Recursive formulation and parallel implementation of multiscale mixed methods

09/16/2020
by   E. Abreu, et al.
0

Multiscale methods for second order elliptic equations based on non-overlapping domain decomposition schemes have great potential to take advantage of multi-core, state-of-the-art parallel computers. These methods typically involve solving local boundary value problems followed by the solution of a global interface problem. Known iterative procedures for the solution of the interface problem have typically slow convergence, increasing the overall cost of the multiscale solver. To overcome this problem we develop a scalable recursive solution method for such interface problem that replaces the global problem by a family of small interface systems associated with adjacent subdomains, in a hierarchy of nested subdomains. Then, we propose a novel parallel algorithm to implement our recursive formulation in multi-core devices using the Multiscale Robin Coupled Method by Guiraldello et al. (2018), that can be seen as a generalization of several multiscale mixed methods. Through several numerical studies we show that the new algorithm is very fast and exhibits excellent strong and weak scalability. We consider very large problems, that can have billions of discretization cells, motivated by the numerical simulation of subsurface flows.

READ FULL TEXT

Authors

page 23

03/15/2021

Towards HPC simulations of Billion-cell Reservoirs by Multiscale Mixed Methods

A three dimensional parallel implementation of Multiscale Mixed Methods ...
03/12/2021

Interface spaces based on physics for multiscale mixed methods applied to flows in fractured-like porous media

It is well known that domain-decomposition-based multiscale mixed method...
04/10/2021

A multiscale Robin-coupled implicit method for two-phase flows in high-contrast formations

In the presence of strong heterogeneities, it is well known that the use...
11/25/2019

The nested block preconditioning technique for the incompressible Navier-Stokes equations with emphasis on hemodynamic simulations

We develop a novel iterative solution method for the incompressible Navi...
11/03/2021

A reduced order Schwarz method for nonlinear multiscale elliptic equations based on two-layer neural networks

Neural networks are powerful tools for approximating high dimensional da...
07/22/2020

Numerical Homogenization of Fractal Interface Problems

We consider the numerical homogenization of a class of fractal elliptic ...
08/19/2021

A Nested Cross Decomposition Algorithm for Power System Capacity Expansion with Multiscale Uncertainties

Modern electric power systems have witnessed rapidly increasing penetrat...
This week in AI

Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.