Related papers: Spectral-based Propagation Schemes for Time-Depend…
Multi-scale wave propagation problems are computationally costly to solve by traditional techniques because the smallest scales must be represented over a domain determined by the largest scales of the problem. We have developed and…
Direct numerical simulations (DNS) are accurate but computationally expensive for predicting materials evolution across timescales, due to the complexity of the underlying evolution equations, the nature of multiscale spatio-temporal…
Computer models are used as replacements for physical experiments in a large variety of applications. Nevertheless, direct use of the computer model for the ultimate scientific objective is often limited by the complexity and cost of the…
Higher-order accurate solution to electromagnetic scattering problems are obtained at reduced computational cost in a {\it p}-variable finite volume time domain method. Spatial operators of lower, including first-order accuracy, are…
PET imaging is widely employed for observing biological metabolic activities within the human body. However, numerous benign conditions can cause increased uptake of radiopharmaceuticals, confounding differentiation from malignant tumors.…
The common exact diagonalization-based techniques to solving tight-binding models suffer from O(N^2) and O(N^3) scaling with respect to model size in memory and CPU time, hindering their applications in large tight-binding models. On the…
Radiative transfer calculations are essential for modeling planetary atmospheres. However, standard methods are computationally demanding and impose accuracy-speed trade-offs. High computational costs force numerical simplifications in…
The simulation of quantum systems has been a key aim of quantum technologies for decades, and the generalisation to open systems is necessary to include physically realistic systems. We introduce an approach for quantum simulations of open…
This paper describes how to efficiently solve time-dependent x-ray dynamic diffraction problems in distorted crystals with an FFT-based beam propagation method (FFT BPM). We show examples of using the technique to simulate the propagation…
The difficulty of simulating quantum dynamics depends on the norm of the Hamiltonian. When the Hamiltonian varies with time, the simulation complexity should only depend on this quantity instantaneously. We develop quantum simulation…
Stochastic spectral methods have achieved great success in the uncertainty quantification of many engineering problems, including electronic and photonic integrated circuits influenced by fabrication process variations. Existing techniques…
The exponential speedups promised by Hamiltonian simulation on a quantum computer depends crucially on structure in both the Hamiltonian $\hat{H}$, and the quantum circuit $\hat{U}$ that encodes its description. In the quest to better…
This work proposes a data-driven method for enabling the efficient, stable time-parallel numerical solution of systems of ordinary differential equations (ODEs). The method assumes that low-dimensional bases that accurately capture the time…
Simulations of scattering processes are essential in understanding the physics of our universe. Computing relevant scattering quantities from ab initio methods is extremely difficult on classical devices because of the substantial…
We propose and analyse numerical schemes for a system of quasilinear, degenerate evolution equations modelling biofilm growth as well as other processes such as flow through porous media and the spreading of wildfires. The first equation in…
In this paper, we propose a general framework to design {efficient} polynomial time approximation schemes (EPTAS) for fundamental stochastic combinatorial optimization problems. Given an error parameter $\epsilon>0$, such algorithmic…
A Gaussian operator basis provides a means to formulate phase-space simulations of the real- and imaginary-time evolution of quantum systems. Such simulations are guaranteed to be exact while the underlying distribution remains…
Accurate derivatives are important for efficiently locally traversing and converging in quantum optimization landscapes. By deriving analytically exact control derivatives (gradient and Hessian) for unitary control tasks, we show here that…
We develop a method for numerical time-domain wave propagation based on the model order reduction approach. The method is built with high-performance computing (HPC) implementation in mind that implies a high level of parallelism and…
Distributed computing is a standard way to scale up machine learning and data science algorithms to process large amounts of data. In such settings, avoiding communication amongst machines is paramount for achieving high performance. Rather…