Related papers: Real-Space Adaptive-Coordinate Electronic Structur…
Quantum simulation of chemical systems is one of the most promising near-term applications of quantum computers. The variational quantum eigensolver, a leading algorithm for molecular simulations on quantum hardware, has a serious…
Elliptic Partial Differential Equations (PDEs) play a central role in computing the equilibrium conditions of physical problems (heat, gravitation, electrostatics, etc.). Efficient solutions to elliptic PDEs are also relevant to computer…
We develop a numerical hydrodynamics code using a pseudo-Newtonian formulation that uses the weak field approximation for the geometry, and a generalized source term for the Poisson equation that takes into account relativistic effects. The…
Kohn-Sham spin-density functional theory provides an efficient and accurate model to study electron-electron interaction effects in quantum dots, but its application to large systems is a challenge. An efficient algorithm for the…
We present a combination of the recently developed double incremental expansion of potential energy surfaces with the well-established adaptive density-guided approach to grid construction. This unique methodology is based on the use of an…
We show how to adapt the quasi-Newton method to the electronic-structure calculations using systematic basis sets. Our implementation requires less iterations than the conjugate gradient method, while the computational cost per iteration is…
As part of our development of a computer code to perform 3D `constrained evolution' of Einstein's equations in 3+1 form, we discuss issues regarding the efficient solution of elliptic equations on domains containing holes (i.e., excised…
A family of Variational Quantum Eigensolver (VQE) methods is designed to maximize the resource of existing noisy intermediate-scale quantum (NISQ) devices. However, VQE approaches encounter various difficulties in simulating molecules of…
A numerical approach for solving evolutionary partial differential equations in two and three space dimensions on block-based adaptive grids is presented. The numerical discretization is based on high-order, central finite-differences and…
The exploitation of space group symmetries in numerical calculations of periodic crystalline solids accelerates calculations and provides physical insight. We present results for a space-group symmetry adaptation of electronic structure…
This research addresses the numerical simulation of the Boltzmann transport equation for semiconductor devices by proposing a multidimensional self-adaptive numerical simulation framework. This framework is applied to two important…
In this paper we propose an accurate, and computationally efficient method for incorporating adaptive spatial resolution into weakly-compressible Smoothed Particle Hydrodynamics (SPH) schemes. Particles are adaptively split and merged in an…
We present a fully adaptive multiresolution scheme for spatially two-dimensional, possibly degenerate reaction-diffusion systems, focusing on combustion models and models of pattern formation and chemotaxis in mathematical biology.…
Variational quantum algorithms on bosonic quantum processors are an emerging paradigm for quantum chemistry calculations, exploiting the natural alignment between molecular structure and harmonic oscillator-based hardware. We introduce the…
A novel low complexity method to perform self-consistent electronic-structure calculations using the Kohn-Sham formalism of density functional theory is presented. Localization constraints are neither imposed nor required thereby allowing…
In this paper, we implement the Adaptive Moving Mesh method (AMM) to the solution of initial value problems involving the Schr\"odinger equation, and more specifically the Schr\"odinger-Poisson system of equations. This method is based on…
A new computationally efficient method has been introduced to treat self-gravity in mesh based hydrodynamical simulations. It is applied simply by slightly modifying the Poisson equation into an inhomogeneous wave equation. This roughly…
Particle-based shape modeling (PSM) is a family of approaches that automatically quantifies shape variability across anatomical cohorts by positioning particles (pseudo landmarks) on shape surfaces in a consistent configuration. Recent…
This paper investigates an adaptive wavelet collocation time domain method for the numerical solution of Maxwell's equations. In this method a computational grid is dynamically adapted at each time step by using the wavelet decomposition of…
Kohn-Sham density functional theory is one of the most widely used electronic structure theories. In the pseudopotential framework, uniform discretization of the Kohn-Sham Hamiltonian generally results in a large number of basis functions…