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Time domain simulations of electromagnetic problems are highly valuable in engineering applications, as they allow for the analysis of transient behavior and broadband responses. These simulations utilize time stepping schemes, where each…
In this paper, a time-domain discontinuous Galerkin (TDdG) finite element method for the full system of Maxwell's equations in optics and photonics is investigated, including a complete proof of a semi-discrete error estimate. The new…
Partition of unity methods, such as the extended finite element method (XFEM) allow discontinuities to be simulated independently of the mesh [1]. This eliminates the need for the mesh to be aligned with the discontinuity or cumbersome…
We present a new approach for the two-temperature molecular dynamics (MD) model for coupled simulations of electronic and phonon heat conduction in nanoscale systems. The proposed method uses a master equation to perform heat conduction of…
In this paper we present a new multiscale discontinuous Petrov--Galerkin method (MsDPGM) for multiscale elliptic problems. This method utilizes the classical oversampling multiscale basis in the framework of Petrov--Galerkin version of…
In this report, we propose a divergence-free preserving mixed finite element method (FEM) for the system of nonlinear fourth-order thermally driven active fluid equations. By introducing two auxiliary variables, we lower the complexity of…
A unified study is presented in this paper for the design and analysis of different finite element methods (FEMs), including conforming and nonconforming FEMs, mixed FEMs, hybrid FEMs,discontinuous Galerkin (DG) methods, hybrid…
Real-time probing of electrons can uncover intricate relaxation mechanisms and many-body interactions hidden in strongly correlated materials. While experimenters have used ultrafast optical pump-probe methods in bulk materials, laser…
Parallel tempering Monte Carlo simulations have been applied to a variety of systems presenting rugged free-energy landscapes. Despite this, its efficiency depends strongly on the temperature set. With this query in mind, we present a…
High-order accurate discontinuous Galerkin (DG) methods have emerged as powerful tools for solving partial differential equations such as the compressible Navier-Stokes equations due to their excellent dispersion-dissipation properties and…
We proposed a provably stable FDTD subgridding method for accurate and efficient transient electromagnetic analysis. In the proposed method, several field components are properly added to the boundaries of Yee's grid to make sure that the…
Thermal FEM (Finite Element Method) simulations can be used to predict the thermal behavior of power semiconductors in application. Most power semiconductors are made of silicon. Silicon thermal material properties are significantly…
In this paper, we propose a general approach called Generalized Multiscale Finite Element Method (GMsFEM) for performing multiscale simulations for problems without scale separation over a complex input space. As in multiscale finite…
A comprehensive numerical solution is developed for the transient thermo-elasto-hydrodynamic (TEHD) characteristics of mechanical face seals. Transient lubrication features of the fluid film, transient thermal deformation features of the…
A new computational methodology, termed "PeleLM-FDF" is developed and utilized for high fidelity large eddy simulation (LES) of complex turbulent combustion systems. This methodology is constructed via a hybrid scheme combining the Eulerian…
In fluid flow simulation, the multi-continuum model is a useful strategy. When the heterogeneity and contrast of coefficients are high, the system becomes multiscale, and some kinds of reduced-order methods are demanded. Combining these…
In this study, a Galerkin finite element method is presented for time-fractional stochastic heat equation driven by multiplicative noise, which arises from the consideration of heat transport in porous media with thermal memory with random…
Incorporation of plasmonic nanostructures in the design of photoconductive devices (PCDs) has significantly improved their optical-to-terahertz conversion efficiency. However, this improvement comes at the cost of increased complexity for…
Superconducting accelerator magnets require sophisticated monitoring and means of protection due to the large energy stored in the magnetic field. Numerical simulations play a crucial role in understanding transient phenomena occurring…
The finite element method (FEM) is among the most commonly used numerical methods for solving engineering problems. Due to its computational cost, various ideas have been introduced to reduce computation times, such as domain decomposition,…