High-performance parallel solver for 3D time-dependent Schrodinger equation for large-scale nanosystems

Gainullin, I. K.; Sonkin, M. A.

doi:10.1016/j.cpc.2014.11.005

Cited by 37 publications

(11 citation statements)

References 43 publications

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“…On the experimental side, challenges associated with preparation and control of the projectile and target species as well as the detection of multiple reaction products, possibly in coincidence, have to be addressed. On the theoretical side, the challenge resides in the description of an interacting few-or many-body system far away from its ground state, a problem that is straightforward to formulate for (nonrelativistic) Coulomb systems, but hard to solve even with present-day supercomputers [1].…”

Section: Introductionmentioning

confidence: 99%

A screened independent atom model for the description of ion collisions from atomic and molecular clusters

2018

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We apply a recently introduced model for an independent-atom-like calculation of ion-impact electron transfer and ionization cross sections to proton collisions from water, neon, and carbon clusters. The model is based on a geometrical interpretation of the cluster cross section as an effective area composed of overlapping circular disks that are representative of the atomic contributions. The latter are calculated using a time-dependent density-functional-theory-based single-particle description with accurate exchange-only ground-state potentials. We find that the net capture and ionization cross sections in p-Xn collisions are proportional to n α with 2/3 ≤ α ≤ 1. For capture from water clusters at 100 keV impact energy α is close to one, which is substantially different from the value α = 2/3 predicted by a previous theoretical work based on the simplest-level electron nuclear dynamics method. For ionization at 100 keV and for capture at lower energies we find smaller α values than for capture at 100 keV. This can be understood by considering the magnitude of the atomic cross sections and the resulting overlaps of the circular disks that make up the cluster cross section in our model. Results for neon and carbon clusters confirm these trends. Simple parametrizations are found which fit the cross sections remarkably well and suggest that they depend on the relevant bond lengths.

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Section: Introductionmentioning

confidence: 99%

A screened independent atom model for the description of ion collisions from atomic and molecular clusters

2018

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“…There is a flourishing literature about use of GPUs in order to accelerate scientific computations, e.g. [6,10,12,13,28]. Reducing the simulation time is of great importance when we aim to model physical phenomena.…”

Section: Introductionmentioning

confidence: 99%

An exponential integrator/WENO discretization for sonic-boom simulation on modern computer hardware

Einkemmer¹,

Ostermann²,

Residori³

2021

Preprint

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Recently a splitting approach has been presented for the simulation of sonicboom propagation. Splitting methods allow one to divide complicated partial differential equations into simpler parts that are solved by specifically tailored numerical schemes. The present work proposes a second order exponential integrator for the numerical solution of sonic-boom propagation modelled through a dispersive equation with Burgers' nonlinearity. The linear terms are efficiently solved in frequency space through FFT, while the nonlinear terms are efficiently solved by a WENO scheme. The numerical method is designed to be highly parallelisable and therefore takes full advantage of modern computer hardware. The new approach also improves the accuracy compared to the splitting method and it reduces oscillations. The enclosed numerical results illustrate that parallelisation on a CPU results in a speedup of 22 times faster than the straightforward sequential version. The GPU implementation further accelerates the runtime by a factor 3, which improves to 5 when single precision is used instead of double precision.

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“…Incorporating this kind of analytic boundary condition into the numerical solution of TDSE will constrain the applicable propagation methods because the singularity of the Coulomb potential at r = 0 and the singularity of the cylindrical radial coordinate at ρ = 0 will introduce Robin and Neumann boundary conditions, overriding the Hamilton operator. As a consequence, typical explicit methods, for example staggered leapfrog [36,37], second order symmetric difference method [38,39], any polynomial expansion method [38,40], and split-step Fourier transformation methods [38,41,42] have been ruled out, leaving only implicit methods.…”

Section: Introductionmentioning

confidence: 99%

Fourth order real space solver for the time-dependent Schrödinger equation with singular Coulomb potential

Majorosi

Czirják

2016

Computer Physics Communications

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We present a novel numerical method and algorithm for the solution of the 3D axially symmetric timedependent Schrödinger equation in cylindrical coordinates, involving singular Coulomb potential terms besides a smooth time-dependent potential. We use fourth order finite difference real space discretization, with special formulae for the arising Neumann and Robin boundary conditions along the symmetry axis. Our propagation algorithm is based on merging the method of the split-operator approximation of the exponential operator with the implicit equations of second order cylindrical 2D Crank-Nicolson scheme. We call this method hybrid splitting scheme because it inherits both the speed of the split step finite difference schemes and the robustness of the full Crank-Nicolson scheme. Based on a thorough error analysis, we verified both the fourth order accuracy of the spatial discretization in the optimal spatial step size range, and the fourth order scaling with the time step in the case of proper high order expressions of the split-operator. We demonstrate the performance and high accuracy of our hybrid splitting scheme by simulating optical tunneling from a hydrogen atom due to a few-cycle laser pulse with linear polarization.

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High-performance parallel solver for 3D time-dependent Schrodinger equation for large-scale nanosystems

Cited by 37 publications

References 43 publications

A screened independent atom model for the description of ion collisions from atomic and molecular clusters

A screened independent atom model for the description of ion collisions from atomic and molecular clusters

An exponential integrator/WENO discretization for sonic-boom simulation on modern computer hardware

Fourth order real space solver for the time-dependent Schrödinger equation with singular Coulomb potential

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