Related papers: Higher Order Charge Conserving Electromagnetic Fin…
In this work, we present a study combining two approaches in the context of solving PDEs: the continuous finite element method (FEM) and more recent techniques based on neural networks. In recent years, physics-informed neural networks…
In this article we consider the widely used immersed finite element method (IFEM), in both explicit and implicit form, and its relationship to our more recent one-field fictitious domain method (FDM). We review and extend the formulation of…
Electrostatic potential fitting method (ESPF) is a powerful way of defining atomic charges derived from quantum density matrices fitted to reproduce a quantum mechanical charge distribution in the presence of an external electrostatic…
A novel electromagnetic particle-in-cell algorithm has been developed for fully kinetic plasma simulations on unstructured (irregular) meshes in complex body-of-revolution geometries. The algorithm, implemented in the BORPIC++ code,…
Rigorous computer simulations of propagating electromagnetic fields have become an important tool for optical metrology and design of nanostructured optical components. A vectorial finite element method (FEM) is a good choice for an…
In this paper, we propose a new approach -- the Tempered Finite Element Method (TFEM) -- that extends the Finite Element Method (FEM) to classes of meshes that include zero-measure or nearly degenerate elements for which standard FEM…
For modern IC design, electromagnetic coupling among interconnect wires plays an increasingly important role in signoff analysis. The requirement of fast and accurate capacitance extraction is becoming more and more urgent.The critical step…
High energy physics aims to understand the fundamental laws of particles and their interactions at both the largest and smallest scales of the universe. This typically means probing very high energies or large distances or using…
A Novel Scaled boundary finite element method, initially developed in Civil Engineering, is reformulated for solving boundary value problems in computational electromagnetics.
Obtaining high-precision guaranteed lower eigenvalue bounds remains difficult, even though the standard high-order conforming finite element (FEM) easily yields extremely sharp upper bounds. Recently developed rigorous approaches using such…
The metriplectic formalism is useful for describing complete dynamical systems which conserve energy and produce entropy. This creates challenges for model reduction, as the elimination of high-frequency information will generally not…
In this paper, we prove that spatially semi-discrete evolving finite element method for parabolic equations on a given evolving hypersurface of arbitrary dimensions preserves the maximal $L^p$-regularity at the discrete level. We first…
In this paper, the generalized finite element method (GFEM) for solving second order elliptic equations with rough coefficients is studied. New optimal local approximation spaces for GFEMs based on local eigenvalue problems involving a…
We extend the recently-developed explicit, energy-conserving particle-in-cell (PIC) scheme of [1] to the relativistic Vlasov-Maxwell system. As in the non-relativistic case, the method is built on an optimization problem that is…
A new weak Galerkin (WG) method is introduced and analyzed for the second order elliptic equation formulated as a system of two first order linear equations. This method, called WG-MFEM, is designed by using discontinuous piecewise…
We establish robust exponential convergence for $rp$-Finite Element Methods (FEMs) applied to fourth order singularly perturbed boundary value problems, in a \emph{balanced norm} which is stronger than the usual energy norm associated with…
The use of energy conservation arguments is ubiquitous in understanding the process of high harmonic generation, yet a complete quantum optical description of exact photon number exchange remained elusive. Here, we solve this gap in…
In this work, we propose a novel formulation for the solution of partial differential equations using finite element methods on unfitted meshes. The proposed formulation relies on the discrete extension operator proposed in the aggregated…
In this paper, we introduce a Lagrange multiplier approach to construct linearly implicit energy-preserving schemes of arbitrary order for general Hamiltonian PDEs. Unlike the widely used auxiliary variable methods, this novel approach does…
A high-order piecewise field-aligned triangular finite element method is developed and implemented for global electromagnetic gyrokinetic particle-in-cell simulations of tokamak plasmas with open field lines. The approach combines locally…