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The study of the continuum radiative transfer problem inside circumstellar envelopes is both a theoretical and numerical challenge, especially in the frequency-dependent and multi-dimensional case. While approximate methods are easier to…
This paper generalizes the earlier work on the energy-based discontinuous Galerkin method for second-order wave equations to fourth-order semilinear wave equations. We first rewrite the problem into a system with a second-order spatial…
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 introduce an $hp$-version discontinuous Galerkin finite element method (DGFEM) for the linear Boltzmann transport problem. A key feature of this new method is that, while offering arbitrary order convergence rates, it may be implemented…
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…
A new hybrid mixed discontinuous Galerkin finite element (HMDGFE) method is constructed for incompressible miscible displacement problem. In this method, the hybrid mixed finite element (HMFE) procedure is considered to solve pressure and…
Discontinuous Galerkin finite element schemes exhibit attractive features for accurate large-scale wave-propagation simulations on modern parallel architectures. For many applications, these schemes must be coupled with non-reflective…
The scalability of time-dependent partial differential equation (PDE) solvers based on the discontinuous Galerkin (DG) method is increasingly limited by data communication and synchronization requirements across processing elements (PEs) at…
We present the numerical methods and GPU-accelerated implementation underlying a Total Lagrangian finite element framework for finite-deformation flexible multibody dynamics, introduced in the companion paper [1]. The framework supports…
SIMD vectorization has lately become a key challenge in high-performance computing. However, hand-written explicitly vectorized code often poses a threat to the software's sustainability. In this publication we solve this sustainability and…
The nonlinear gyrokinetic equations describe plasma turbulence in laboratory and astrophysical plasmas. To solve these equations, massively parallel codes have been developed and run on present-day supercomputers. This paper describes…
A novel approach is presented for fast generation of synthetic seismograms due to microseismic events, using heterogeneous marine velocity models. The partial differential equations (PDEs) for the 3D elastic wave equation have been…
This study presents a meshfree two-dimensional fractional-order Element-Free Galerkin (2D f-EFG) method as a viable alternative to conventional mesh-based FEM for a numerical solution of (spatial) fractional-order differential equations…
This work analyzes a high order hybridizable discontinuous Galerkin (HDG) method for the linear elasticity problem in a domain not necessarily polyhedral. The domain is approximated by a polyhedral computational domain where the HDG…
An hp-adaptive Discontinuous Galerkin Method for electromagnetic wave propagation phenomena in the time-domain is proposed. The method is highly efficient and allows for the first time the adaptive full-wave simulation of transient problems…
Parametric partial differential equations (PDEs) are fundamental for modeling a wide range of physical and engineering systems influenced by uncertain or varying parameters. Traditional neural network-based solvers, such as Physics-Informed…
Discontinuous Galerkin (DG) discretizations with exact representation of the geometry and local polynomial degree adaptivity are revisited. Hybridization techniques are employed to reduce the computational cost of DG approximations and…
Several recent tropical cyclones, e.g., Hurricane Harvey (2017), have lead to significant rainfall and resulting runoff. When the runoff interacts with storm surge, the resulting floods can be greatly amplified and lead to effects that…
In this study, three-dimensional simulations of a reacting hydrogen jet in supersonic crossflow using a structure-preserving discontinuous Galerkin (DG) formulation are examined. The hydrogen jet, with a momentum flux ratio of five, is…
This paper presents a space-time finite element method (FEM) based on an unfitted mesh for solving parabolic problems on moving domains. Unlike other unfitted space-time finite element approaches that commonly employ the discontinuous…