Related papers: StaRMAP - A second order staggered grid method for…
Stimulated Raman adiabatic passage (STIRAP) is a standard technique to combat experimental imperfections and can be used to realize robust quantum state control, which has many applications in physics, chemistry, and beyond. However, STIRAP…
In this work, we present a new high order Discontinuous Galerkin time integration scheme for second-order (in time) differential systems that typically arise from the space discretization of the elastodynamics equation. By rewriting the…
A matrix inverse free method to solve time-dependent Schrodinger equation is presented. The method is not subject to form of Hamiltonian and adopting real space grid system such as structured and unstructured grid, and achieves the order N…
The implementation of a three-level Lambda System in artificial atoms would allow to perform advanced control tasks typical of quantum optics in the solid state realm, with photons in the $\mathrm{\mu m}$/mm range. However hardware…
A novel numerical approach to solving the shallow-water equations on the sphere using high-order numerical discretizations in both space and time is proposed. A space-time tensor formalism is used to express the equations of motion…
A finite difference scheme for the numerical treatment of the (3+1)D Dirac equation is presented. Its staggered-grid intertwined discretization treats space and time coordinates on equal footing, thereby avoiding the notorious fermion…
We study a multigrid method for solving large linear systems of equations with tensor product structure. Such systems are obtained from stochastic finite element discretization of stochastic partial differential equations such as the…
We present a first order scheme based on a staggered grid for the shallow water equations with topography in two space dimensions, which enjoys several properties: positivity of the water height, preservation of constant states, and weak…
We describe a new algorithm to solve the time dependent, frequency integrated radiation transport (RT) equation implicitly, which is coupled to an explicit solver for equations of magnetohydrodynamics (MHD) using {\sf Athena++}. The…
We consider numerical approximations for a phase field dendritic crystal growth model, which is a highly nonlinear system that couples the anisotropic Allen-Cahn type equation and the heat equation together. We propose two efficient,…
In this paper two new families of arbitrary high order accurate spectral DG finite element methods are derived on staggered Cartesian grids for the solution of the inc.NS equations in two and three space dimensions. Pressure and velocity…
The paper investigates a non-intrusive parallel time integration with multigrid for space-fractional diffusion equations in two spatial dimensions. We firstly obtain a fully discrete scheme via using the linear finite element method to…
This study presents an efficient, accurate, effective and unconditionally stable time stepping scheme for the Darcy-Brinkman equations in double-diffusive convection. The stabilization within the proposed method uses the idea of stabilizing…
A new parallel-in-time iterative method is proposed for solving the homogeneous second-order wave equation. The new method involves a coarse scale propagator, allowing for larger time steps, and a fine scale propagator which fully resolves…
In this paper, we present a block-oriented scheme for adaptive mesh refinement based on summation-by-parts (SBP) finite difference methods and simultaneous-approximation-term (SAT) interface treatment. Since the order of accuracy at SBP-SAT…
In order to solve partial differential equations numerically and accurately, a high order spatial discretization is usually needed. Model order reduction (MOR) techniques are often used to reduce the order of spatially-discretized systems…
Calculating dynamical diffraction patterns for X-ray topography and similar x-ray scattering-imaging techniques require the numerical integration of the Takagi-Taupin equations. This is usually performed with a simple second order finite…
This work theoretically investigates possibilities of using the Stimulated Raman Adiabatic Passage (STIRAP) and its variants to control a coherent superposition of quantum states. We present a generalization of the so-called fractional…
A STIRAP-like scheme is proposed to exploit a three-photon resonance taking place in alkaline-earth-metal ions. This scheme is designed for state transfer between the two fine structure components of the metastable D-state which are two…
High-dimensional transport equations frequently occur in science and engineering. Computing their numerical solution, however, is challenging due to its high dimensionality. In this work we develop an algorithm to efficiently solve the…