Research
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A benchmark study of the multiscale and homogenization methods for fully implicit multiphase flow simulations
Abstract
Abstract Accurate simulation of multiphase flow in subsurface formations is challenging, as the formations span large length scales (km) with high-resolution heterogeneous properties. To deal with this challenge, different multiscale me...
Publication · March 06, 2026
A numerical scheme for two-scale phase-field models in porous media
Abstract
A porous medium is a highly complex domain, in which various processes can take place at different scales. Examples in this sense are the multi-phase flow and reactive transport. Here, due to processes like dissolution or precipitation,...
Publication · March 06, 2026
Numerical homogenization of non-linear parabolic problems on adaptive meshes
Abstract
Abstract We propose an efficient numerical strategy for solving non-linear parabolic problems defined in a heterogeneous porous medium. This scheme is based on the classical homogenization theory and uses a locally mass-conservative for...
Publication · March 06, 2026
A two-scale iterative scheme for a phase-field model for precipitation and dissolution in porous media
Abstract
Abstract Mineral precipitation and dissolution processes in a porous medium can alter the structure of the medium at the scale of pores. Such changes make numerical simulations a challenging task as the geometry of the pores changes in ...
Publication · March 06, 2026
Error Estimates for the Gradient Discretisation Method on Degenerate Parabolic Equations of Porous Medium Type
Publication · March 06, 2026
Deep Fourier Residual method for solving time-harmonic Maxwell's equations
Abstract
Solving PDEs with machine learning techniques has become a popular alternative to conventional methods. In this context, Neural networks (NNs) are among the most commonly used machine learning tools, and in those models, the choice of a...
Publication · March 06, 2026
Adaptive Deep Fourier Residual method via overlapping domain decomposition
Abstract
The Deep Fourier Residual (DFR) method is a specific type of variational physics-informed neural networks (VPINNs). It provides a robust neural network-based solution to partial differential equations (PDEs). The DFR strategy is based o...
Publication · March 06, 2026
Optimizing Variational Physics-Informed Neural Networks Using Least Squares
Abstract
Variational Physics-Informed Neural Networks often suffer from poor convergence when using stochastic gradient-descent-based optimizers. By introducing a Least Squares solver for the weights of the last layer of the neural network, we i...
Publication · March 06, 2026
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