations and the Python driver, as well as allowing the Python layer to call specific GEOS packages outside of standard GEOS c++ workflow.
Expand All @@ -125,6 +124,8 @@ The coupling strategy applied in GEOS is to require the capability of a tightly
In cases where such tight coupling is not required, one may decompose the monolithic system into blocks and apply a sequential coupling approach.




# Acknowledgements


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