A fourth-order compact time-splitting Fourier pseudospectral method for the Dirac equation
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 …
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 …
for the time integration of linear partial differential equations with imaginary eigenvalues …
Solving the Vlasov–Maxwell equations using Hamiltonian splitting
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 …
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 …
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 …
nonlinear Schrödinger equations. Different methods for local error estimation are assessed …
Operator splitting for abstract cauchy problems with dynamical boundary condition
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" …
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 …
main result, the new methods preserve the maximum principle unconditionally or with a mild …
A Conservative Discontinuous Galerkin Method for Nonlinear Electromagnetic Schrödinger Equations
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 …
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
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 …
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
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 …
space dimensions. The Pauli equation is a semi-relativistic generalization of the …