A fourth-order compact time-splitting Fourier pseudospectral method for the Dirac equation

W Bao, J Yin - Research in the Mathematical Sciences, 2019 - Springer
We propose a new fourth-order compact time-splitting (S_ 4c S 4 c) Fourier pseudospectral
method for the Dirac equation by splitting the Dirac equation into two parts together with …

[HTML][HTML] An accurate and time-parallel rational exponential integrator for hyperbolic and oscillatory PDEs

M Caliari, L Einkemmer, A Moriggl… - Journal of Computational …, 2021 - Elsevier
Rational exponential integrators (REXI) are a class of numerical methods that are well suited
for the time integration of linear partial differential equations with imaginary eigenvalues …

Solving the Vlasov–Maxwell equations using Hamiltonian splitting

Y Li, Y He, Y Sun, J Niesen, H Qin, J Liu - Journal of Computational Physics, 2019 - Elsevier
In this paper, the numerical discretizations based on Hamiltonian splitting for solving the
Vlasov–Maxwell system are constructed. We reformulate the Vlasov–Maxwell system in …

Exact splitting methods for kinetic and Schrödinger equations

J Bernier, N Crouseilles, Y Li - Journal of Scientific Computing, 2021 - Springer
Abstract In (Bernier in Exact splitting methods for semigroups generated by inhomogeneous
quadratic differential operators. arXiv: 1912.13219,(2019)), some exact splittings are …

Practical splitting methods for the adaptive integration of nonlinear evolution equations. Part II: Comparisons of local error estimation and step-selection strategies for …

W Auzinger, I Březinová, H Hofstätter, O Koch… - Computer Physics …, 2019 - Elsevier
We compare the practical performance of adaptive splitting methods for the solution of
nonlinear Schrödinger equations. Different methods for local error estimation are assessed …

Operator splitting for abstract cauchy problems with dynamical boundary condition

P Csomós, M Ehrhardt, B Farkas - arXiv preprint arXiv:2004.13503, 2020 - arxiv.org
In this work we study operator splitting methods for a certain class of coupled abstract
Cauchy problems, where the coupling is such that one of the problems prescribes a" …

Some splitting methods for hyperbolic PDEs

R Hosseini, M Tatari - Applied Numerical Mathematics, 2019 - Elsevier
In this work, a new splitting technique is implemented for solving hyperbolic PDEs. As the
main result, the new methods preserve the maximum principle unconditionally or with a mild …

A Conservative Discontinuous Galerkin Method for Nonlinear Electromagnetic Schrödinger Equations

N Yi, Y Huang, H Liu - SIAM Journal on Scientific Computing, 2019 - SIAM
Many problems in solid state physics and quantum chemistry require the solution of the
Schrödinger equation in the presence of an electromagnetic field. In this paper, we …

INFFTM: Fast evaluation of 3d Fourier series in MATLAB with an application to quantum vortex reconnections

M Caliari, S Zuccher - Computer Physics Communications, 2017 - Elsevier
Although Fourier series approximation is ubiquitous in computational physics owing to the
Fast Fourier Transform (FFT) algorithm, efficient techniques for the fast evaluation of a three …

A time splitting method for the three-dimensional linear Pauli equation

TS Gutleb, NJ Mauser, M Ruggeri… - … Methods in Applied …, 2024 - degruyter.com
We analyze a numerical method to solve the time-dependent linear Pauli equation in three
space dimensions. The Pauli equation is a semi-relativistic generalization of the …