A nonlinear space-time upscaling framework, using constraint-based test functions and machine-learned local maps, achieved 0.3-3.5% coarse-grid errors on two porous-media flow tests.
A Multiscale Method for Porous Microstructures
1 Pith paper cite this work. Polarity classification is still indexing.
1
Pith paper citing it
abstract
In this paper we develop a multiscale method to solve problems in complicated porous microstructures with Neumann boundary conditions. By using a coarse-grid quasi-interpolation operator to define a fine detail space and local orthogonal decomposition, we construct multiscale corrections to coarse-grid basis functions with microstructure. By truncating the corrector functions we are able to make a computationally efficient scheme. Error results and analysis are presented. A key component of this analysis is the investigation of the Poincar\'{e} constants in perforated domains as they may contain micro-structural information. Using a constructive method originally developed for weighted Poincar\'{e} inequalities, we are able to obtain estimates on Poincar\'{e} constants with respect to scale and separation length of the pores. Finally, two numerical examples are presented to verify our estimates.
fields
math.NA 1years
2019 1verdicts
CONDITIONAL 1representative citing papers
citing papers explorer
-
Space-Time Nonlinear Upscaling Framework Using Non-local Multi-continuum Approach
A nonlinear space-time upscaling framework, using constraint-based test functions and machine-learned local maps, achieved 0.3-3.5% coarse-grid errors on two porous-media flow tests.