Related papers: tRecX -- an environment for solving time-dependent…
We introduce a space-time finite element method for the linear time-dependent Schr\"odinger equation with Dirichlet conditions in a bounded Lipschitz domain. The proposed discretization scheme is based on a space-time variational…
A strategy is developed for writing the time-dependent Schr\"{o}dinger Equation (TDSE), and more generally the Dyson Series, as a convolution equation using recursive Fourier transforms, thereby decoupling the second-order integral from the…
In this article, I present a very fast and high-precision (up to 33 decimal places) C++ implementation of the semi-global time propagation algorithm for a system of coupled Schr\"odinger equations with a time-dependent Hamiltonian. It can…
In this paper we propose fast solution methods for the Cauchy problem for the multidimensional Schr\"odinger equation. Our approach is based on the approximation of the data by the basis functions introduced in the theory of approximate…
A method is proposed for extracting ionization amplitudes from the solution of the time-dependent Schr\"odinger equation (TDSE) describing a system in a time-dependent external field. The method is a hybrid of two earlier developed methods,…
A closed expression for the harmonic oscillator wave function after the passage of a linear signal with arbitrary time dependence is derived. Transition probabilities are simple to express in terms of Laguerre polynomials. Spontaneous…
With the stagnation of processor core performance, further reductions in the time-to-solution for geophysical fluid problems are becoming increasingly difficult with standard time integrators. Parallel-in-time exposes and exploits…
To achieve scalability with today's heterogeneous HPC resources, we need a dramatic shift in our thinking; MPI+X is not enough. Asynchronous Many Task (AMT) runtime systems break down the global barriers imposed by the Bulk Synchronous…
The generalized Crank-Nicolson method is employed to obtain numerical solutions of the two-dimensional time-dependent Schrodinger equation. An adapted alternating-direction implicit method is used, along with a high-order finite difference…
We develop an approach to solving numerically the time-dependent Schrodinger equation when it includes source terms and time-dependent potentials. The approach is based on the generalized Crank-Nicolson method supplemented with an…
We consider a class of linear programs on graphs with total variation regularization and a budgetary constraint. For these programs, we give a characterization of basic solutions in terms of rooted spanning forests with orientation on the…
RMT is a program which solves the time-dependent Schrodinger equation for general, multielectron atoms, ions and molecules interacting with laser light. As such it can be used to model ionization (single-photon, multi-photon and…
It is shown that exterior complex scaling provides for complete absorption of outgoing flux in numerical solutions of the time-dependent Schr\"odinger equation with strong infrared fields. This is demonstrated by computing high harmonic…
We present an algorithm for the numerical solution of systems of fully nonlinear PDEs using stochastic coded branching trees. This approach covers functional nonlinearities involving gradient terms of arbitrary orders, and it requires only…
In this paper we are concerned with Trefftz discretizations of the time-dependent linear wave equation in anisotropic media in arbitrary space dimensional domains $\Omega \subset \mathbb{R}^d~ (d\in \mathbb{N})$. We propose two variants of…
We present a program to simulate the dynamics of a wave packet interacting with a time-dependent potential. The time-dependent Schr\"odinger equation is solved on a one-, two-, or three-dimensional spatial grid using the split operator…
We consider continuous linear programs over a continuous finite time horizon $T$, with a constant coefficient matrix, linear right hand side functions and linear cost coefficient functions, where we search for optimal solutions in the space…
We construct a pseudospectral method for the solution of time-dependent, non-linear partial differential equations on a three-dimensional spherical shell. The problem we address is the treatment of tensor fields on the sphere. As a test…
On modern supercomputers, asynchronous many task systems are emerging to address the new architecture of computational nodes. Through this shift of increasing cores per node, a new programming model with the focus on handle the fine-grain…
Recently we presented TTC, a domain-specific compiler for tensor transpositions. Despite the fact that the performance of the generated code is nearly optimal, due to its offline nature, TTC cannot be utilized in all the application codes…