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Computer simulations are becoming an essential tool in many scientific fields from molecular dynamics to aeronautics. In glaciology, future predictions of sea level change require input from ice sheet models. Due to uncertainties in the…

Imaging the bio-impedance distribution of a biological sample can provide understandings about the sample's electrical properties which is an important indicator of physiological status. This paper presents a multi-frequency electromagnetic…

Multi-frequency Electrical Impedance Tomography (mfEIT) is an emerging biomedical imaging modality to reveal frequency-dependent conductivity distributions in biomedical applications. Conventional model-based image reconstruction methods…

In this paper, we develop a computational multiscale to solve the parabolic wave approximation with heterogeneous and variable media. Parabolic wave approximation is a technique to approximate the full wave equation. One benefit of the…

We develop a new meshfree geometric multilevel (MGM) method for solving linear systems that arise from discretizing elliptic PDEs on surfaces represented by point clouds. The method uses a Poisson disk sampling-type technique for coarsening…

It is important to develop fast yet accurate numerical methods for seismic wave propagation to characterize complex geological structures and oil and gas reservoirs. However, the computational cost of conventional numerical modeling…

In this paper, the first large-scale application of multiscale-spectral generalized finite element methods (MS-GFEM) to composite aero-structures is presented. The crucial novelty lies in the introduction of A-harmonicity in the local…

In this work, we propose a generalized multiscale inversion algorithm for heterogeneous problems that aims at solving an inverse problem on a computational coarse grid. Previous inversion techniques for multiscale problems seek a…

This paper introduces an accurate edge-based smoothed finite element method (ES-FEM) for electromagnetic analysis for both two dimensional cylindrical and three dimensional cartesian systems, which shows much better performance in terms of…

We derived an approximate non-linear interference (NLI) closed-form model (CFM), capable of handling a very broad range of optical WDM system scenarios. We tested the CFM over 8500 randomized C-band WDM systems, of which 6250 were…

In this work, we employ the Constraint Energy Minimizing Generalized Multiscale Finite Element Method (CEM-GMsFEM) to solve the problem of linear heterogeneous poroelasticity with coefficients of high contrast. The proposed method makes use…

This paper presents and analyses a Constraint Energy Minimization Generalized Multiscale Finite Element Method (CEM-GMsFEM) for solving single-phase non-linear compressible flows in highly heterogeneous media. The construction of CEM-GMsFEM…

The Controlled Source Electromagnetic (CSEM) method aims to image electrical resistivity at intermediate depths (0-3 km) for geothermal, mineral, and groundwater exploration. It was developed both as a deeper extension of DC resistivity…

In this paper, a novel linear method for shape reconstruction is proposed based on the generalized multiple measurement vectors (GMMV) model. Finite difference frequency domain (FDFD) is applied to discretized Maxwell's equations, and the…

Precise magnetic field modeling is fundamental to the closed-loop control of electromagnetic navigation systems (eMNS) and the analytical Multipole Expansion Model (MPEM) is the current standard. However, the MPEM relies on strict physical…

We provide a concise review of the exponentially convergent multiscale finite element method (ExpMsFEM) for efficient model reduction of PDEs in heterogeneous media without scale separation and in high-frequency wave propagation. ExpMsFEM…

We develop a new, efficient, and accurate method to simulate frequency-domain borehole electromagnetic (EM) measurements acquired in the presence of three-dimensional (3D) variations of the anisotropic subsurface conductivity. The method is…

We present a 2.5-dimensional charge-conservative electromagnetic particle-in-cell (EM-PIC) algorithm optimized for the analysis of vacuum electronic devices (VED) with cylindrical symmetry (axisymmetry). We explore the axisymmetry present…

Accurate numerical simulations of interaction between fluid and solid play an important role in applications. The task is challenging in practical scenarios as the media are usually highly heterogeneous with very large contrast. To overcome…

Numerical simulations of waves in highly heterogeneous media have important applications, but direct computations are prohibitively expensive. In this paper, we develop a new generalized multiscale finite element method with the aim of…