Related papers: On Geometric Fourier Particle In Cell Methods
Symplectic schemes are powerful methods for numerically integrating Hamiltonian systems, and their long-term accuracy and fidelity have been proved both theoretically and numerically. However direct applications of standard symplectic…
Recently, fictitious identical particles have provided a promising way to overcome the fermion sign problem and have been used in path integral Monte Carlo (PIMC) to accurately simulate warm dense matter with up to 1000 electrons (T.…
Using the Wilson formulation of lattice gauge theories, a gauge invariant grid discretization of a one-particle Hamiltonian in the presence of an external electromagnetic field is proposed. This Hamiltonian is compared both with that…
This paper contributes with a new formal method of spatial discretization of a class of nonlinear distributed parameter systems that allow a port-Hamiltonian representation over a one dimensional manifold. A specific finite dimensional…
We propose and analyze an extended Fourier pseudospectral (eFP) method for the spatial discretization of the Gross-Pitaevskii equation (GPE) with low regularity potential by treating the potential in an extended window for its discrete…
In the recent years, photonic Chern materials have attracted substantial interest as they feature topological edge states that are robust against disorder, promising to realize defect-agnostic integrated photonic crystal slab devices.…
We introduce a quasi-static particle-in-cell (PIC) code -- WAND-PIC -- which does not suffer from some of the common limitations of many quasi-static PICs, such as the need for a predictor-corrector method in solving electromagnetic fields.…
We consider a wide class of semi linear Hamiltonian partial differential equa- tions and their approximation by time splitting methods. We assume that the nonlinearity is polynomial, and that the numerical tra jectory remains at least uni-…
We compare different Poisson solvers within the context of an electrostatic Vlasov-Poisson system. These schemes are implemented as part of the IPPL (Independent Parallel Particle Layer) library (Frey et al., 2024), which provides…
We present a novel Relativistic Semi-Implicit Method (RelSIM) for particle-in-cell (PIC) simulations of astrophysical plasmas, implemented in a code framework ready for production runs. While explicit PIC methods have gained widespread…
In this paper we propose a novel approach to discretize linear port-Hamiltonian systems while preserving the underlying structure. We present a finite element exterior calculus formulation that is able to mimetically represent conservation…
The particle-in-cell (PIC) method is successfully used to study magnetized plasmas. However, this requires large computational costs and limits simulations to short physical run-times and often to setups in less than three spatial…
Recently a number of theoretical studies of the uniform electron gas (UEG) at finite temperature have appeared that are of relevance for dense plasmas, warm dense matter and laser excited solids and thermodynamic density functional theory…
There are many interesting physical processes which involve the generation of high density plasmas in large volumes. However, when modeling these systems numerically, the large densities and volumes present a significant computational…
We present an embedding scheme for periodic systems that facilitates the treatment of the physically important part (here the unit cell) with advanced electronic-structure methods, that are computationally too expensive for periodic…
In recent years, the immersed finite element methods (IFEM) introduced in \cite{Li2003}, \cite{Li2004} to solve elliptic problems having an interface in the domain due to the discontinuity of coefficients are getting more attentions of…
High-resolution simulations of particle-based kinetic plasma models typically require a high number of particles and thus often become computationally intractable. This is exacerbated in multi-query simulations, where the problem depends on…
Hybrid particle-field molecular dynamics combines standard molecular potentials with density-field models into a computationally efficient methodology that is well-adapted for the study of mesoscale soft matter systems. Here, we introduce a…
Mathematical models of protein-protein dynamics, such as the heterodimer model, play a crucial role in understanding many physical phenomena. This model is a system of two semilinear parabolic partial differential equations describing the…
An explicit high-order noncanonical symplectic algorithm for ideal two-fluid systems is developed. The fluid is discretized as particles in the Lagrangian description, while the electromagnetic fields and internal energy are treated as…