Publication

Time-reversible and norm-conserving high-order integrators for the nonlinear time-dependent Schrödinger equation: Application to local control theory

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Dealing with strong shocks while retaining low numerical dissipation traditionally has been one of the major challenges for high order methods like discontinuous Galerkin (DG). In the literature, shock capturing models have been designed for DG based on va ...

GLOBAL SCIENCE PRESS2020

Efficient geometric integrators for nonadiabatic quantum dynamics. I. The adiabatic representation

Jiri Vanicek, Seonghoon Choi

Geometric integrators of the Schrödinger equation conserve exactly many invariants of the exact solution. Among these integrators, the split-operator algorithm is explicit and easy to implement but, unfortunately, is restricted to systems whose Hamiltonian ...

2019

A time-reversible integrator for the time-dependent Schrödinger equation on an adaptive grid

Jiri Vanicek, Seonghoon Choi

One of the most accurate methods for solving the time-dependent Schrödinger equation uses a combination of the dynamic Fourier method with the split-operator algorithm on a tensor-product grid. To reduce the number of required grid points, we let the grid ...

2019

Efficient geometric integrators for nonadiabatic quantum dynamics. II. The diabatic representation

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Exact nonadiabatic quantum evolution preserves many geometric properties of the molecular Hilbert space. In the first paper of this series ["Paper I," S. Choi and J. Vaníček, J. Chem. Phys. 150, 204112 (2019)], we presented numerical integrators of arbitra ...

2019

In a recent work we constructed future-global-in-time large solution to the Cauchy problem for semi-linear wave equation on R3+1 with nonlinear terms satisfying the null conditions. In this article we show that the method also applies to energy-supercritic ...

AMER MATHEMATICAL SOC2019

Dynamical Low Rank approximation of PDEs with random parameters

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EPFL2017

High-order methods inspired by the multi-step Adams methods are proposed for systems of fractional differential equations. The schemes are based on an expansion in a weighted space. To obtain the schemes this expansion is terminated after terms. We study t ...

Springer Verlag2017

High-order adaptive methods for fractional differential equations are proposed. The methods rely on a kernel reduction method for the approximation and localization of the history term. To avoid complications typical to multistep methods, we focus our stud ...

Springer Verlag2017

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Association for the Sciences of Limnology and Oceanography2016

Solar energy has seen tremendous advances in the past years. For thin film photovoltaics, which use less of the expensive semiconductor materials, insufficient light absorption can be a limiting factor. It is hoped that by using diffractive optics to impro ...

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