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Deformable fractured porous media appear in many geoscience applications. While the extended finite element (XFEM) has been successfully developed within the computational mechanics community for accurate modeling of the deformation, its…
The accuracy and computational cost of a large eddy simulation are highly dependent on the computational grid. Building optimal grids manually from a priori knowledge is not feasible in most practical use cases; instead, solution-adaptive…
We present a direct Poisson solver for massively parallel simulations on three-dimensional Cartesian grids with non-uniform spacing. The method uses a tensor-based formulation in which the operator is diagonalized numerically along two…
Accurately depicting multiphysics interactions in interfacial systems requires computational frameworks capable of reconciling geometric adaptability with strict conservation fidelity. However, traditional spatiotemporal discretisation…
In this paper we consider the numerical upscaling of the Brinkman equation in the presence of high-contrast permeability fields. We develop and analyze a robust and efficient Generalized Multiscale Finite Element Method (GMsFEM) for the…
A surface integral representation of Maxwell's equations allows the efficient electromagnetic (EM) modeling of three-dimensional structures with a two-dimensional discretization, via the boundary element method (BEM). However, existing BEM…
The magnetohydrodynamics (MHD) equations are continuum models used in the study of a wide range of plasma physics systems, including the evolution of complex plasma dynamics in tokamak disruptions. However, efficient numerical solution…
We introduce the multivariate decomposition finite element method (MDFEM) for solving elliptic PDEs with uniform random diffusion coefficients. We show that the MDFEM can be used to reduce the computational complexity of estimating the…
A multitude of individuals across the globe grapple with motor disabilities. Neural prosthetics utilizing Brain-Computer Interface (BCI) technology exhibit promise for improving motor rehabilitation outcomes. The intricate nature of EEG…
Seismic full waveform inversion (FWI) is a widely used technique in geophysics for inferring subsurface structures from seismic data. And InversionNet is one of the most successful data-driven machine learning models that is applied to…
In this paper, we proposed two new types of edge multiscale methods motivated by \cite{GL18} to solve Partial Differential Equations (PDEs) with high-contrast heterogeneous coefficients: Edge spectral multiscale Finte Element method…
This paper proposes a spectrum-efficient nonorthogonal affine frequency division multiplexing (AFDM) waveform for reliable high-mobility communications in the upcoming sixth-generation (6G) mobile systems. Our core idea is to introduce a…
In this work, we extend the meshfree generalized multiscale exponential integration framework introduced in Nikiforov et al. (2025) to the simulation of three-dimensional advection--diffusion problems in heterogeneous and high-contrast…
Multiscale Finite Element Methods (MsFEMs) are now well-established finite element type approaches dedicated to multiscale problems. They first compute local, oscillatory, problem-dependent basis functions that generate a suitable…
We consider finite element methods of multiscale type to approximate solutions for two-dimensional symmetric elliptic partial differential equations with heterogeneous $L^\infty$ coefficients. The methods are of Galerkin type and follow the…
This study presents a finite difference method (FDM) to model the electromagnetic field propagation in eccentric coaxial waveguides filled with lossy uniaxially anisotropic media. The formulation utilizes conformal transformation to map the…
Precise tracking and measurement of the energy carried by the individual magnetohydrodynamic (MHD) modes has important implications and utility in astrophysical and laboratory plasmas. Previously, this was only achievable in limited linear…
This study presents an experimental investigation of the recently established generalized linear sampling method (GLSM) for non-destructive evaluation of damage in elastic materials. To this end, ultrasonic shear waves are generated in a…
This article analyses the simulation methodology for wall-modeled large-eddy simulations using solvers based on the spectral-element method (SEM). To that end, algebraic wall modeling is implemented in the popular SEM solver Nek5000. It is…
In diffusion MRI (dMRI), a good sampling scheme is important for efficient acquisition and robust reconstruction. Diffusion weighted signal is normally acquired on single or multiple shells in q-space. Signal samples are typically…